Speaker 1phone wallet house keys check but this meeting's across town there's not enough time to walk there well what is a ride gonna cost me that ride might be more expensive than a week's worth of coffees oh wait let me check lift too real quick before i book this lesson i thought i guess those savings can go towards getting that pastry with it so whether you need to get to uptown or way downtown taking a few seconds to check lift when you book your next ride could save you money save the money
Speaker 2check lift jan on the street hi it's jan from toyota summer's not over at the national sales event so i'm taking to the streets to see how people are keeping summer fun going with a new toyota excuse me sir how are you making summer last longer with your toyota dropping my bz to the park to play kickball with friends kickball is life love the passion jan on the street event
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Speaker 4toyota let's go places hello everyone and welcome to the mindscape podcast i'm your host sean carroll i do hope everyone listening understands that they are witnessing an historic occasion this is the first time ever that on mindscape we've had a two-part episode we always just make history in interesting ways here at mindscape i know that uh in the past i've been happy to just go on at great length in individual episodes but i do think that this one kind of naturally breaks into two different parts and you know you don't have to listen to one part to get a lot out of the other one so it made sense to do it this way the overall topic of course is dark energy and the accelerating universe theories of how dark energy works what it might possibly be so i planned out the episode and i realized i need to give background about vacuum energy and the cosmological constant einstein's old idea and then of course that led to talking about the cosmological constant the particle physics of it all and so that made its own episode that was the previous episode and where we left off was we have a discovery experimentally that the universe is accelerating we can explain that by invoking a cosmological constant much like einstein did years ago for a slightly different reason but it raises questions we don't know the answers to the the two big ones are roughly speaking the cosmological constant problem which is why is the value so much smaller than you might expect it to be if you think about effective field theory which is an enormously successful paradigm to think about all of quantum field theory and particle physics the cosmological constant appears as a number in the effective field theory and we have expectations for how big that number should be and the actual number is smaller than the expectation by something like 10 to the minus 122 so that's bad and it might be a clue to some interesting physics underlying the cosmological constant problem so i'm going to go ahead and explain what's going on and it certainly wasn't what a lot of particle physicists ever expected the other problem is okay if you think that you've measured the vacuum energy the energy density in empty space itself and that's making the universe accelerate etc etc then why are we so lucky that the value of the vacuum energy is approximately the same as the value of the matter energy density in the universe today by approximately the same we mean you know 3 or 4 times or 5 times as much something like that but not 10 to the 100 times as much this is called the coincidence problem because the relative amounts of vacuum energy and matter density change as the universe expands the vacuum energy stays constant as an energy density the amount of matter in the universe as a density goes away as the universe expands it dilutes away to zero so if they're approximately the same order of magnitude today in the past there was way more matter density than vacuum energy in the future there'll be way more vacuum energy than matter why is it that we got so lucky to be born at just the right time it almost suggests that there is some kind of anthropic human-centered explanation for this and maybe there is but maybe there isn't maybe we can do better in terms of thinking of new physical explanations so when the idea of the accelerating universe became established and the idea of the accelerating universe became established in the late 90s early 2000s physicists immediately said we can't simply say it's the cosmological constant and stop there that is causing the acceleration of the universe maybe it's something else we should be open-minded we were surprised once we could be surprised again and that led people to the idea of dynamical dark energy something that's not quite the cosmological constant but looks that way is a pretty good approximation and that's something that we can look for experimentally as well as writing down theoretical models for what it might be and so that is what we're getting to today we're going to talk about dynamical theories of what the dark energy could be and as i said in the previous episode i'm not doing a hundred percent historically fair and balanced treatment of this subject by any stretch of the imagination i was involved in writing papers and thinking about this for a long time so i'm just telling you what i was thinking at the time and how that intersects with what other people were thinking at the time and it's going to cover a pretty decent amount of ground in terms of the different possibilities for what could be going on we still don't know what is actually going on out there in the world so in some sense i'm preparing you to think about new ideas as they get noticed and explained to people or maybe even come up with some new ideas of your own so with that let's go i really do want to stress that at least back in the late 90s early 2000s when people first started thinking about dynamical dark energy there was essentially zero empirical reason to do so by which i mean there was no data that said oh the cosmological constant doesn't really fit very well from the start the cosmological constant fit quite well there's always a little bit of error bars and therefore tensions with your predictions but nothing that was worrying people at all today as we'll talk about very briefly because i'm actually not an expert on and nobody is an expert because it's in flux but there are tiny bits of empirical evidence that maybe something is changing and we do need dynamical dark energy but i would say that they're too premature to get excited about right now but back in the day 25 years ago people were definitely motivated by theoretical motivations they were saying look we were wrong before about the naturalness of the cosmological constant uh maybe making things dynamical is even less natural but nevertheless true so we should be open-minded and even i think this was definitely a major motivation if you have just a number the vacuum energy there's really nothing you can do with it right like it's just sitting there you can try to come up with some deep explanation for it but you're not getting any extra data it's not flexible it's not you know surprising you in some dynamical time-dependent way whereas if you have some new vibrant thing something that is dynamical something that can change with time then maybe it can help you explain some of these puzzles that you had before the cosmological constant problem the coincidence problem and so on roughly speaking that ambition did not pan out you know it's absolutely worth being ambitious and people were um try it out see what happens but i think roughly speaking it didn't really work but maybe we're not clever enough maybe we just haven't come up with the right idea so what do you need so you you know from the observations uh let's let's recap the observational situation um there's something called the critical density of the universe that's a theoretical number given einstein's equation given the way we relate the expansion rate of the universe to the stuff inside the universe there is a certain amount of energy density that the universe could have as a function of its expansion rate as a function of its its hubble constant which would say okay you're exactly balanced between negative curvature and positive curvature okay you have a flat a geometrically flat universe that you live in and that's if you have the right density for that that's the critical density if you have less than the critical density then you're going to be in a negatively curved universe if you have more than the critical density you'll be in a positively curved universe a spatial section of the universe and notice that those words and phrases have nothing to say about what kind of energy density it is it could be cosmological constant matter radiation something new something different whatever but the observations uh let's group together all the observations we made like between 1998 and 2005 or so both from the supernovae and from the solar system and from the supernova measurements of the hubble diagram velocity versus distance for faraway supernovae in different galaxies and the microwave background and there were other kinds of observations from large-scale structure and things like that all of these i'm not going into the details here because it's a whole story by itself how you go from measuring statistical properties of temperature and isotropies and the microwave background radiation left over from the big bang to the or statistical properties of galaxies and large-scale structure, and therefore saying, oh, I now know what the density of the universe is, or the Hubble parameter, or the cosmological constant, or something like that. But people did that. We're going to group all those observations together in that time period, 25 or so years ago. And what they were telling us was, we were at the critical density. The critical density of the universe that makes it spatially flat is the density of the universe. But that is not simply one component. As it turns out, it's divided up about 70% cosmological constant in the simplest model, and about 30% matter. Now, matter to cosmologists, as we said, just means particles that are moving slowly compared to the speed of light. And why that's so important that they're moving slowly compared to the speed of light, if they're moving close to the speed of light, or at the speed of light, like honest-to-goodness photons would be, then they lose out on the density of the universe. And so, we're going to energy as the universe expands, because of the redshift as the universe gets bigger. But matter doesn't lose energy per particle. It's energy per particles, E equals mc squared, mass times the speed of light squared. There's a tiny bit of kinetic energy, but it's small compared to the rest energy, because the particle's moving slowly compared to the speed of light. So, one-half mv squared, the kinetic energy, is negligible compared to mc squared, the rest energy. That's what matter is to cosmologists, and about 30% of it is, uh, 30% of the total density of the universe today is in the form of matter. And it's about 25% dark matter, 5% ordinary matter. I haven't even mentioned dark matter yet, and I'm not going to talk about dark matter, roughly speaking, because it's a completely different kind of thing than dark energy. It's an interesting story, an important story, but not a story that is relevant to the cosmological constant story. It's matter, and it's a story that is relevant to the cosmological constant story. Matter, that's the only thing that is relevant, and it's part of the 30% of the universe that is matter. But just because the word dark is there doesn't mean there's any necessary connection. I mean, maybe there is. Again, that's something to speculate about as a theoretical physicist, but we have no reason to suspect that's true. Okay. So, we have the critical density of matter, 70%, critical density of energy in the universe, uh, 70% of it is in the form of the cosmological constant, or something like it. So, to be like it, what you need is something that is almost constantly spread throughout space, right? Because if this new energy, this dark energy, were clumping into galaxies and clusters of galaxies, then you would see it in the microwave background, in large-scale structure, in gravitational lensing, in the orbits of stars around galaxies, in a million different local ways. That's all exactly what we missed before the supernovae came along. The real reason why supernovae were such a good way to measure the cosmological constant, and indeed, to measure the total density of the universe, was that they were really responsive to the whole amount of energy in the universe, not just the amount of energy in an individual galaxy or cluster, which you would then try to extrapolate to larger scales. That was exactly the hope of the Supernova Cosmology Project and the hope was borne out. So, you need something to be dark energy that is almost smooth throughout space, and also almost constant throughout time. Remember, if you go back to the Friedmann equation, and we said that there is this sort of complicated explanation, if you have an energy density that is constant, it leads to a constant Hubble parameter, which gets seen visibly as an accelerating universe. So, all of those sentences still go through if you replace constant with almost constant. If you have an almost constant energy density, then you get an almost constant Hubble parameter, and an almost constant energy density, then you get an almost constant Hubble parameter. So, all of those sentences still go through if you replace constant with almost constant. If you have an almost constant energy density, then you get an almost constant Hubble parameter, and an almost constant energy density, then you get an almost constant Hubble parameter. Well, you still get an accelerating universe. It's not quite exponential, okay? It's sub-exponential, but still accelerating. The function, which is called the scale factor, telling you how big the relative distances are between galaxies as a function of time, is still curved upwards, like a smile, not curved downward like a frown, as a function of time. That's what it means for the universe to be accelerating. So, that's not that hard. You want something that is smooth over space and constant over time. Of course, the constant, the cosmological constant, the vacuum energy, is perfectly good at this. And again, there's no experimental reason to go beyond that, but let's just broaden our horizons by thinking a little bit more carefully. So, let me let you in on a little jargon that cosmologists used to discuss this issue. It's called the equation of state parameter. Remember that the thing about the universe is that it has a pressure that is negative, that is, in fact, minus the energy density of the vacuum. Of course, I shouldn't say the pressure is negative just because it's the cosmological constant. We can imagine cosmological constants that are themselves negative, and then the pressure would be positive. That's what you get in anti-de Sitter space, okay? If you're interested in the ADS-CFT correspondence, et cetera, that's a universe with a negative cosmological constant, and therefore there's a positive pressure, that doesn't seem to be relevant to explaining our world as we observe it right now. So, let's put that aside, and I'm going to talk about a positive energy density, a negative pressure. So, for the strict cosmological constant, p equals minus rho. Pressure is minus the energy density. So, for something that is not quite the cosmological constant, what we can do is, we can say, let p equal w times rho, where w is some number, number that would be minus one if it were exactly the cosmological constant, and it would be not quite minus one, but something close to it, if it were something that were close to the cosmological constant, but not quite. I'm Glenn Washington. This is Snap Judgment from KQED, when everything
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Speaker 6from KQED, wherever you get your podcasts. Hey, everyone. It's Cal Penn, host of Earsay, the Audible and iHeart audiobook club. This week on the podcast, I'm sitting down with comedian Emily Lin to talk about the Audible original series, Heads Will Roll, Air Apparent. The second installment of the gloriously unhinged fantasy comedy she co-created with her sister, Kate McKinnon. An evil queen has to produce an heir before her 40th birthday, or a swamp demon comes to collect, and her best friend is a cursed raven who gets turned into a toad.
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Speaker 4So P equals minus rho, sorry, P equals W times rho, and W is this equation of state parameter. And we're trying to think of that as a new measurable quantity that we can go out and look at the universe and ask, what is W? We know there's dark energy, but it fits the data to have W being minus one. But is it exactly minus one? Any data always has error bars and that, you know, maybe it's minus 0.9 or something like that. Okay. And that sounds a little, you know, not immediately tangible. Like, how do we know what the pressure of the dark energy is? How are you going to measure that separately from measuring its energy density? But there's a very nice way to measure that. There's a very nice and immediate connection between the equation of state parameter W and the rate of change of the energy density in the dark energy as the universe expands. If W is exactly minus one, then the energy density stays precisely constant. That's the cosmological constant. If W is greater than minus one, so what that means is minus 0.9, minus 0.8, something like that, right? Those numbers are greater than minus one because minus one is a negative. Then the dark energy density gradually fades away. It decreases over time. You can remember this because W equals zero is saying that there's no pressure at all and that's just matter, right? And matter fades away quite quickly. For radiation, for a gas of photons or something like that, W would be one-third. P equals one-third rho. So for vacuum energy, W is minus one. For gas of photons or something like that, W is minus one. So for vacuum energy, W is minus one. So for vacuum energy, W is minus one. So for vacuum energy, W is minus one. So for vacuum energy, minus two-thirds, who knows? It depends on the details. You could also imagine W being less than minus one. So it could be minus 1.2 or something like that. That would mean that the dark energy density is growing with time, okay? So not just the amount of dark energy growing with time because the universe is expanding. That happens with any dark energy model. Energy is not conserved in general relativity. If what you mean by energy is the energy on the right-hand side of Einstein's equation, it's by coincidence conserved if there's matter in the universe and nothing else because it's just e equals mc squared the number of particles per cubic centimeter goes down as the universe expands but the energy per particle stays the same and the number of cubic centimeters goes up and exactly cancels but if the universe is full of radiation the energy is not conserved it goes down because the individual radiation particles redshift away some of their energy if it's dark energy the total energy goes up so for w being less than minus one we're saying something more dramatic than that we're saying that the energy density goes up that might bother you maybe should bother you a little bit we'll get back to whether or not it really should bother you but it's certainly allowed to plug into the equations and ask what happens okay so one of the very first things that people started doing after the acceleration of the universe was discovered was asking themselves could we constrain this parameter w uh the equation of state parameter for the dark energy so this is a sort of what we call a phenomenological approach to doing physics because we're not saying i have a theory right i'm not saying here is my model of dark energy and here's what it predicts we're saying very specifically i don't have a theory i'm parameterizing the possibilities of my ignorance right i'm saying there's some theory out there it's not quite the cosmological constant how close is it or how far away is it so you have a new parameter that you add to your model fitting and that gives you more room to play and you know this is exactly what scientists know something about and are pretty good at you know dealing with this kind of situation so i actually got to be a co-author one of the first papers to do this not the very first paper um i think there was a paper by maybe seljok and white perhaps uh that did it but one of the first papers from the supernova groups to do this and by do this i mean the supernova groups to do this and by do this i mean the supernova groups to do this and by do this i mean the supernova groups to do this and by do this i mean the supernova groups to do this and by do this i mean not just find the best fit value of the cosmological constant but find the simultaneous best fit value for the energy density of the dark energy and its equation of state parameter for just the cosmological constant you choose the equation of state is exactly minus one and now you're letting it vary so you have more room to play like we said and like i said um in the previous episode i was friends with some of the people on the supernova teams in particular the high z supernova teams and i was able to friends with some of the people on the supernova teams and i was able to friends with some of the people on the supernova teams and i was able to team led by brian schmidt at the time team led by brian schmidt at the time team led by brian schmidt at the time and peter garnevich was yet another friend of and peter garnevich was yet another friend of and peter garnevich was yet another friend of ours who at the time had become a professor ours who at the time had become a professor ours who at the time had become a professor at notre dame and he was a member of the at notre dame and he was a member of the at notre dame and he was a member of the team and he led the effort to write a team and he led the effort to write a team and he led the effort to write a paper to do the analysis and write a paper to do the analysis and write a paper to do the analysis and write a paper saying okay we discovered the paper saying okay we discovered the paper saying okay we discovered the universe is accelerating what can we say universe is accelerating what can we say universe is accelerating what can we say about the equation of state parameter about the equation of state parameter about the equation of state parameter and so they had a question the group and so they had a question the group and so they had a question the group you know like i was friends with all of you know like i was friends with all of you know like i was friends with all of them and so they had this question um them and so they had this question um them and so they had this question um could the equation of state parameter be could the equation of state parameter be could the equation of state parameter be less than minus one could w be less than less than minus one could w be less than minus one that it seemed like there's no minus one that it seemed like there's no minus one that it seemed like there's no problem to them putting it in their problem to them putting it in their problem to them putting it in their equations and their plots and things like equations and their plots and things like equations and their plots and things like that that that but maybe there was something but maybe there was something but maybe there was something physically not allowed about it and they physically not allowed about it and they physically not allowed about it and they didn't know the answer so they asked me didn't know the answer so they asked me didn't know the answer so they asked me um in part because i knew something um in part because i knew something um in part because i knew something about general relativity and and stuff about general relativity and and stuff about general relativity and and stuff like that and so uh i had never thought like that and so uh i had never thought like that and so uh i had never thought about that question before about that question before about that question before and i did think about it and i came up and i did think about it and i came up and i did think about it and i came up with this sort of with this sort of with this sort of weasel worded answer and i wrote a weasel worded answer and i wrote a weasel worded answer and i wrote a couple paragraphs couple paragraphs couple paragraphs uh and added we added them to the paper uh and added we added them to the paper uh and added we added them to the paper and what i said if i'm recalling and what i said if i'm recalling and what i said if i'm recalling correctly i haven't read the paper in a correctly i haven't read the paper in a correctly i haven't read the paper in a one from a general relativity point of one from a general relativity point of one from a general relativity point of view view view violates energy conditions there's a very violates energy conditions there's a very violates energy conditions there's a very traditional thing you do in general traditional thing you do in general traditional thing you do in general relativity because general relativists relativity because general relativists relativity because general relativists care about the left-hand side of care about the left-hand side of care about the left-hand side of einstein's equation right that's the part einstein's equation right that's the part einstein's equation right that's the part where you have the curvature of where you have the curvature of where you have the curvature of spacetime and it's all fun and it's spacetime and it's all fun and it's interesting the right hand side interesting the right hand side interesting the right hand side where you have energy and and pressure where you have energy and and pressure where you have energy and and pressure and heat and all those things and heat and all those things and heat and all those things that's harder to understand because you that's harder to understand because you that's harder to understand because you know it depends on your model of what know it depends on your model of what know it depends on your model of what the matter is or whatever the matter is or whatever the matter is or whatever so what general relativists do is they so what general relativists do is they so what general relativists do is they invent energy conditions they basically invent energy conditions they basically invent energy conditions they basically say well something like energy density say well something like energy density say well something like energy density should be positive or pressure should should be positive or pressure should should be positive or pressure should not be bigger than the energy density not be bigger than the energy density not be bigger than the energy density and absolute magnitude things like that and absolute magnitude things like that and absolute magnitude things like that and there's not any law of physics that and there's not any law of physics that and there's not any law of physics that say these energy conditions must be true say these energy conditions must be true say these energy conditions must be true but they sort of guarantee that gravity but they sort of guarantee that gravity but they sort of guarantee that gravity isn't repulsive and things are stable isn't repulsive and things are stable isn't repulsive and things are stable and stuff like that so i explained that and stuff like that so i explained that and stuff like that so i explained that w being less than minus one would w being less than minus one would w being less than minus one would violate energy conditions that's not a violate energy conditions that's not a violate energy conditions that's not a guarantee that it can't be done guarantee that it can't be done guarantee that it can't be done but it provides you a license to say okay but it provides you a license to say okay but it provides you a license to say okay we're not going to consider we're not going to consider we're not going to consider that possibility so in fact in the paper that possibility so in fact in the paper that possibility so in fact in the paper garnevich at all 1999 i think garnevich at all 1999 i think garnevich at all 1999 i think we didn't consider the possibility we we didn't consider the possibility we we didn't consider the possibility we cut off the values of w we were looking cut off the values of w we were looking cut off the values of w we were looking at at minus one i might have said at minus one i might have said at minus one i might have said um but you know if you want to look for um but you know if you want to look for um but you know if you want to look for w less than minus one you should be w less than minus one you should be w less than minus one you should be allowed to do that because looking at allowed to do that because looking at allowed to do that because looking at the data is looking at the data you the data is looking at the data you the data is looking at the data you shouldn't be too blinded by theoretical shouldn't be too blinded by theoretical shouldn't be too blinded by theoretical prejudice i know that i had that thought prejudice i know that i had that thought i'm not sure if it actually ever made it i'm not sure if it actually ever made it i'm not sure if it actually ever made it into the paper and then the funny thing into the paper and then the funny thing into the paper and then the funny thing about that paper you know astronomers at about that paper you know astronomers at about that paper you know astronomers at the time were still learning their way the time were still learning their way the time were still learning their way around large collaborations right there around large collaborations right there around large collaborations right there weren't a lot of large collaborations in weren't a lot of large collaborations in weren't a lot of large collaborations in astronomy like there are in particle astronomy like there are in particle astronomy like there are in particle physics so in particle physics everyone physics so in particle physics everyone physics so in particle physics everyone is very happy just putting the author is very happy just putting the author in theoretical physics where uh we have only in theoretical physics where uh we have only in theoretical physics where uh we have only a tiny amount of authors we just do a tiny amount of authors we just do a tiny amount of authors we just do alphabetical order most of the papers alphabetical order most of the papers alphabetical order most of the papers i've ever written have been in i've ever written have been in i've ever written have been in alphabetical order usually benefits me alphabetical order usually benefits me alphabetical order usually benefits me sometimes i lose out that's okay that's sometimes i lose out that's okay that's sometimes i lose out that's okay that's life life life so what what the high z supernova team so what what the high z supernova team so what what the high z supernova team had as their had as their had as their strategy for the author list was they strategy for the author list was they strategy for the author list was they would would would say that okay for any given paper say that okay for any given paper say that okay for any given paper someone is basically in charge of making someone is basically in charge of making someone is basically in charge of making sure everything works right someone is sure everything works right someone is sure everything works right someone is the lead author on the paper they're the lead author on the paper they're the lead author on the paper they're carrying out the analysis they're carrying out the analysis they're carrying out the analysis they're checking everything very carefully checking everything very carefully checking everything very carefully there's contributions from everyone in there's contributions from everyone in there's contributions from everyone in the collaboration but there's one person the collaboration but there's one person the collaboration but there's one person who's the boss of that particular paper who's the boss of that particular paper who's the boss of that particular paper and uh different papers will have and uh different papers will have and uh different papers will have different bosses so peter garnovich was different bosses so peter garnovich was different bosses so peter garnovich was the boss of this paper and so in in the boss of this paper and so in in the boss of this paper and so in in their strategy the boss their names their strategy the boss their names their strategy the boss their names comes first and then the whole rest of comes first and then the whole rest of comes first and then the whole rest of the team comes in alphabetical order okay the team comes in alphabetical order okay the team comes in alphabetical order okay as it would have turned out though if as it would have turned out though if If we had done that for this paper that I became a co-author on, Peter Garnovich would be first, and then I would have been second, just because of alphabetical order, right? And then the whole rest of the Hi-Z Supernova team. But I was clearly not a real member of the Hi-Z Supernova team. I didn't do, like, it's work to be a member of one of those teams. You have to sort of earn your bones or whatever, putting in a lot of effort to earn your right to be an author on those papers and then go to the Nobel Prize ceremony, et cetera. And I hadn't done any of that. So the strategy for our paper was Peter Garnovich came first, the whole rest of the Hi-Z Supernova team came next in alphabetical order, and then I came last, just to let everyone know I did a little bit of work but not too much work. And I thought that was completely, entirely fair. I have no problems with it. Anyway, in our paper, what we found, and in subsequent papers have found very similar things, W equals minus one, the equation of state parameter corresponding to a real cosmological constant. And I think that's what we're going to talk about in a little bit. So the first thing we're going to talk about is the W. Fits great. No problems with it at all. Perfect fit. But there is some wiggle room there. And indeed, back in 1999, there was a good amount of wiggle room. So there's room to play, and the data tell you exactly how much room you have to play. You need to, like, increase the energy density in the dark energy a little bit and then compensate for it by having it fade away a little bit, and you can still fit the data pretty well. And now one of the games to be played, if you're in this... And it's a vibrant, active subset of cosmology, is not just playing that game, but deciding, okay, what data counts, right? Like, so you have the supernova data, but that's not all you have. You have data from large-scale structure, from the cosmic microwave background. These days, you have data from baryon acoustic oscillations and maybe some lensing statistics or stuff like that. There's a bunch of different things that you have. So different analyses will put different sets of data into their analysis. And then you... It becomes very complicated to figure out what the paper is actually saying. So all of these, by the way, I should say that, you know, the paper we wrote, Gornovich et al., in the earlier paper, Seljok and White, I think it was. I hope it's those guys. I really should look it up. Sorry. But, you know, this idea started, you know, the experimental program of constraining the properties of the dark energy. And that has become a huge deal in cosmology. Many experiments, satellites and ground-based experiments, were motivated by the idea we are going to probe the dark energy. We're going to learn about the dark energy. And I kind of have mixed feelings about that, just to be super-duper honest. It's like a on-this-hand, on-the-other-hand, on-the-third-hand situation. On the one hand, of course, you should probe the dark energy. You should try to learn something about it. That's a good, useful, scientific thing. On the other hand, if it is... ...the cosmological constant, then we're done probing it. We're not going to learn any more by these probes. We're just going to measure this one number to increasing precision. But the precision doesn't really tell us that much about what the underlying physics is. It's still just a number that we have no explanation for. So... In some sense, this program of probing and experimentally constraining the dark energy is a bit overblown because there's not that much to constrain if it is the cosmological constant. But if it's not, then you've got to do it. And so I think it's a good thing that people are doing it, especially because, and I think this is the killer argument here, maybe we learn something completely different. Maybe even though we're motivating doing these experiments by testing theories of dark energy, we're still doing cosmology. We're still collecting data. We're learning about supernovae and structure and early galaxies and whatever it is. And I think that's good. So that's wonderful. So it's not like we're simply targeting one thing and only learning about that one thing and it's kind of unlikely to come true. That's just not how observational cosmology generally works. So these days there's a lot of effort. Satellites, the Nancy Grace Roman satellite is recently up there. The Rubin telescope, which used to be the large scale synoptic telescope, LSST, here on the ground is doing surveys of lensing and supernovae and things like that. So many different complementary efforts. The Euclid satellite, all trying to, among other things, learn something about dark energy. And so that's an ongoing thing. Not. Not to mention other smaller scale things that have already given results, like the DESI collaboration, et cetera. OK. So that's the experimental phenomenological side of things. What about the theoretical side of things? Is there any motivation, really, for thinking about this sort of sector of physics? So as I said, a big motivation was, even though the idea of the cosmological constant fits the data perfectly well, it leaves us with these puzzles. The cosmological constant problem, the coincidence problem, et cetera. Maybe by expanding our horizons and looking at dynamical models of dark energy, we could solve some of these problems, or at least learn something that points us in the direction of a solution to these problems. So roughly speaking, it hasn't worked, by the way. It never was going to work, really, for the cosmological constant problem. The cosmological constant problem is not impossible. It's not improved by saying that what is making the universe accelerate is not the cosmological constant. Because the cosmological constant problem is still a problem even if the vacuum energy is zero, right? That's still out there. So the puzzle, why is the vacuum energy so much smaller than its natural value? That's a puzzle whether or not the thing that is making the universe accelerate is vacuum energy or whether it's something else. OK. So we're not even trying that hard. You never had any expectations. You never had any expectations that making the dark energy dynamical would somehow help you with the cosmological constant problem. That's always there lurking in the background. In fact, what's going to happen is we're going to add more problems by inventing dynamical dark energy. But there might have been a hope to help with the coincidence problem. Why is it today that the dark energy seems to be important? And again, I don't think it quite worked, but there was a lot of excitement in the early days. There was an early paper by Robert. . . . . Caldwell, Rahul, Dave, or Dave, I don't know how to pronounce his last name, and Paul Steinhardt, where they dubbed the idea quintessence, the idea of dynamical dark energy. In particular, they had a scalar field, which I'll talk about that in a second, but a scalar field model of what dynamical dark energy is. And they called it quintessence. That's the fifth element in ancient Greek physics, right? Earth, air, fire, water, quintessence was the heavenly element. And they had this hope, I think it was in that paper, but certainly in follow-up papers, of developing what they called tracker models, or what people called tracker models. And the idea of a tracker model was, maybe you could explain the coincidence problem by making it not be a coincidence anymore. Maybe you could have, you could take advantage of the dynamics of the scalar field of the dark energy, so that it would sort of track the total amount of energy density of matter at all times. Or maybe it tracked at some era in the history of the universe, and then stopped tracking later on. Or some other dynamical story you could tell that would help explain why it's only now that the dark energy is becoming important. Now, roughly speaking, it didn't really work, or it didn't become convincing, or something like that. I mean, when you have these aspirations to explain more things, then your theories are going to have certain goals, and they're going to have certain goals, and they're going to have certain goals. And therefore, certain constraints, like you have to fulfill the goal, and that means they're not infinitely flexible anymore. And my impression, I haven't followed it very carefully, but my impression is that that hope of getting like tracker-like behavior doesn't actually fit the data very well. So it's a simple ruled out by an ugly fact kind of situation. But it was a perfectly good try, right? I think again and again in this story, you're going to see people making legitimate college tries at getting the data right. And I think that's a good thing. And I think that's getting a better understanding of what the dark energy might be and how it's working. And those college tries not quite panning out, okay? So that was a big aspiration, a big motivation, I should say, for dynamical models of dark energy. Could you help explain the coincidence problem in some way without just being anthropic, without just saying it's because there's a multiverse or something like that? Okay. So let's talk about the actual models that you would think about to develop. I already mentioned the scalar field, and that's absolutely the first thing that you're going to think about. So this is something that theoretical physicists were already good at thinking about because they had done this before, 20 years before, in the context of the inflationary universe scenario. Remember I mentioned inflation. This is a model of the early universe based on scalar fields, quantum fields that don't pick out a direction in space. They just have a value, and a scalar field can have a potential energy that is an amount of energy that is just sort of packed into the value of the scalar field. And you literally imagine in your head a picture of a ball rolling on a hill. And you probably have seen plots like this. Maybe you haven't. I don't know. But if you hang out in the same circles that I hang out in, you see plots of potential energy as a function of value of the scalar field, okay? I'm Glenn Washington. This
Speaker 5is Snap Judgment from KQED when everything is falling apart. What do you do? Hurricane Helene shut everything down. No roads, no cars, no way through. But his daughter was getting married. And somehow, someway, he was going to walk her down that aisle. All systems down. A new Snap Judgment miniseries from KQED, wherever you get your podcasts.
Speaker 6Everyone, it's Cal Penn, host of Earsay, the Audible and iHeart audiobook club. This week on the podcast, I'm sitting down with comedian Emily Lin to talk about the Audible original series Heads Will Roll, Heir Apparent, the second installment of the gloriously unhinged fantasy comedy she co-created with her sister, Kate McKinnon. An evil queen has to produce an heir before her 40th birthday, or a swamp demon comes to collect. And her best friend is a cursed raven who gets turned into a toad.
Speaker 7There was only one character that immediately were like, we need Richard Kind for this. We had written this love addict, this like neurotic love addict. And originally, we were just calling him General Richard Kind. And he was like, could you change my name? I don't necessarily want to be associated with this freak. And we were happy to do that.
Speaker 6Listen to Earsay on the iHeartRadio app or wherever you get your podcasts.
Speaker 4And inflation, interestingly, is a very similar idea in spirit to the idea of dark energy being dynamical today. What you want to make inflation work is something that makes the universe accelerate at an enormous amount, enormously fast rate in the very, very early universe. It's that acceleration that smooths everything out, makes everything homogeneous and isotropic, just like we see today. So theoretical cosmologists had a lot of practice writing down scalar fields with potential energies and asking what properties they needed to have to make the universe accelerate. And roughly speaking, what you want is a slowly rolling scalar field. Now, that's actually a technical term in inflationary cosmology. And that's not what I'm referring to here. I'm referring to the informal idea that if you have a scalar field, that scalar field has kinetic energy. And if you have a scalar field, that scalar field has energy from its change over time and also its potential energy. And what you want is the potential energy is approximately constant. The kinetic energy is approximately zero. Then the potential energy in your scalar field is acting almost kind of like a cosmological constant. It's acting like dark energy. So this was the idea of what is called new inflationary cosmology. In old inflation, in Guth's first idea, the scalar field literally sat on top of a potential called the false vacuum. And it did quantum tunneling to get out of the false vacuum. And that idea never really worked. In Guth's original paper, he admitted it never really worked. What other people realized, Albrecht and Steinhardt and also Andre Linde, is that there is basically friction in the early universe. If you look at the equations of motion for these scalar fields, they're being pushed by the slope of the potential. Again, it's just like a ball rolling down a hill. So if the potential is steep, the field wants to roll down quickly. If the potential is almost flat, it wants to move slowly. But there's also friction from the expansion of the universe that's literally called Hubble friction. The bigger the Hubble parameter is, the Hubble parameter telling you how fast the universe is expanding, the more friction there is. So if you have a potential energy function, which is more or less flat, then the Hubble friction teams up with the flatness of the potential to keep the scalar field not moving very quickly, slowly rolling. And its energy density will be approximately constant, and it will make inflation happen in the early universe. And it would also... Analogously, a similar thing would make the universe accelerate today. Now, the numbers are very, very different. The energy density that you need for inflation is hilariously high, much higher than any particle physics scale we've actually probed experimentally. Whereas the energy you need for making the universe accelerate today is hilariously low. It's the average energy density of the universe, which is not very much. The universe is mostly empty, okay? But the basic equations look almost exactly the same. In fact... There are two ways... People sort of forget this because, you know, once you know the answer, you forget about the controversies. But the discovery that the universe is accelerating was hugely good news for the inflationary universe scenario for two separate reasons. The obvious reason is the big prediction inflation had made is that the universe should be spatially flat, that the density of energy in the universe should be the critical density. And in the 1990s, that was not coming true. We were measuring the energy density. We were not getting there. We were only getting a third of the way there. And so the vacuum energy or the cosmological constant or the dark energy provided the extra amount of energy density you needed to explain that. That was beautiful news for inflation. It made a prediction that came true. The other thing, which is a little bit more subtle, is remember we always had the cosmological constant problem, right? That was known about since the 60s. And we didn't know the answer to that. So there was somehow always the possibility. That something about vacuum energy made it not gravitate. In the previous episode, I talked about self-tuning solutions to the cosmological constant problem. And that's basically what they were doing. They were inventing a clever way that the particular exact thing called vacuum energy would have zero gravitational effect by replacing rho, the energy density, with rho plus p, energy density plus pressure. And for vacuum energy, p equals minus rho. So if that had been true, if that had been the correct solution to why the cosmological constant was so small, you could imagine mechanisms, again, imagining in the space of all theories we haven't invented yet. But you could imagine mechanisms that would kill off the cosmological constant and at the same time kill off the possibility of inflation. Because inflation and the cosmological constant or modern-day dark energy act very similarly from the equation standpoint. So there might be something that made it impossible. Impossible. Impossible. For the universe to accelerate. And that would have made inflation not work. So the discovery that our universe actually is accelerating was very good news for inflation because it said, yes, your prediction came true. And it is possible for the universe to accelerate. We know that because it's doing it now. OK. So that was a big boost for inflation overall. And inflation returned the favor by saying, hey, I have this idea of a scalar field that is slowly rolling that could make the universe accelerate. Why don't you go play with it? OK. So the simplest model for dark energy, for something dynamical that sort of mimics a cosmological constant, is a slowly rolling scalar field, also called quintessence. But I say that the numbers are different. The energy scales are different. Let me just emphasize how super different they are. OK. The mass of a proton, particle physicists like to measure masses in electron volts for various reasons. An electron volt is the amount of energy it takes to move a proton. The mass of an electron is the amount of energy it takes to move an electron across one volt of voltage. I don't know why that has anything relevant about particle physics, but there you go. Since we set the speed of light equal to one, mc squared is just m, and energy and mass are interchangeable. So we use this energy unit to discuss the masses of elementary particles. So the mass of a proton, for example, is of order one billion electron volts. The mass of an electron is of order half a million electron volts. So it's about as much as one billion electron volts. It's about 1,800th the size of a proton. The mass of a neutrino, we don't know. They're not zero mass, the neutrinos. But the order of magnitude that we're talking about for neutrinos is like a hundredth of an electron volt or something like that. So you see that the energy scales of particle physics, or mass scales if you want to call them that, span quite a range, right? A billion electron volts for the proton, a hundredth, one percent of an electron volt for the neutrino. And, of course, they keep going up. But places we don't know about yet. The Higgs boson is over a hundred times more massive than a proton. And these energy scales that we're talking about for inflation and things like that are like a quadrillion times the mass of a proton, a quadrillion electron volts, way, way higher than we can actually reach here in experiments done here on Earth. So what if you wanted to make a dark energy theory that applied to the universe today? So you want the scalar. Field to be rolling very slowly. So by slowly rolling, we mean this is a scalar field that is rolling down its potential and has been rolling down its potential for the entire history of the universe, 14 billion years. And it hasn't gotten very far. We want this scalar field to not, like, roll all the way to the bottom and start rocking back and forth. That would not be dark energy anymore. That would not be approximately constant energy density because those oscillators. Back and forth would be damped by the expansion of the universe. That energy density would go away. The way to get approximately constant energy is to have the scalar field be approximately not rolling at all. And then its potential energy just remains constant. And so you can kind of roughly and here's some hand waving going on, but you can parameterize the slope of the potential by thinking about the mass of the scalar field. It's not an exact fit because. The slope is the first derivative and the mass is the second derivative. But OK, you're going to you're going to go along with me, hopefully, for these purposes, you can work the observational facts about our universe today into, roughly speaking, an idea of what the mass of the scalar field that is the dark energy might have to be. And the answer, remember, proton is a billion electron volts. Electron is half a million neutrinos, point oh one, and the quintessence field has to have. A mass of about ten to the power minus thirty three electron volts. So it's hugely tiny compared to any known particle physics scale. That ten to the minus thirty three electron volts is not pulled out of nowhere. It's just the Hubble constant in energy units. So it's the single parameter that tells you roughly the size and age and scope of the present day universe. So it's not surprising that it's that number so already. You're kind of proposing something weird, right? You're saying, like, OK, I have a scalar field that has energy, that energy is recently taken over the total energy density of the universe, and the mass of this scalar field is ten to the minus thirty three electron volts, which is really, really tiny. And why why should it be so tiny? So let me put it this way again. It's a sort of naturalness question for four from a particle physics perspective, the Higgs boson, which I said is about a hundred times. The mass of the proton. So that's about a hundred billion electron volts. Famously, there's a puzzle called the hierarchy problem, and you can phrase that puzzle by saying, why is the mass of the Higgs boson so small, by which we mean it's very small compared to things like the grand unification scale or the Planck scale or these ultra high energy particle physics scales? It's a hundred times bigger than the mass of the proton and, you know, two hundred thousand times bigger than the mass of the electron. Or whatever. But those are things that we know, symmetries that protect their masses. There's reasons that we have in particle physics as to why the mass of the proton, the mass of the electron, the mass of neutrino are so incredibly tiny, not to mention the mass of the photon, which is zero. All these are very tiny compared to grand unification scale or the Planck scale or whatever, but there are good reasons why for the Higgs boson, there's no good reason why that's the hierarchy problem. Why should the mass be so small, even though it's still a hundred times the mass of the proton? The mass of our new quintessence boson is 10 to the minus 33 electron volts, that's just incredibly tiny, so that's a new puzzle to solve. Okay, so that's one thing to keep in mind, we have these scalar fields, we have some unnaturalness in their values, so can we possibly explain this? I came into the game because two things are going on. This is 1998, 1999, right? So what's important for the world is that we're discovering dark energy and beginning to think about it. What's important for me, Sean, is that I'm looking for a job because I am a postdoc at the ITP Institute for Theoretical Physics at UC Santa Barbara. And it's about time for me to get a faculty job if I'm ever going to do it. It's my second postdoc. And I had realized recently that, you know, I was writing papers, I was productive, but the papers weren't that especially interesting to the rest of the world. I thought they were fun, but other people were working on other things. And they weren't that intersecting with what other people thought was interesting. And that's why I was not especially attractive on the job market. So I realized that I had to, like, do something that was both interesting to me, but also interesting to the rest of the world, and make an impact there if I was going to get any faculty jobs. And happily, my friends discovered the acceleration of the universe. And I just happened to be the world's expert in that, because I had written this review article with Bill Press, and I was an expert on general relativity and all that stuff. So I said, okay, good. I'm going to think about the acceleration of the universe and what we can do about it. And there had already been these papers by Steinhardt and Caldwell and Dave and other people. There were earlier papers by Jim Peebles and Bharat and others saying, oh, maybe there's a scalar field that is making the universe accelerate. So that had been done. But all of those papers really bugged me, because I knew enough particle physics to say, like, this is all really unnatural, right? Like, the Higgs field is already anomalously low mass. This field is just crazy low mass. And it's actually worse than that, okay? It's not just that the mass is small. That's one number that has to be small. But the danger when you go from constant vacuum energy to a dynamical field is that the field can do things. Not only can it do things by itself, like evolve with time, it can interact with other fields. That's generally what happens in particle physics. This is, again, part of the effective field theory paradigm. Even if nothing else, your new field that you're proposing will interact with gravity. You know that. And gravity will interact with gravity. And gravity will interact with gravity. And gravity interacts with other fields. So in the infrared effective theory, your new field should be interacting with other fields. And maybe you can say, well, okay, I'm just going to make those interactions very, very small. Fine. But there is, once again, a set of expectations for the sizes of these interactions. And that means that your new quintessence field should lead to fifth forces of nature. If I have a pendulum, a torsion pendulum, so they're called, in a laboratory like they have at the University of Washington, you can look for tiny, really, really weak forces between ordinary matter over and above the gravitational force, the electromagnetic force, et cetera. And this new quintessence boson, which is essentially massless on the scale of laboratory experiments, right? It's easy to make. It's easy to source it. And therefore, you can roughly predict order of magnitude, like, should you have seen the fifth force due to quintessence in your laboratory experiments? And I worked out, back of the envelope kind of thing, yes, you certainly should have seen this already. And that's not all, because you not only have a new fifth force you could see in the laboratory, but this scalar field is supposed to be slowly changing with time. So what that means is it's slowly changing the values of everything else. There's feedback mechanisms that you would expect to exist if this field is interacting with other fields. So things like the fine structure constant, which tell you the strength of electromagnetism, or the masses of other particles, the mass of the Higgs boson, the mass of the electron and things like that, all of these should be slightly time-dependent over cosmological scales. You can invent new scalar fields and call them the dark energy, but those scalar fields should be talking to all the other fields in the world, and those should be leading to observable effects, and you can even estimate the sizes of the observable effects. And so I did that, and I realized, you know, basically in order to hide from the experiments and to be empirically phenomenologically viable, this new scalar field has to have all of its couplings suppressed by something like a factor of 10 to the minus 5. Small, but not like crazily small, but still pretty darn small. So this added up to this feeling that, look, you can invent these new scalar fields, but they're very, very unnatural from a particle physics perspective, and we have a perfectly good theory, the cosmological constant, that fits all the data already. Let's just stick with that, okay? So I started, I sort of was debating back and forth, should I, like, is this the kind of insight that's worth writing a paper about, or should I just tell people about it, right? Like, it's kind of just bringing a bit of knowledge from one subfield into another subfield that's not necessarily worth writing a paper about just to inform your colleagues, right? But I was invited to give a talk at Fermilab. You know, a whole workshop was going on on dark energy in the accelerating universe and thinking about all these things. I'm not sure if the phrase "dark energy" had even been coined yet at that time. And on the — I think it was on the plane ride — to the conference while I was working on my talk, as one does, I realized, you know, okay, so you have this unnaturalness of the values of the mass and all the coupling constants for this scalar field, but that's something we've seen before in particle physics, unnaturally small coupling constants, and there are strategies for dealing with that. Basically, you can imagine that there is a symmetry that prohibits the existence of these coupling constants and even prohibits the existence of the mass. And so this goes back to a discourse that especially was associated with Gerard de Tuft, famous Nobel Prize-winning physicist in the 1970s, and Tuft proposed that anomalously small coupling constants can be what is called "technically natural." And "technically natural" means that if the coupling constants were exactly zero, there would be some symmetry that had been slightly broken that you have restored. So if these coupling constants are breaking a symmetry, they're allowed to break it by just a little bit, and that would still count as technically natural. And then you can argue for why that's true using renormalization group and things like that. So could there be a symmetry that allows for squelching all of these couplings between the quintessence field and the fifth forces and things like that, and the fine structure constant and the masses of all the other particles? And the answer is yes. You just have a very simple thing. You imagine that there is a shift symmetry, phi, the scalar field. Phi goes to phi plus a constant. You just move the value of the scalar field. Now, you can't do this as an exact symmetry because that would mean there's no potential energy, right? The whole point of your quintessence field is you're trying to make the universe accelerate. You're trying to have a potential that does change as a function of phi and that phi is slowly rolling down it. But that's okay in this case because you're not saying that the symmetry phi goes to phi plus a constant is exact. You're saying it's approximate. And indeed, that's exactly what you need to explain why the mass of the scalar field is so small. This symmetry is protecting the mass. It's still a puzzle why it's so small. It's like really, really, really small. But it is technically natural for this kind of scalar field to be small, for the mass of this kind of scalar field to be small. And if you do that, that actually immediately gives you an analogous smallness to all the other coupling constants. So basically, implementing this idea of a proximate shift symmetry for the quintessence field helps you explain both the masses and the couplings and everything is now good. And indeed, I was beginning to think that I knew what was going on here because this idea of a scalar field with an approximate shift symmetry, the technical term here is a pseudo-Nambu-Goldstone boson or PNGB. Yoichiro Nambu, a famous physicist from the University of Chicago, Jeffrey Goldstone at MIT, did pioneering work on symmetry breaking all the way back in the 60s. And they showed that you could have these bosons that would come up if you spontaneously broke a symmetry to both spontaneously break the symmetry and then explicitly break it by a little bit, gives you a pseudo-Nambu-Goldstone boson. Okay, so this was a known thing. And in fact, it was known that you could make dark energy out of this. There was a paper by Josh Freeman, a cosmologist at Fermilab and UChicago and other people. I think even before we discovered the accelerating universe, they pointed out that if you wanted to have energy in the, you know, again, people were skeptical or surprised to find the universe was accelerating, but they were still thinking about the possibility even before it was actually discovered. It was just sort of low level thinking. It was not, you know, very big deal thinking. So Josh and his friends wrote a paper pointing out that pseudo-Nambu-Goldstone boson quintessence, as we would now call it, was technically natural and provided I did a nice way of explaining why the masses should be so small. They weren't worried about the coupling constants, but I could help with that and certainly followed immediately. I'm Glenn Washington. This is Snap Judgment from KQED.
Speaker 5When everything is falling apart, what do you do? Hurricane Helene shut everything down. No roads, no cars, no way through. But his daughter was getting married. And somehow, someway, he was going to walk her down that aisle. All Systems Down, a new Snap Judgment miniseries from KQED, wherever you get your podcasts.
Speaker 6Hey, everyone. It's Cal Penn, host of Earsay, the Audible and iHeart audiobook club. This week on the podcast, I'm sitting down with comedian Emily Lin to talk about the Audible original series, Heads Will Roll, Air Apparent, the second installment of the gloriously unhinged fantasy. The comedy she co-created with her sister, Kate McKinnon. An evil queen has to produce an heir before her 40th birthday, or a swamp demon comes to collect. And her best friend is a cursed raven who gets turned into a toad.
Speaker 7There was only one character that immediately were like, we need Richard Kind for this. We had written this love addict, this like neurotic love addict. And originally, we were just calling him General Richard Kind. And he was like, could you change my name? I don't necessarily want to be associated with this freak. And we were happy to do that.
Speaker 6Listen to Earsay on the iHeartRadio app or wherever you get your podcasts.
Speaker 4And this also connected in my brain to work that I had done earlier and that, you know, you can, I've talked about it a lot. And you can find it on Preview. And you can find it on my podcast episodes where I talk about birefringence and the screwy universe. OK, so I'll just give you the very quick version right now. If you have a pseudo scalar field, and this is a different word, different definition of the prefix pseudo. Pseudo as in pseudo nambugles dombozon means you've broken a symmetry by a little bit. Pseudo as in pseudo scalar field means it is a negative parity field. By parity. You mean what happens to the field when you change the orientation of space. So you change the X, Y and Z axes. So you're like looking in a mirror, right? Parity, P-A-R-I-T-Y. So a scalar field has positive parity. You change the orientation of the axes. Nothing happens to it. A pseudo scalar field has negative parity. You change the orientation of your axes. It goes to minus itself. Phi goes to minus phi. OK. And so with George Field and Roman Chekiv and in different. Various combinations, we had pointed out that a slowly rolling pseudo scalar field would couple to electromagnetism in a very particular way. Basically, what we're pointing out is this symmetry in the in this slightly tilted pseudo scalar field that eliminates almost all of the couplings to ordinary matter leaves one coupling untouched. And that is a coupling to a pseudo scalar. Electromagnetic coupling that you can make. It's basically the electric field dot magnetic field. So for those of you who are a little bit physics-y inclined here, the electric field is a vector. The magnetic field is a pseudo vector. So the electric field has positive parity. The magnetic field has negative parity. When you take E dot B, take the dot product of those two electric and magnetic fields, you get a negative parity thing. When you multiply. That by phi, the pseudo scalar, you get a positive parity thing. So phi E dot B is allowed. The symmetry does not rule it out in any way. And there's a longer reason I can explain why that's true. Having to do with total derivatives and things like that. But the point is this pseudo nambu's Goldstone boson idea. So Josh and his friends just said it makes a good potential energy function. What I realized is it also helps you get rid of all the fifth forces. But it leaves one interaction allowed and that interaction makes a prediction that makes a prediction. It can happen. And as the scalar field is changing its value, the pseudo scalar field, it will rotate the plane of polarization of light from distant galaxies and the microwave background. So you have distant sources giving off photons and they're polarized and in ordinary electromagnetism, that direction of polarization just stays fixed. As the photon travels across empty space. But in the presence of this scalar field, it would slightly push the polarization angle of these photons. And in principle, that's detectable. And you could even and this is me on a plane in 1998 or 1999. I forget exactly when figuring out that you could again estimate what is a natural value for the amount of rotation. And it's small because there's like factors of velocity. One over four pi and the fine structure constant and things like that. But it's not that small. It's about one degree is your general prediction. One degree of rotation between us and very, very distant galaxies. And then you can look at the data that people already had to constrain this effect. And at the time, the data said, well, we know that the rotation is less than five degrees. OK, so one degree is like it's just perfect. This never happens in science or it very rarely happens in the course of a long scientific career. And so I think that the numbers come out this nicely when you make an experimental prediction, what you most strongly want is a number that has not yet been ruled out, but could be ruled out in your lifetime. So if the current limit is five degrees or less and you're predicting a feature of one degree, that's perfect for you. And so basically, I ended up giving a talk at Fermilab and I said, you know, look, we're all talking about rolling scalar fields. Now, as theoretical physicists faced with the accelerating universe, they're all hilariously unnatural from a particle physics perspective. Maybe that's OK because, you know, we were wrong about the cosmological constant. That's unnatural. So we can just live with that. But we can also try to fix it. And here's a way to fix it. You know, impose this symmetry and it gets it both. It helps explain the low mass of the quintessence field and explains why the coupling constants are small and it leaves you with one prediction, which has. Hasn't yet been tested, which is kind of pretty cool. And so people got excited about that. And that's basically what got me faculty jobs a year later. Like, that's just how the game works. Like suddenly I was saying something interesting. I didn't become any smarter, but I was putting my smarts to use in ways that the rest of the world thought were interesting. And the to skip ahead to the present day to 25 years later or so, we still haven't gotten the limit on the rotation. Of polarization down to where we wanted, but we're getting very, very close. And there have been a couple of claims in the literature recently, especially by Ichiro Komatsu, who is a well-known cosmologist who is analyzing data from the cosmic microwave background. And he says that in the data there is a sign that it looks like the polarizations are rotating by a little bit, a tiny bit, and it's like, you know, not quite statistically significant. Yet, but it's getting there. These things don't have momentum. So the fact that it's getting there is not very definitive, but it's a suggestion. And we're going to absolutely be super duper interested in following up with data from better data sets that are more targeted exactly at looking for this. It turns out it's really, really hard to measure rotations of polarizations because that's usually not what the telescopes are built to do. You have to sort of trick them into doing it. But it's so interesting that people are now. Building telescopes with detectors, I should say, for telescopes, radio telescopes that are specifically trying to look for this. And so if they find it, that would be direct detection of dark energy or, you know, probably they would come up with 100 other explanations for it also. But it's at least plausibly a direct detection of dark energy, which is kind of fun. OK, so that was, I thought, an interesting set of ideas bandied back and forth by the theoretical physics community. 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So I'm going to go ahead and get back to the question. positive parity field sometimes scalar field just means either positive or negative parity in fact usually it means that so when i just say the quintessence scalar field that's what i mean i'm not gonna i'm not picking whether or not it's positive parity or not either possibility counts okay so if you just have an ordinary scalar field with an ordinary kinetic energy rolling down an ordinary potential you will predict the w the equation of state parameter is indeed less than or equal to sorry i just said it wrong greater than or equal to minus one okay something between zero and minus one are the allowed values for the equation of state parameter of a scalar field so it's a good candidate to be dark energy but of course the whole thing is like free employment for theoretical physicists so you can play other games what if if w is just less than minus one and again you can play the game phenomenologically like forget about scalar fields what happens if you just set w to be minus 1.1 and you don't tell me why you just say that's what it is and again this is robert caldwell thought about this along with mark kamienkowski um and they called it phantom energy i think that um rob caldwell was the first to call it that in a solo paper um it was near the time when the phantom menace was being released so you can sort of date all of the physics um progress papers by what popular culture references they're making at the time so he called uh phantom energy something that would have the feature that its energy density would increase over time and so um caldwell and kamienkowski and others said okay um just again forget about the actual underlying model just say w is less than minus one and let it stay that way what's going to happen well you're saying that not only is the energy density increasing with time but it's increasing at a sort of a constant rate so you might expect that sort of makes things go crazy right if the energy density is just constant if you have the cosmological constant then the energy density then sorry then the expansion rate is a constant and that leads to an exponential growth in the scale factor the size of the universe a of t a is the letter often given to the scale factor a of t goes as e to the ht where h is the constant double parameter t is time and exponential growth is pretty fast growth okay so if you have w less than minus one the energy density is increasing in its own right and so the scale factor of the universe is going to increase even faster than exponential and in fact what they showed is it hits a singularity at a finite time in the future it goes you know if you if you imagine in your mind a plot of the graph one over x as a function of x so at positive values of x it trails off at large values of x 1 over x but 1 over x blows up becomes infinity as x goes to 0. so sort of take that kind of behavior but flip it around and have it go into the future the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe is so the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe is so the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach infinity at a finite time and that's what the scale factor of the universe would approach but it's one of the possibilities it's not but it's one of the possibilities it's not but it's one of the possibilities it's not often often often that in your career you get to invent a that in your career you get to invent a that in your career you get to invent a whole new possibility for what the whole new possibility for what the whole new possibility for what the universe could do universe could do universe could do right so the invention of the big rip i right so the invention of the big rip i right so the invention of the big rip i thought was a very very good thought was a very very good thought was a very very good idea but it so it's a sufficiently good idea but it so it's a sufficiently good idea but it so it's a sufficiently good idea that it's worth taking it seriously with time. As I said way back in my paper with Garnovich et al., it would violate the energy conditions of general relativity, but that's not an absolute ruling out factor. That's just sort of a warning sign, like, you know, dragons ahead. You know, you should be careful here. So I became interested in this, and I started working with Mark Trodden, who was an old friend of mine from postdoc days, who was at the time a professor of physics at Syracuse. He has since moved to the University of Pennsylvania, and we wrote lots of papers together over the years. And so he and I and Mark Hoffman, who was my first ever graduate student at the University of Chicago, we wrote a paper that analyzed this question. Could the dark energy equation of state parameter W be less than minus one? And by that, we meant, could you invent a good particle physics model, or what would go wrong if you did? Now, I think way back in Rob Caldwell's early papers, he had an attempt at a particle physics model, which is just the following. When you have a scalar field, and you have, you want to write down its equations of motion, right? So you want to say, what does a scalar field do as a function of time? Well, you know, if you've read quanta and fields or whatever, basically, you have a kinetic energy, and you have a potential energy, right? And we've already said that. The kinetic energy gives you the energy in the motion of the field. The potential energy just gives you the amount of energy that the field has, just because it has a certain value. And the potential energy, in the usual way physicists think about things, potential energy can be positive or negative or zero. Kinetic energy for an ordinary scalar field is going to be minus, sorry, is going to be plus one half phi dot squared. Phi dot is the velocity of phi dot squared. And so, phi dot is just the derivative of phi with respect to t. So phi dot squared is positive, or zero. And the kinetic energy is one half phi dot squared. So by the ordinary construction, the kinetic energy is always positive. Potential energy can be positive, negative, or zero. What Rob Caldwell realized is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what he suggested should be called the positive energy. What Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the kinetic energy. That's what Rob Caldwell suggested is that in order to get W less than minus one, all you have to do is put a minus sign in front of the does is you instantly specialize to the case where the field is not fluctuating, right? It's just constant throughout space. It's only changing as a function of time. So if I have no spatial gradients from place to place, I only have dependence on t, the time parameter, and I put down my equations of motion with a negative kinetic energy and a positive potential, in an ordinary scalar field theory, you say, well, I have a field in the potential and the field rolls down its potential, just like a ball rolling down a hill. But now I've changed the sign of the kinetic energy. And what that means is the ball rolls up the hill. So it rolls up to greater and greater amounts of energy, which is exactly what you want if you want phantom energy, if you want the big rip, okay? And that's fine. And they wrote papers about that. But in the real world, you will have at least a little bit. of fluctuation in space as well. So what is that going to do? Like, you're going to quantize this theory, you're going to get particles, etc. In fact, you just crank through and you crack open your old quantum field theory textbook. This is literally what we did. And you replace a bunch of plus signs with minus signs. And you see, so what happens if I have a negative energy density? And I think a lot of particle physicists were, did not do this correctly at the time, because there's a way of dealing with ghost particles in quantum field theory, where you say, oh, this corresponds to a negative norm in Hilbert space, and I can project them out, there's a whole set of things you're doing. But that's all because these particles are only arising as virtual particles in Feynman diagrams, not because they're real particles out there making the universe accelerate. So you had to sort of relearn what you'd been taught in your quantum field theory class, replacing a bunch of plus signs with minus signs. And the particle excitations of this field turn out to have a negative energy density. So you have a negative energy density, and you have a negative mass. Negative kinetic energy, even if you don't change the potential, turns into a negative mass for the particle. And people hadn't really talked about this that much, or at least we didn't know when we were writing our paper of any work on it that had been done before. And so we thought about what's going on, we realized that there was a kind of a bad thing that could happen, which is that if you have a negative mass particle, when you have particle physics, and you have Feynman diagrams telling you what the different possibilities are, you can't do anything about it. And so you have to think about what the different possibilities are, you know, energy is conserved in those Feynman diagrams. So a heavy particle can decay into a light one, the neutron can decay into a proton by spitting off an electron in a neutrino, and the total mass afterward is less than the mass before, and that extra energy gets turned into the kinetic energy of the particles but the proton can't decay into a neutron right because proton is lighter there's not enough energy for the proton to decay into a neutron except now you're telling me there exists somewhere in the universe particles with negative mass so that allows for the proton to decay into a neutron by spitting off a positron a neutrino and a bunch of negative mass particles okay and it can turn into a heavier particle while still conserving energy and you might say well okay but that must be very very rare i can make the coupling constant such that that's a very unlikely process no as it turns out um this is what we did we checked in fact it's infinitely likely if you sort of sum up over all the different possibilities you've made phase space the space of possible energies for the particles you're making and you've made phase space for the particles you're making and you've made phase space for the particles you're making and you've made phase space the space of possible energies for the particles you're making and you've made phase space the space of possible energies for the particles you're making and you've made phase space the space of possible energies for the particles you're making and you've made phase space the space of possible energies for the particles you're making and you've made phase space the space of possible energies for the infinitely big in an ordinary particle physics calculation if you have the neutron decaying into a proton there's only a finite number of ways you can distribute the extra energy between the electron and the neutrino etc but now you can have this negative energy particle and you can make as many of them as you want these negative mass particles so phase space becomes infinitely big and something that you might have thought was unlikely becomes super duper infinitely likely and maybe you can try to cut it off with and maybe you can try to cut it off with and maybe you can try to cut it off with an effective field theory blah blah blah an effective field theory blah blah blah an effective field theory blah blah blah so basically the paper that we wrote said so basically the paper that we wrote said so basically the paper that we wrote said no no no w cannot be less than minus one w cannot be less than minus one w cannot be less than minus one because it would be catastrophically because it would be catastrophically because it would be catastrophically unstable unstable unstable forget about protons decaying into forget about protons decaying into forget about protons decaying into neutrons empty space neutrons empty space neutrons empty space with zero energy can decay into a bunch with zero energy can decay into a bunch with zero energy can decay into a bunch of positive mass particles and negative of positive mass particles and negative of positive mass particles and negative mass particles the vacuum mass particles the vacuum mass particles the vacuum would be catastrophically unstable in would be catastrophically unstable in would be catastrophically unstable in this way of doing things this way of doing things this way of doing things so um we suggested so um we suggested so um we suggested that the big rip and phantom energy that the big rip and phantom energy that the big rip and phantom energy were were not as plausible as people had were were not as plausible as people had were were not as plausible as people had thought now of course thought now of course thought now of course the whole history of particle physics is the whole history of particle physics is the whole history of particle physics is a back and forth right so you should go a back and forth right so you should go a back and forth right so you should go back and forth the whole history of back and forth the whole history of physics like someone physics like someone physics like someone comes up with a good idea someone comes up with a good idea someone comes up with a good idea someone points out a problem with it someone points out a problem with it someone points out a problem with it someone else comes up with a way of fixing the else comes up with a way of fixing the else comes up with a way of fixing the problem problem problem and so after our paper came out there and so after our paper came out there and so after our paper came out there was work by people was work by people was work by people like nimar khani hamed and others that like nimar khani hamed and others that like nimar khani hamed and others that talked about something called ghost talked about something called ghost talked about something called ghost condensation so these were ghost condensation so these were ghost condensation so these were ghost particles negative mass particles that particles negative mass particles that particles negative mass particles that could could could settle into a stable equilibrium so settle into a stable equilibrium so settle into a stable equilibrium so there were ways there were ways there were ways to get negative mass particles hidden in to get negative mass particles hidden in to get negative mass particles hidden in the the the details of your theory it still details of your theory it still details of your theory it still wouldn't lead to a big rip or anything wouldn't lead to a big rip or anything wouldn't lead to a big rip or anything like that like that like that so i'm still pretty much on the side of so i'm still pretty much on the side of so i'm still pretty much on the side of thinking that w thinking that w thinking that w is not going to be less than minus one is not going to be less than minus one is not going to be less than minus one i think it's very very hard to make a i think it's very very hard to make a i think it's very very hard to make a theoretically theoretically theoretically legitimate respectable model in which legitimate respectable model in which legitimate respectable model in which something like that happens something like that happens something like that happens so of course i'm open to the possibility so of course i'm open to the possibility so of course i'm open to the possibility that someone comes up with a clever way that someone comes up with a clever way that someone comes up with a clever way of doing it there's more to life than of doing it there's more to life than of doing it there's more to life than scalar fields and negative kinetic scalar fields and negative kinetic scalar fields and negative kinetic energies right energies right energies right in fact we followed up our paper um in fact we followed up our paper um in fact we followed up our paper um mark and the two marks and i with a mark and the two marks and i with a mark and the two marks and i with a paper called can you be tricked into paper called can you be tricked into paper called can you be tricked into thinking that w is less than minus one thinking that w is less than minus one thinking that w is less than minus one so there's another game you can play so there's another game you can play so there's another game you can play with scalar fields which is you can um with scalar fields which is you can um with scalar fields which is you can um let them affect the value of newton's let them affect the value of newton's let them affect the value of newton's constant of gravity constant of gravity this is an old old idea going back at this is an old old idea going back at this is an old old idea going back at least to the 60s least to the 60s least to the 60s with braunce and dickey and people like with braunce and dickey and people like with braunce and dickey and people like that where you have scalar tensor that where you have scalar tensor that where you have scalar tensor theories of gravity so when your scalar theories of gravity so when your scalar theories of gravity so when your scalar field moves around it makes the field moves around it makes the field moves around it makes the effective value of newton's constant effective value of newton's constant effective value of newton's constant change change change and that can lead to all sorts of crazy and that can lead to all sorts of crazy and that can lead to all sorts of crazy behavior for behavior for behavior for things like the strength of gravity and things like the strength of gravity and things like the strength of gravity and therefore the expansion rate of the therefore the expansion rate of the therefore the expansion rate of the universe universe universe so we looked into the question like even so we looked into the question like even so we looked into the question like even without without without true phantom energy and all the true phantom energy and all the true phantom energy and all the instabilities that it implied instabilities that it implied instabilities that it implied could you have a model of cosmology could you have a model of cosmology could you have a model of cosmology perhaps with a time-dependent newton's perhaps with a time-dependent newton's perhaps with a time-dependent newton's constant constant constant data i want to constrain my theory the data i want to constrain my theory the data i want to constrain my theory the constraints you get out depends on the constraints you get out depends on the constraints you get out depends on the theoretical possibilities that you allow theoretical possibilities that you allow theoretical possibilities that you allow for that you put in when you start your for that you put in when you start your for that you put in when you start your analysis analysis analysis so we were saying that if you didn't so we were saying that if you didn't so we were saying that if you didn't take into consideration the possibility take into consideration the possibility take into consideration the possibility that newton's constant was changing that newton's constant was changing that newton's constant was changing and just naively and just naively and just naively said you know i have some data from said you know i have some data from supernova and large scale structure and supernova and large scale structure and supernova and large scale structure and whatever whatever whatever what would i infer were the values of what would i infer were the values of what would i infer were the values of the energy density the dark energy and the energy density the dark energy and the energy density the dark energy and its equation of state parameter its equation of state parameter its equation of state parameter you could be tricked into getting a best you could be tricked into getting a best you could be tricked into getting a best fit value of w that was a little bit fit value of w that was a little bit fit value of w that was a little bit less than minus one now to be fair we less than minus one now to be fair we less than minus one now to be fair we what we found by doing the numerical what we found by doing the numerical what we found by doing the numerical constraints we already have and still constraints we already have and still constraints we already have and still open yourself to the possibility open yourself to the possibility open yourself to the possibility of getting w less than minus one but of getting w less than minus one but of getting w less than minus one but it's it's possible and i bring this up it's it's possible and i bring this up it's it's possible and i bring this up of course because of course because of course because people have recently found people have recently found people have recently found possibilities found hints in the data possibilities found hints in the data possibilities found hints in the data that number one the dark energy is not that number one the dark energy is not that number one the dark energy is not constant constant constant and number two it might even have w and number two it might even have w and number two it might even have w less than minus one so as soon as less than minus one so as soon as less than minus one so as soon as people got these hints from the data that people got these hints from the data that people got these hints from the data that w might be less than minus one um i'm w might be less than minus one um i'm w might be less than minus one um i'm still skeptical that it really is still skeptical that it really is still skeptical that it really is something like phantom energy but i i'm something like phantom energy but i i'm something like phantom energy but i i'm open to the possibility that we could be open to the possibility that we could be open to the possibility that we could be tricked into thinking that w is less tricked into thinking that w is less tricked into thinking that w is less than minus one by um constraining an than minus one by um constraining an than minus one by um constraining an incomplete theory incomplete theory incomplete theory and uh but then i looked at the papers and uh but then i looked at the papers and uh but then i looked at the papers and i think that their and i think that their and i think that their im implication the w is less than minus im implication the w is less than minus im implication the w is less than minus one is actually not that one is actually not that one is actually not that believable i think they did a um too believable i think they did a um too believable i think they did a um too quick a job quick a job quick a job in fitting the parameters and it's pretty in fitting the parameters and it's pretty in fitting the parameters and it's pretty easy to find easy to find easy to find models that would fit the data even with models that would fit the data even with models that would fit the data even with years years years the w is not exactly minus one if you ask the w is not exactly minus one if you ask the w is not exactly minus one if you ask me right now i would still say that me right now i would still say that me right now i would still say that the smart money is the w is minus one that the smart money is the w is minus one that the smart money is the w is minus one that is just the cosmological constant is just the cosmological constant is just the cosmological constant uh there's a lot of theoretical virtues uh there's a lot of theoretical virtues uh there's a lot of theoretical virtues there there there but we need to be open-minded and uh but we need to be open-minded and uh but we need to be open-minded and uh let me sort of round this out let me sort of round this out let me sort of round this out by uh well actually there's two things by uh well actually there's two things by uh well actually there's two things there's there's two more things to talk there's there's two more things to talk there's there's two more things to talk about about about one is um you can get more complicated one is um you can get more complicated one is um you can get more complicated right like the these scalar fields right like the these scalar fields right like the these scalar fields rolling down potentials are just the rolling down potentials are just the rolling down potentials are just the simplest things that you can do simplest things that you can do simplest things that you can do and in fact um like i said people were and in fact um like i said people were and in fact um like i said people were doing it in physics with greg anderson a doing it in physics with greg anderson a doing it in physics with greg anderson a friend of mine friend of mine friend of mine who had been a fellow postdoc at mit we who had been a fellow postdoc at mit we who had been a fellow postdoc at mit we wrote a paper on what we called wrote a paper on what we called wrote a paper on what we called variable mass particles or vamps variable mass particles or vamps variable mass particles or vamps so here is the idea for that so here is the idea for that so here is the idea for that what if you have a scalar field and what if you have a scalar field and what if you have a scalar field and what if it can roll down a potential what if it can roll down a potential what if it can roll down a potential and what if the potential doesn't have a and what if the potential doesn't have a and what if the potential doesn't have a minimum minimum minimum right this is and something that these right this is and something that these right this is and something that these days is very common in days is very common in days is very common in dark energy investigations what if the dark energy investigations what if the dark energy investigations what if the potential energy function potential energy function potential energy function is not like phi squared but something is not like phi squared but something is not like phi squared but something like one over phi like one over phi like one over phi or e to the minus phi or something like or e to the minus phi or something like or e to the minus phi or something like that so the scalar field can just roll that so the scalar field can just roll that so the scalar field can just roll off to phi equals infinity forever off to phi equals infinity forever off to phi equals infinity forever and in fact things like this are not and in fact things like this are not and in fact things like this are not impossible in um supersymmetric theories impossible in um supersymmetric theories impossible in um supersymmetric theories and string theory and things like that i and string theory and things like that i and string theory and things like that i think that was part of greg's think that was part of greg's think that was part of greg's original idea like is there a way to original idea like is there a way to original idea like is there a way to control control control these potential runaways of the scalar these potential runaways of the scalar these potential runaways of the scalar field that wants to run off to infinity field that wants to run off to infinity field that wants to run off to infinity because we didn't have data then that uh because we didn't have data then that uh because we didn't have data then that uh there was an acceleration of the there was an acceleration of the there was an acceleration of the universe universe universe and what he knew about he he didn't know and what he knew about he he didn't know and what he knew about he he didn't know about the cosmology aspects of things about the cosmology aspects of things about the cosmology aspects of things but what he realized is that these but what he realized is that these but what he realized is that these scalar fields scalar fields scalar fields very much like the higgs mechanism can very much like the higgs mechanism can very much like the higgs mechanism can have a feedback where the value of the have a feedback where the value of the scalar field feeds into the masses of the particles around it so you have um it wouldn't work phenomenologically or experimentally i should say with things like electrons and protons because electrons and protons have pretty darn constant masses in the universe since early times we know that from experiments from observations from looking at the fine structure constant early on from looking at big bang nucleosynthesis etc it's just very very hard to make the masses and couplings of the known particles change with time but what if you had dark matter okay which you do you do have dark matter what if the dark matter was a field that got its mass just like electrons get their mass from the higgs boson what if dark matter gets its mass from a scalar field and what if that scalar field doesn't have a minimum its potential so it wants to run off to infinity just wants to roll off it's a ball rolling down a hill and the hill just rolls on forever but here's the problem as the scalar field rolls it gives mass to the particles around it to all the dark matter particles okay and that costs energy so basically we pointed out you could stabilize the potential energy of the scalar field because there's effectively a contribution from the fact that it costs energy to give mass to all the ambient dark matter particles all around it so instead of just the scalar field having a potential energy one over phi or something like that in the presence of some dense collection of dark matter particles you know some number density of dark matter particles there's also an effective term in the scalar field that is proportional to phi and is positive the value of phi is increasing the masses of the scalar field that's sorry the masses of the dark matter particles and the energy density in the dark matter particles is the number of dark matter particles times their masses and so that's an effective contribution to the potential for the scalar field and therefore you could stabilize it you have a value of phi that was constant because of this ambient collection of dark matter particles with an energy density and then you say you keep going and you say but the universe expands so the universe expands and so the density the number density of the dark matter particles changes with time it goes down and as a result of that the effective contribution to the potential energy for the scalar field shifts because it's proportional to the number density of the dark matter particles and that's going down as the universe is expanding so basically the scalar field keeps adjusting its minimum to sit at a happy place where it's a balance of its potential energy one over phi and its effective contribution which is proportional to the number density of dark matter particles and that changes with time as the universe expands so we get variable mass particles or vamps as we called them and this was supposed to be a candidate for both dark matter and dark energy all at once it doesn't quite work in the naive form because again you should allow the dark matter particles to be not completely homogeneous right they have some inhomogeneities and there's an instability where those inhomogeneities grow with time which can be bad but this helped inspire other people there was something called chameleon fields where as i i said a while ago you know there's a problem with fifth force experiments when you have all these light scalar fields going around and so what if you could give those scalar fields a temporary mass when they were in the vicinity of ordinary matter right so if the scalar field gets an effective contribution to its potential from its coupling to ordinary matter that could pin it and stop it from giving rise to fifth forces this is called the chameleon mechanism and um um amanda weltman and justin corey suggested this idea and so i'm i'm not trying to i'm sorry if i'm breezing through this too quickly but i'm not trying to go into all the details because the details of no one model are all that interesting the idea is the interesting thing is that there exist models that there exists whole different worlds to play in where the possibilities are very exciting and interesting so the data will help guide us if we eventually do figure something out here but in the meantime the theorists are coming up with all these fun ideas and you can't just sit around and wait for the data because sometimes coming up with the theoretical ideas suggests to you that you should go look for certain pieces of data right like if we hadn't discovered the acceleration of the universe no one would be trying to measure the equation of state parameter of the dark energy so you can't just wait for the experiments to come in there's a constant give and take an eternal interplay between the theory and the experiments in physics and this is all part of that okay the final idea i want to get on the table is what if there isn't dark energy and by that i mean not that we've made a mistake in the data i think the universe is accelerating i think that's what the data are telling us the universe is accelerating what if the acceleration of the universe is not due to dark energy that's something that you absolutely are allowed to think about the alternative of course is that it's due to modified gravity so one thing that is in common between dark matter and dark energy is that in so far to date we haven't detected either one directly what we've done is inferred their existence by looking at the behavior of space-time by looking at the gravitational fields and galaxies and clusters and the expansion rate of the universe and so it's a very old idea that what if gravity is different than we think it is on cosmological scales that could trick us into thinking that there is dark matter and or dark energy in the case of dark matter this goes uh the most famous version of this is mond which has been developed into more theories in various ways but you can try to play that same game with dark energy modify einstein's equation of general relativity to make the universe accelerate even without dark energy that's a game that you could imagine playing and in fact so i was thinking about this again as a young assistant professor and the way that i thought about it it's again a funny story like the the history behind these things is always kind of amusing and sometimes a little bit embarrassing because you made mistakes so i was thinking along the following lines um there is something that we know about dark matter that motivates modifying gravity so by the way nowadays it doesn't work modifying gravity to get rid of dark matter just doesn't work and the reason why as opposed to 25 years ago is we have data from the cosmic microwave background and the idea of mond and other modifications of gravity made predictions for the microwave background and isotropies and they came out false they have been ruled out by the data i know there's some people who sort of stubbornly insist that they're going to keep thinking about it it's a free world you can keep thinking about it but the data rule it out um now that's never a 100 statement right because well maybe i can change my theory a little bit to hide from it but to a very very good approximation but i think it's a very good approximation so i'm going to give you a very very good approximation the data have ruled out this idea but in the year 2000 that was not true or the year 2003 or whatever i don't know exactly when it was um so i was thinking about the following idea right i started saying a motivation for uh mond is a numerical coincidence so mond uh milgram's idea of modified newtonian dynamics is the following idea you know he noticed in the data that if you look at something like a spiral galaxy like the milky way or other spiral galaxies famously there's evidence for dark matter because the rotation curves of the galaxies which is to say the speed the velocity of rotation of things going around the galaxy as a function of the distance from the center if you look near the center it's exactly what you would predict like you count the stars you count the amount of matter in there you do newtonian gravity you figure out the gravitational field the rotation is exactly what you expect but what you also expect is that if you look at the center it's exactly what you expect but what you also expect is that if you look at the center it's exactly what you expect but what you also expect is that if you look at the center it's exactly what you expect but what you also expect is that if you look at the center it's exactly what you expect but what you also expect is that if you look at the center it's exactly what you expect but what you also expect is that if you look at the center it's exactly what you expect but what you also expect is that as you go further and further out into the fringes of the galaxy the rotation curve should get lower and lower the velocity should be smaller and smaller because the gravitational field is weaker right uranus and neptune move much more slowly than mercury and venus because the gravitational field is much stronger near mercury and venus but what you see going back to the data collected by vera rubin and others is that the rotation curves do not diminish to nothing they more or less flatten out so there is more gravitational force at the distant fringes of the galaxy than you would expect from ordinary physics this is evidence for dark matter if you have dark matter dark matter if it's just cold dark matter non-interacting into the simplest kind of model dark matter doesn't bump into other dark matter it doesn't dissipate the reason why in a galaxy there's so much density of matter near the center is ordinary matter like made of atoms with electrons and they can bump into each other and radiate away energy and by fall by losing energy they fall into the center of the galaxy and the centers of the galaxies become very dense dark matter doesn't do that dark matter doesn't bump into itself and radiate away energy it just moves under the force of gravity so it becomes slightly more dense in the center but not that much really the galactic halo of dark matter as we talk about it has a much lower density contrast between the middle and far away than the density contrast in ordinary matter so the 100 natural prediction the expectation in a theory with dark matter is that the ratio of ordinary matter to dark matter should be very high in the center of a galaxy and very low far away and that's exactly what you see in the data the numerics you know you can try to work out exactly where the crossover should be etc that's fun to do and people do it but the general qualitative expectation is exactly what you see but what milgram realized is there is a weird and legitimately puzzling numerical coincidence that if you look at different spiral galaxies and there's always a crossover point where you go from you don't need dark matter near the middle of the galaxy to you do need dark matter near the outskirts right so there's some radius there's some distance from the center where you go from not needing dark matter to needing it to explain the rotation curves and milgram noticed that uh this radius at which you suddenly need dark matter is not the same in every spiral galaxy and it's not so it's not a constant distance but if you calculate the acceleration due to gravity okay at that radius so the acceleration due to gravity in just a newtonian sense like if you're an expert in general relativity the phrase acceleration due to gravity bothers you because there is no such thing but in the newtonian limit perfectly legitimate talk about acceleration due to gravity you calculate in many different spiral galaxies the acceleration due to gravity at the point where you're apparently crossing over from not needing dark matter to needing dark matter and it's roughly speaking the same number in all these different galaxies even though the galaxies themselves are very different from each other and furthermore if you do the plug in the numbers and plug in appropriate factors of the speed of light and things like that that acceleration due to gravity is the hubble parameter today numerically it's approximately the same numeric value as the hubble constant and that makes no sense at all or at least it at first blush it makes no sense because the hubble parameter is a statement about the overall expansion rate of the universe and this acceleration in a galaxy where suddenly you need dark matter to explain what's going on has nothing to do with the overall expansion rate of the universe it has to do with the local dynamics of the galaxy now secretly maybe it does have something to do with the hubble parameter because that galaxy came from everywhere from somewhere and it it was formed somehow and maybe that's relevant to this uh dynamics but okay at least again at first blush that seems very surprising so this was the motivation for milgram for proposing modified newtonian dynamics the universality of this phenomenology of the fact that in all these many different spiral galaxies you saw the same number creeping up over and over again and the fact that it's approximately equal to the hubble constant is also kind of provocative now again it doesn't work like if you go to clusters of galaxies and things like that suddenly the dark matter doesn't appear at that acceleration it's a different thing which again makes perfect sense in the dark matter models doesn't make sense in the mond models but okay put that aside here i am thinking about this in the early 2000s and i said so not only is modified newtonian dynamics motivated by this universality of the acceleration but that acceleration is numerically about the same size as the hubble parameter today and we have another numerical coincidence which is the coincidence problem for dark energy in the cosmological constant namely the dark energy density needed to fit the data is approximately equal to the matter density needed to fit the data today in the current universe and today the current universe is parameterized by a certain value for the hubble parameter right today's value so when i say that the galaxies according to the mon phenomenology have an acceleration radius that is equal to the hubble constant i mean equal to the hubble constant today the hubble constant is not a constant it changes over time so there was this numerical coincidence just in the dark matter sector and there's sort of a similar numerical coincidence in the dark energy sector like this is just very juicy and provocative to a theoretical physicist right so i tried to say to myself you know is there a way to unify this together is it possible that if it is um i mean dark matter and dark energy are just very different seeming things uh so there's no obvious connection between them but if you modify gravity maybe you can connect these two phenomena maybe there's no dark matter no dark energy you see how it's very seductive right and you have to be able to be seduced by it but also be able to give it up if it doesn't work so if if you can modify gravity to explain both of these things away then you only need one number you need the hubble constant today like okay we're not going to explain that number we're just going to put it in but maybe you could explain away both the rotation curves of galaxies and the acceleration of the universe so okay that's it's easy to be inspired it's hard to actually come up with the theory so what is going on what is the common feature that the dark matter phenomenon and the acceleration of the universe share well the common feature is that they're both things phenomena that kick in when gravity becomes weak when the curvature of space-time becomes small right this is in entirely incompatible with or in a certain way entirely uh flying in the face of your expectation as an effective field theory person in effective field theories you expect things to go crazy in the ultraviolet at high energies but you expect everything to just be normal and and under control in the infrared you don't expect things to become weird when space-time becomes approximately flat fields become weak distances become large any of those things in fact when i when i later was talking to a very famous theoretical physicist who i won't name about this uh idea he said you know i should write a paper just saying why none of this will ever work and you know there probably was such a paper to be written that the paper was never written but uh it is it certainly will never work in the sense that it's absolutely not what you expect from effective field theory but you know there's things we don't understand so maybe you shouldn't be too wedded to those possibilities so i took off my effective field theory hat and just thought phenomenologically and said could i fit the data so how would you change gravity in such a way that the change would only become noticeable when the gravitational field was weak rather than the gravitational field being strong being strong is easy to change being weak is hard so i knew about you know how to think about general relativity from the point of view of a field theorist and i'll just get a little bit technical because it helps with understanding the vocabulary here you know i mentioned um in the previous podcast when we're talking about euclidean quantum gravity one way of thinking about general relativity is through the action the principle of least action there is a formula it was actually written down by david hilbert and used to derive einstein's equation very close to the time when einstein himself was first doing it so there's a formula for the action associated with a space-time geometry and you can derive einstein's equation just by saying let's look at all the possible space-time geometries subject to some boundary conditions and find the one that has the minimum action right the principle of least action that's what's going on and the formula that hilbert wrote down is like the simplest dumbest formula you can write down so that's again always a sign that you're on the right track when the simplest formula actually works there is a scalar quantity that is to say a quantity that has no directionality in space-time it's just a number called the curvature scalar it's a way of taking the riemann curvature the curvature tensor that has a lot of directionalities and boiling it down to a number the curvature scalar sometimes called the ritchie's scalar and it's given the name capital r and that's it that's hilbert's action principle the integral of capital r plus the the action for whatever is matter and and particles in your theory that gives you einstein's equations of general relativity it's just that simple so that's the simplest thing you could possibly do from an effective field theory point of view you would expect that that action the integral of r so again one more little vocabulary word here and all this is explained in quantum fields if you're interested in um the action is an integral over all of space time of a quantity called the lagrangian if you've ever heard of lagrangians that's what they are they're just quantities you make from the fields in your theory like the metric and the electromagnetic field and whatever you make different quantities you add them together to make a lagrangian you integrate that over the space-time manifold to make the action and it's that action that you minimize to get the equations of motion so so hilbert's lagrangian is just r the curvature scalar there's some details in there about the measure over space-time volume but let's ignore that okay it's just r it's the simplest thing you could write down as an effective field theorist you expect this term r to just be the first term in your effective field theory and you should have plus r squared and r to the fourth and a whole bunch of other things that's exactly what you would expect but because r the curvature scalar is a very very tiny number in the real world um r squared is even tinier and r to the fourth is tinier than that so all these other things are completely different so you don't have to worry too much about that because that's what you'd expect you can just go with r you can just go with the simplest thing everything works fine that gives you general relativity so what we're asking is okay just just because it fits the data or just because the data cries out for some help not because there's any theoretical motivation for it could we modify the action for general relativity in such a way that it didn't change things at large curvatures but changes things at small curvatures again no motivation for this theoretically but we want to try to fit the data because both the dark matter data and the accelerating universe data are saying something weird is going on when gravity is weak which means something weird is going on when space-time is close to flat which means something weird is going on when r the curvature scalar is close to zero well if the ordinary action is just r the simplest thing you can do is to add a constant right that would change things when r is small but we've already done that that's the cosmological constant and adding a constant to the action for gravity is exactly just adding the possibility of vacuum energy. So that already existed. So the next obvious thing to do would be to add 1 over r, the reciprocal of r. No reason to do that, except it's something that would begin to kick in when the gravitational field became weak, right? When r went close to zero. Now, the experts in general relativity are shaking their heads here because even you can have a strong gravitational field with r close to zero, because r, the curvature scalar, is just part of the overall curvature. In fact, near a black hole, which in some sense has a strong gravitational field, r is still close to zero. But that's okay. We have to work with what we got. And what we have is an attempt to change the action of general relativity. So let's add the reciprocal, r plus 1 over r. So instead of just having the curvature scalar, r, add r plus 1 over r. And then you hope, the idea is, you hope that this can explain both the dark matter phenomenon and the dark energy phenomenon. So it'd explain the rotation curves of spiral galaxies and the acceleration of the universe today. So I did that. I wrote it down, wrote down the equation. I worked out the equations of motion. I solved the equations of motion in certain extra special symmetric circumstances. And I got disappointed. What I realized was that the Schwarzschild solution, which is the solution for Einstein's ordinary equations for a spherically symmetric distribution, is 100% exactly also a solution for this new theory with 1 over r added to the action. So even though I had modified, it's exactly this technicality that I was worried about. Before, r does not capture everything. Okay, so even though r is zero for the Schwarzschild solution, that solution is still a perfectly good solution to this new equation. And what that means is that in the Newtonian limit, the Newtonian limit is just the Schwarzschild solution far away from the event horizon or the Schwarzschild radius. And that's what's going on in a galaxy, etc. So this theory, this 1 over r theory, doesn't make any new predictions for the Schwarzschild solution. So what's going on in the Newtonian limit, though, is that the Schwarzschild solution is still a solution for this new theory with 1 over r added to the action. So what's going on in the Newtonian limit, though, is that the Schwarzschild solution far away from the event horizon or the Schwarzschild radius. And that's what's going on in the Newtonian limit. So what's going on in the Newtonian limit, though, is that the Schwarzschild solution far away from the event horizon or the Schwarzschild radius. It could help explain the acceleration of the universe. So I realized by reading, not by actually thinking, that people had thought about theories of gravity based on functions of r that were not simply r, right? So r is Hilbert's solution. And I think that's what's going on in the Newtonian limit. So I realized by reading, not by actually thinking, that people had thought about theories of gravity based on functions of r that were not simply r, right? So I realized by reading, not by actually thinking, that people had thought about theories of gravity based on functions of r that were not simply r, right? So I realized by reading, not by actually thinking, that people had thought about theories of gravity based on functions of r that were not simply r, right? So I realized by reading, not by actually thinking, that people had thought about theories of gravity based on functions of r that were not simply r, right? So I realized by reading, not by actually thinking, any arbitrary function of r is something other people have thought of. And they realized there is a way to do a clever change of variables and rewrite this theory with a function of r as your Lagrangian into a theory with the ordinary general relativity Lagrangian plus a scalar field doing something interesting. And this is a feature of field theory, just a classical field theory that is really sort of weird and worth exploring that, you know, you write down these tensors like you have in general relativity, etc. And these tensors hide many different degrees of freedom in them. And so sometimes you can write a theory that you thought was just describing a certain tensor field like the metric, but it's actually describing other tensor fields as well. So that's why you can take an f of r theory, and rewrite it as what is called a scalar tensor theory, just a theory with a scalar field as well as a tensor field. And from looking at that theory, you could look pretty obviously and show that an accelerating universe is a solution to the equations. At early times, it would look like an ordinary general relativistic cosmology, and at late times, it could accelerate. Now, I later realized that the that solution is unstable. So that's an issue. But okay, in principle, it could accelerate, it could basically accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized that the theory could accelerate. And so I realized dark energy, basically. But here's where my not very cleverness comes in. I've been clever up to that point, and then I became very non-clever. I said to myself, well, that's too bad. This theory seems to maybe work to make the universe accelerate, but it doesn't help at all with dark matter or the rotation curves of spiral galaxies. And it's just a scalar tensor theory at end of the day. People knew about them already. Therefore, it is not interesting. And so I took the files I had written up and just left them on my computer. And I think like at least a year or probably two years passed after that. And within the course of a week, two things happened. One is that Vikram Dvuri, who was a graduate student working with Michael Turner at the University of Chicago, knocked on my door and said, hey, has anyone ever thought of a theory of gravity where you add one over r? To the Lagrangian. And I said, well, yeah, I thought about that. I told him the story. And I said, it's not very interesting. It doesn't help with dark matter. And he goes, oh, okay, I guess not. And then I got a phone call, I think it was, maybe an email from Mark Trodden, the guy who we'd worked together on W less than minus one. And Mark says to me, has anyone ever thought about a theory of gravity where they added one over r to the Lagrangian? And I said, well, you know, I thought about that. And I decided it wasn't interesting. And I said, well, you know, I thought about that. And I decided it wasn't interesting. And I said, well, you know, I thought about that. And I decided it wasn't interesting. But you and a graduate student just came up to me and suggested it. So maybe it is interesting. Maybe if people keep inventing it, we should write a paper about it. And we did. And so we wrote a paper also with Michael Turner. So there was four of us. And it has a goofy title, Can Cosmic Speed Up be Explained by a New Theory of Gravity or something like that. And this became, like I said, the idea of modifying gravity by having a function of r in the Lagrangian, was an older idea. But we were either the first or among the first to very, very explicitly say this can be used to explain the acceleration of the universe. And again, I wasn't that excited about the paper because I thought, you know, it's a model. It kind of works, but it doesn't have that many new interesting properties. But what I didn't get right, and I constantly make this mistake, I'm trying not to make it as I get older now, what I realized it's a new tool for people to play with. And I think it's a new tool for people to play with. And I think it's a new like once you say, oh, maybe I can modify gravity in this way. Maybe other more clever people than you can modify gravity in more clever ways and make progress. So the whole program of what is now called f of r gravity became super duper popular. And we were not the only paper. Like I said, we were one of the first, if not the first, but there were other papers near the same time saying somewhat similar things, you know, so you can look up all the references. I don't want to credit. But there's a million questions that come up. Can you fit the data like beyond just saying the universe accelerates? Can you literally fit the data very carefully? Can you be avoiding all the various experimental tests of modified gravity that people have done? And is one over r the best thing to do? Maybe it's not. Maybe you want some other function of r. What about couplings of this scalar degree of freedom to matter? And oh, maybe you want to impose the mechanism and things like that. So other people at Chicago and elsewhere followed up on this, and it became very popular. And I did a couple of small things with it, you know, one looking at the cosmological consequences, one with a slightly different modified theory of gravity, which we called modified source gravity, which avoided some of the problems, but then raised others. And it's fun. I feel always somewhat ambivalent about it, because it's a good idea, I don't think it quite works. And it's really popular. And so I don't want to disown it. But I can't be that excited about it myself. If you want to ask me, right now in 2026, the middle of the year, I still think that the vast amount of smart money is on the good old cosmological constant being the source of dark energy making the universe accelerate. We don't know we're trying to be good Bayesians. We're trying to say there's a credence for it being a scalar field or modified gravity or various other kinds of things we haven't thought of yet. We need to allow space in our credences for new data to come in and let us update our credences. Knowing what new data to look for is sometimes driven by theoretical speculation. So even before the data comes in, we need theorists to come up with new models and propose new tests of those models. Science moves slowly these days. And that's for different reasons. So different different parts of science, some science moves very quickly. Fundamental physics and cosmology moves slowly in part because you know, you say you make a prediction in 1999. That says, Oh, a certain kind of scalar field can cause photons polarizations to rotate across the universe. And it takes decades to make telescopes that are good enough to test that kind of prediction. So it's not like we're not trying. Right? Yeah, we're trying our best to learn things. And as mentioned, there have been hints from the DESI collaboration and things like that, that maybe it's not the cosmological constant. I'm not I'm not talking about those hints in detail here. Because I don't want to rely on them. I'm not trying to give you the impression that We have discovered that W is not minus one, and therefore it's not a cosmological constant. It's some dynamical dark energy, and therefore we should be building models that fit that. That's not my point. My point is we don't know, and therefore we should keep an open mind, and we should collect data, and we should nod approvingly when the data comes in and keep it in mind, knowing that the data might be on the borderline of being statistically significant, and maybe it will go away, or maybe it gets stronger in the future. We have to have the patience to be able to wait and see what's happening. Where I can finish is where I began one and a half or two podcasts ago with the idea that this discovery that the universe is accelerating is the single most surprising and profound discovery in fundamental physics in the time that I've been doing fundamental physics professionally. So. It's important. It's a big deal. Even the paper I recently wrote about a cyclic universe, even though it's not precisely, you know, trying to explain the dark energy or whatever, it's 100% motivated by the idea that there's a cosmological constant, and that gives rise to a horizon, and that gives rise to a finite dimensional decider space, and we need to look at the implications of that. So I'm still very much interested in figuring out what are the implications of the accelerating universe, and it'll remain until we totally figure it out, one of the most important things for us to stretch our brains around. Hopefully that stretching gets us somewhere good, and we find some new discoveries along the way. So thanks for listening. Thanks for putting up with a two-part solo podcast, and I will talk to you next time. I'll see you next time.
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