Lambda CDM and Future Outlook

Everyone talks about summer like it's supposed to be carefree. But if this season brings up money stress, body stress, family stress, or social stress, that's real too Growth therapy can help with that Whether it's your first time in therapy or your fiftieth, GroO makes it easier to find a therapist who fits you, not the other way around They connect you with thousands of independent licensed therapists across the US, offering both virtual and in person visits nights and weekends You can search by what matters, like insurance, specialty, identity, or availability, and get started in as little as two days. And if something comes up, you can cancel up to twenty four hours in advance at no cost There are no subscriptions, no long term commitments. You just pay per session The Gow helps you find therapy on your time whatever challenges you're facing, growth theraapy is here to help The Gro accepts over one hundred insurance plans, including Medicaid in some states. Sessions average about twenty one dollars with insurance, and some pay as little as zero dollars depending on their plan Visit growthraapy. com slash book now to get started That's growthapy d. com slash book now theapy. com slash book now Availability and coverage by state and inssurance Plan. Running a business shouldn't feel like surviving a software group project. One app for accounting, another for inventory, another for sales, and somehow None of them talk to each other That's where Odu comes in An all in one business management software that brings every part of your business together from sales and accounting to inventory and marketing all in one powerful platform No messy integrations, no bouncing between tabs, And best of all, no spreadsheets Stop managing software and start managing your business with one unified system Try for free today at odu. com That's ODOo. com. Hello, everyone and welcome to the Mindscape podcast. I'm your host, Seaan Carroll In physics, which is a very broad field, includes, you know, atomic physics, plasma physics, condensed matter physics, biophysics, particle physics, gravity, cosmology, and all these things. Different fields, of course have different rates of progress, both because of theoretical ideas and experimental input. If you focus just on fundamental physics and let's not argue about what that means or should mean I take it to mean figuring out the most fundamental laws of nature the best we can So not including things like biophysics and conced matter physics, not because they're not important. It's just a different thing. I once tried to get the field to change the name fundamental physics to the name elementary physics the most elementary laws of physics being the idea, but no one agreed with that. That's okay. Fundamental physics is here to stay In this subfield of fundamental physics, which includes sort of particle physics and gravity, things like that There haven't been a lot of helpful experimental, surprising discoveries in the past several decades, Arguably since the nineteen seventies, There've been a few here and there, masses of neutrinos, things like that Also things that we expected like the Higs bs on, gravitational waves, but in terms of true surprises ' been feel and far between. that makes it hard to make progress in fundamental physics because Experiments are what drive us to great ideas And there's one, of course, shining counterxple to this idea that there haven't been many surprises, which is the acceleration of the universe Back in nineteen ninety eight, we were told by results from two competing. astrophysics groups looking at type one A supernoae, using them to measure the expansion rate of the universe and how it changed over time Against all expectations, the universe is actually accelerating, not decelerating in its expansion rate And of course, this was a big deal. Nobel prizes were handed out and the whole bit. We still don't understand with complete confidence what is going on with the acceleration of the universe, which is great for fundamental physicists such as myself for theorists who are trying to figure out what's going on. It would be nice if we had more than that one fact, the acceleration of the universe, it would be helpful to our project of inventing theoretical models to explain it, but it doesn't slow us down. We're going invent them anyway There is a leading candidate, the cosmological constant, as proposed by Einstein many, many years ago, but there's other ideas as well So recently, through a set of circumstances that I won't go into, I fell behind personally in my recording of podcasts and I'm doing traveling and things like that And so even though I just did a solo podcast on quantum mechanics not that long ago, I figured I can fill in by doing some more solo podcasts. I figured just one solo podcast, but what you're going do is you're going to get two in two separate weeks What happened was I went to Patreon where I sometimes turn for advice from my Patreon listeners. If you ever curious, about what it would be like to be in the cool in crowd of Patreon listeners. justust go to patreon. com slash Sean M Carrool and you can sign up And I asked them what would be a good topic for a solo podcast. And I gave them some suggestions. And I think that a pretty clear tendency, even though there's a lot of diversity in the answers was for the suggestion of theories of dark energy and the accelerating universe And in some sense it's shocking I haven't done that already. This is something that I do know something about. Indeed, my My first ever attempt at publishing a trade book at writing a popular level book and getting it published was proposed a book on the accelerating Universe and Dark Energy, and no one wanted to publish it This was like two thousand six, maybe, and people were already like, well, we've done that already. That's old news. nineteen ninety eight, two thousand six. The ship has sailed. So I don't think that was right. I think there's plenty of room for a really good book on that topic, but I never did write it. So Plenty to say about that. and I thought that was a very good choice on the part of my Patreon listeners. so I thought, sure. And then I started sketching it out and I realized, you know what? there's actually too much to say about this topic. Sove broken into two episodes I know that I have in the past gone on a great length in solo episodes, but I do think that there's sort of a natural dividing line here. You can talk about The cosmologrical constant as Einstein came up with it and as we really wondered about what it means in relationship to quantum field theory and what the Observations are telling us about it. And then you go beyond that to what if it's not a cosmological constant? What if it's something else? What if it's something dynamical, a modification of gravity or something like that So those will be the two solo podcasts. I'm going to talk in this one that you're listening to right now about the cosmosial constant, the energy of the vacuum because that's an equivalent idea. They're precisely identical And then I'm going to do another one on dynamical Dark ennergy, which, on the one hand, contains a whole bunch of really exciting, interesting ideas, and would be a tremendously exciting discovery whereere we to find evidence for it. On the other hand, there is no evidence for it Right now, so it's still completely speculative. We're a little bit less constrained in that part of the world so we can let our imaginations roam All great physics, it's all cutting edge. it's all very perplexing and confusing. and that's exactly what you like as a working physicist. You want to have problems you don't know the answer to struggling to figure out what those answers are. So I'm going to try in these two podcasts to sort of let you in on both what the questions are and why certain answers look the way they do, certain other answers are less promising, things like that Hopefully to give you roadmaps you can understand better what we're trying to do in cosmology and fundamental physics with this problem and what might happen next. So with that in mind, let's go. When we're talking about the cosmological constant, the energy andcy of the vacuum or whatever, there's a very obvious starting point for us, which is Einstein. He's the guy who came up with the idea back in the day. and it provides a fun excuse to think historically about how these ideas came about because it's useful to think historically because we have different pree existing ideas than they had back then, right? We have different things that we think are really important and other people in different historical eras might not have cared about that much or they might have had other things that they care about that we don't care about very much. So that's very much the case for Einstein, who was absolutely not the shut up and calculate kind of guy. He was someone who had very strong ideas about how things should be. and he thought them through in a very rigorous and careful way. But he was open to changing his mind and realizing that he was wrong, but he definitely had a style that opened his mind to different possibilities. So You pictuure that around nineteen fifteen, Einstein had put the finishing touches on the general theory of relativity The general theory of relativity says that spacetime, which was an idea that went back to Minkkowski Right after Einstein had figured out special relativity in nineteen oh five, his old professor Minkkowski had pointed out that it was better formulated as a theory of a unified spacet time And Einstein didn't like that suggestion by Menkowsky, but he eventually came around to realize that was a good idea And in fact, that we could incorporate gravity into the ideas of relativity by allowing spaceet timee to have a geometry, by allowing it to be curved. And that was the basis for his theory of general relativity. So that's nineteen fifteen. and I just can't even imagine how much fun it must have been to be a physicist at that time and to have this new playground to run around in and explore new things. Of course, Einstein had the head start on everybody else. So many of the fun ideas that one could explore in the context of general relativity were first explored by Einstein very soon after he invented the theory. He didn't do everything, like the short shield solution, the metric tensor, the curvature of spacetime for something like the solar system or a black hole or whatever, was found only two years after Einstein invented the theory, But Einstein himself didn't find it. It was short Shield, of course, who did it One thing that Einstein did do was to think about the universe as a whole And now it's kind of interesting. this is why I mentioned the philosophical predispositions that different people have Einstein was heavily influenced by Erennst Mach who was a physicist and a philosopher of physics, to be honest, in Germany at the time who had very definite ideas about the relationship between space and time and matter and things like that I would say that Mock's influence on Einstein was maybe inspirational, like maybe he nudged Einstein in the right direction to say some good things But ultimately, the answers that Einstein came up with are completely disconnected from any of Mock's ideas. And it's a weird historical thing that people keep trying to fit it in. People keep trying to have Mock's principle, which connects the rest frame of the universe to the existence of matter in the universe, to general relativity, Einstein's theory, even though they're not really actually very closely connected. But I bring this up because Einstein thought that they were closely connected. And when he first turned his attention to the universe as a whole He was very influenced by Mck And there was also in the back of Einstein's mind, and people today forgot about this there was this puzzle that people knew about in Newtonian physics in Newtonian gravity The puzzle is the following. You can sort of imagine solving Newton's equations for gravity, using this way of writing things that's actually due to Pierceimon Laplace in terms of the gravitational potential. okay? So rather than just saying that the sun reaches out ninety three million miles to the Earth and pulse it via the gravitational field you can say, well I shouldn't even say by the gravitational fields, that's not how Newton talked by the gravitational force, by action at a distance in Newton's way of thinking about it Plus replaced Newton's equations with a field equation And then there's no action at a distance. The sun is pushing the gravitational potential field, the Earth moves in it All that makes perfect sense If you're talking about the solar system, but it was puzzling when you try to talk about the universe as a whole because it turns out that if you just imagine a universe filled with a absolutely constant density of matter. It is undefied potential you should have. There are multiple solutions that work equally well. You can add a constant to it, things like that. And it didn't seem to be a good starting point for investigating the universe So Einstein had that in mind when he started doing relativistic cosmology. And therefore, rather than just assume that the universe was spatially flated because remember, the whole point of general relativity is it's the geometry of space and time that defines what we think of as gravity Einstein said, Well, what if space is finite What if space doesn't go to infinity then you can both help understand how to get out of this puzzle in Newtonian gravity. and you can be consistent maybe, he thought With Mox's principle that it's the matter in the universe that is fixing what we think of locally as our standard of rest and our inertial frames and things like that. So Einstein had these ideas and he was pretty convinced as far as I can tell, I'm not a super expert on the history here, so maybe someone can correct me. But as far as I could tell, like he thought that there were just really good philosophical reasons to think that space is finite, not infinite Personally, myself, I'd rather be open minded about that. I don't have any strong pree existing opinions about whether space is finite or infinite. I'll let the data or a better theory decide that But anyway, He tackled the problem of cosmology. and he said, lookook, let's just start by assuming that matter is distributed uniformly throughout the universe He had no idea whether that was true or not. There was some indication from cosmology Circa of the nineteen teens that Maybe there was some uniform distribution of matter in the galaxy, but we didn't even know in nineteen fifteen, sixteen, seventeen about the existence of other galaxies, right? That idea didn't, well, the idea was there, but the knowledge, the data didn't come along until the nineteen twenties. So you was sort of open season for speculating. There wasn't enough data to really tie you down. So Einstein said, Okaykay, let's imagine a uniform universe O where the density of matter is statistically the same everywhere. He knew that the density of matter is not the same on the Earth as in the sun and things like that. You're imagining that you're thinking about very, very large scales throughout the universe and the average density of matter could be the same everywhere. And he said, Okay, what if I take a spherical universe? And bypherical, of course, we know that space is three dimensional on large scales. So that means a three dimensional sphere. that's no problem to differential geometry and general relativity. So space in Einstein's model is a three dimensional sphere and time is just a line. time goes from wherever it goes on into the future. And he said, okay, I'm going to plug this into my equation called Heinstein's equation. And I'm going to ask what that implies for the evolution of the universe, a constant density in the spherical universe And what he found was that two things happen, you plug into Einstein's equation and you get an equation for either the expansion or contraction of the universe. Space wants to change its size. That's not really something that was very well defined in the Newtonian point of view, but in general relativity, it makes perfect sense. You have a three dimensional sphere, and the three dimensional sphere can get bigger or smaller And it turns out that both that geometry of space and the existence of matter contribute to this change in the size of the universe, and you can find a solution where at one moment of time The universe is not changing size. okay? So you can set the sort of the velocity of the universe, if you want to call it that to zero by balancing the curvature of space versus the matter What you can't do is keep it there. But basically what Einstein realized is that the equations he was looking at kind of implied a universe that would St from somewhere. it was all very vague at the time, right? We're talking about nineteen seventeen or so. Start from somewhere, expand and then reach a point of zero expansion, right? but then just start collapsing again This is very familiar to modern cosmology students. This is a closed finite time universe that we can absolutely think about. Do doesnn't seem to be the universe we liive in as far as we know, but as far as Einstein knew he wasn't sure. So he seemed to find, again, you could find a solution where the universe is not expanding, but it would instantly start either expanding or contracting depending on how you set up the different numbers Imagine buying your kid a toy only to find that the batteries aren't included We're buying furniture, but it's missing the tools you need to build it. That's so frustrating, right Now imagine that exact same feeling, but you're paying way more That's what buying business software usually feels like. It's fragmented, disconnected, and incredibly expensive. Odu completely changes that Odoo is a complete, fully integrated business suite where all your apps actually talk to each other We're talking automated leadle routing for your sales teams, seamless AI integration, and an intuitive point and click website builder It's everything your business needs to scale, saving you time, headaches, and money So stop piecing your software together Go to odoo. com That's o doo. com to learn more Now that I live somewhere with real seasons, there's a difference between the winter wardrobe and the summer wardrobe When summer arrives, I'm looking for clothes that are lighter and more breathable, but still put together That's why I keep coming back to Quince They focus on high quality essentials that feel and look amazing like breathable linen and soft organic cot They're well made basics but without the luxury markupps. Quinces has European linen pants and shirts that look as good as they feel. Their tees are soft and easy to wear, and their lightweight cotton sweaters are perfect for cooler summer nights And the whole range is perfectly affordable. Quince's clothes are priced fiftycent to eighty percent less than what you'd find at similar brands That's because Quinince works directly with ethical factories and cuts out the middlemen So you're getting premium materials without the markup I have a blue, long sleeved quins linen shirt that is one of the first things I reach for in the closet. It's effortless and goes with everything So elevate your summer wardrobe by going to quince dot com slash minindscape for free shipping on your order and three hundred and sixty five day returns. Now available in Canada too That's QuincE d. com slash minindscape for free shipping and three hundred and sixty five day returns. Qince d. com slash Mindscape And so that was puzzling. And there's this somewhat of a myth that says that Einstein was just philosophically devoted to the idea of a static universe. As far as I can tell, that's not true is closer to the truth. though again, I'm not a historian here Is it Einstein asked his astronomer friends? He said, Wait, is the universe expanding? and no one told me? And they said, No, no, no, it seems to be constant. seems to be more or less static as far as we can tell Again, they didn't know there were other galaxies. They were just looking at stars within our galaxy So Einstein was said, you know, he said I'm going to listen to the data. and he went back and said, can I findind a different solution to the equations where the universe is not expanding or contracting. And To do it, he changed his equation. He added a new term to Einstein's equation for atial the spaceetime geometry in general relativity days you might go like, well, that was a little bit of a panic move there, Professor Einstein. like you didn't stick by your guns. you went and changed your equation right away But you had to realize, you know, it was Einstein who invented the equation, right? Like it wasn't sacred to him. It hadn't been tested and put through decades of hoops that it all successfully passed He had written it down, he can write down a new one. you know, why not? It was a very adventurous time in theoretical physics in that sense So he added a new term to the equation. and, he didn't do it just willilly nilly. He said, Well, what am I allowed to add to this equation There's of course, famously the metric tensor in general relativity. If you want to know more details about some of this general relativity stuff Pick up my book. The biggest idea is in the universe volume one, spaceime in Motion, where we explain what all these things mean And he realized that he could just add a term that was proportional to the metric tensor. The metric tensor is what tells you distances and times in the spacetime geometry that you have in general relativity absolutely nothing wrong with adding such a term It's one hundred percent compatible with the principles of relativity, with the symmetries, with all the language that he had, the notation, etcetera. So it's fine. You can just add it And there is a constant. there's a new constant of nature which Einstein called the cosmological term, or we would call the cosmological constant So he added to his equation And very roughly speaking, very informally, there's the effect of the cosmologial constant. if this number, the cosmontial constant is positive resists the tendency of matter to pull the universe together. It sort of pushes the universe apart So by cleverly choosing the value of the cosmological constant, Einstein could find a solution to his equations Where space was a three dimensional sphere, matter was uniformly distributed, and there was a positive cosmologrical constant that kind of resisted the gravitational field of the matter to give you a static universe over time. And indeed, this solution, which is perfectly good, exact solution to Einstein's equations, is now known as the Einstein static universe Now, almost right away, people realized this was not a good idea Um For one thing, people talk about it as if The Einstein static universe is unstable That's a little bit not quite accurate. I mean, I get it. I know what they mean. It means something real See, what you're doing is you're balancing the density of matter versus the amount of the cosmological constant. and you have to balance it exactly If there was a slight mismatch between the proper value of the matter versus cosmologrical constant, the universe could be almost static for a long time, but ultimately you begin to expand or contract That's not quite an instability, but that's just pointing out that any deviation from this very, very precise number, which had no good reason to be true, would lead you to a non static universe. There's a better objection, which I don't know whether anyone raised at the time, which is the universe is not perfectly smooth, right As I said, Einstein knew that the density of matter on Earth is different than in the sun or in interstellar space And so at best, this assumption that the mattertered density of the universe is constant is an approximation Right It can't be exactly right. There are inhomogeneities in the universe And those in homogeneities will generally grow with time if you solve the equations Over dense regions, regions in which there's a little bit more matter than average will pull more matter onto them And that is an instability. Denser regions go more dense, less dense regions go less dense, and the universe becomes lumpier and lumpier over time The only reason that's a problem. I mean, we think that's exactly what does happen. in the real world, that's the origin of structure in the universe But in the modern world, we know that that has only been going on for a finite period of time because there was a big bang about fourteen billion years ago Einstein rememember was proposing a solution which had supp was supposed to last for infinity years. There was no bigig bang in his model So why hasn't all the structure already formed? Why isn't the universe sort of arbitrarily in homogeneous was a question for him that he wouldn't have been able to answer So anyway, those sort of puzzles became a little bit less pressing. T years later or twelve years later,, ten years later, actually, I think, when Edwin Hubble and others put forward the data that said that the universe is not static after all. I mean, Hubble actually did two things. First he showed that these little fuzzy nebulae that people were taking pictures of in their telescopes are in fact, whole separate galaxies. They're very, very far away Then he compared the distances of those galaxies to their redsifts and showed that the universe is expanding He was very cautious about interpreting these data in the light of general relativity. He was an observer at heart, not a theorist So he just said, I have a relationship between Redshift and distance. And of course, all the theorists like Einstein, but also people like Lemetra and Deidter and others, instantly knew that what he was seeing was the expansion of space So there's some controversy in the historical literature about whether Einstein said that this was the greatest blunder of his life to have invented the cosmological constant rather than just saying that his theory predicted that the universe should be expanding or contracting. He could have predicted expansion of the universe, then he could have become famous, who knows But we don't know. that was a story that was apparently told by George Gamov who liked telling stories. I think it might very well be true. Einstein certainly did say that he should get rid of the cosmological constant. once he realized the universe was expanding, you don't need it. The whole point of it was to make the universe static And with the universees expanding, you can do that without any cosmological constant there The problem with that move, the problem with saying you know, I don't need it anymore is Who cares whether you think you need it anymore? It's there as an open possibility, right? Like I said, it was a perfectly legitimate addition to the equations. So the scientific thing to do is not to say, I don't need it, I'm going to set it aside But to say, is it there? ask the question, what would the effects of this weird thing be? How would we know it? Can we put, you know either Observational limits on it or could we even detect it or something like that U And since really ever since then, ever since Einstein suggested it There was a sort of a cycle of phases of people suggesting that the cosmologial constant could help with this particular problem that we have in observational cosmology and then realizing, oh, we don't need it and we go away. So it waxed and waned. quite a bit Okay So that was the situation. And honestly, you know, cosmology was not at that time, nineteen twenties, even in thirties, forties, fifties, maybe sixties. Not the most respectable part of physics. The ratio of theory to data was quite large, and so it was hard to make progress, just as it's hard to make progress right now in all sorts of questions in fundamental physics And so people moved on to other things. The really good physicists were thinking about quantum mechanics and particle physics and things like that And so let's talk about that. Let's talk about quantum mechanics and particle physics and things like that. It was very quickly realized, well, I shouldn't say very quickly pretty quickly realized by people like Lem Metre, Geores Lem Metre, a famous cosmologist and really the pioneer of the idea of the Big Bang theory U By the nineteen thirties, L Metra had thought about the cosmological constant and he had realized that You don't need to think of the cosmological constant as a change in Einstein's equation. You can just include it in terms of the original equation that Einstein wrote down back in nineteen fifteen And this is a point that I think is really perfectly transparent, but people sometimes fumble it. so it's worth getting exactly right here When Einein wrote down his equation in nineteen fifteen, There's a left hand side and a right hand side, okay? The left hand side are some symbols. I'll tell you what the symbols are. It's R munu minus one half R G munu. okay? These are symbols that are constructed from the metric tensor and the rememon tensor and they all have to do with curvature of space time And then there's the right hand side to Einstein's equation, where you see eight pi G T youu And eight and pi and G are all constants of nature. There's also like a one over C to the fourth or something like that, but I don't ever remember where the speed of light goes because it's set equal to one in my brain. So to me it's just eight by G G is Newton's constant of gravity goes back to Isaac Newton and his famous inverse square law, eight in Pre numbers that you are familiar with team you knew is the energy ensor, the stress energy tensor or the energy momentum tensor, different people call it different things. It doesn't matter. It basically sums up and includes all the different forms of energy and momentum and stress and strain and all those things, pressure and density that could be Pausing space timee to curve. Okaykay? So the right hand side says that there's matter and stuff. The left hand side says their spacetime curvature and the equation sets them proportional to each other So when Einstein first invented the cosmetrical constant Put it on the left hand side. grouped it in with the curvature of spaceetime terms. He wrote Lambda times little G muu where little G Muu is the metric tensor. What Lemetra realizes is you can just do math That is to say you can subtract. You can move lambda GUu from the left hand side to the right hand side of the equation, make it minus lambda GU and then just identify that as a new form of energy. Indeed, it is the form of energy that would exist even in empty space So the metr says you can think of the cosmological constant as the amount of energy in the vacuum, AKA, the vacuum energy And he talked about the different properties of this vacuum energy. It's constant. it never changes by hypothesis There is a pressure that is associated with the energy density. Really there's two numbers in cosmology that you need when you have some new source of energy momentum, you need the energy density and you need the pressure And for the vacuum energy, Lem Metro pointed out that the pressure was negative That is to say it's more like a tension. The classic example is if you have a rubber band and you pull it, Right? The rubber band pulls back on you. That is a negative pressure. pressure pushes, negative pressure pulls you back, okay And so That was fine, you know, Lemetra realized that you don't need to think of the cosmologrical constant as a change in Einstein's equation, you can think of it or identify it with the energy density of empty space And what I want to emphasize is there literally isn't any difference between those two ideas It's not some people still insist that it is, but they're just wrong. It's not as if either you're changing the geometry side of Einstein's equation or you're adding vacuum energy. There's no difference between those two things. They're literally exactly the same. But from that perspective, it's once again making the Cosmarthial constant term even more inevitable sounding, right? Like, okay, now there is a number There's a constant of nature, the energy density of empty space. and you got to go measure it. I mean, maybe you can set it to zero for convenience as a simplifying assumption to start. But it is in principle something you should go out and constrain by taking data Now, the other thing I want to mention, this is sort of jumping ahead to more modern times a little bit, but this negative tension thing, sorry, negative pressure thing, which is tension leads to some weird explanations for why the cosmosical constant makes the universe accelerate So you will hear things that sound something like the following Ordinary matter or radiation or things like that have positive energy density positive pressure. So they make the universe decelerate. They basically pull things together. If you imagine a universe full of galaxies and it's expanding, all of those galaxies are pulling on all the other galaxies. so the expansion rate would naturally want to slow down And this particular way of saying things, which I don't like, so don't trust me on this. says, but now the vacuum energy has a negative pressure And therefore it pushes things apart And you're like wait a min Where did that therefore come from? After all, you just told me that the idea of negative pressure is tension, which pulls things together, doesn't push things apart And then you're told, aha But what I mean is the gravitational effect of negative pressure is to pull things is to push things apart because The expansion of the universe responds not to just the energy density, but the energy density plus three times the pressure Which is true, and that number three, three times the pressure is the number of dimensions of space. Okaykay? So it's not arbitrarily chosen. It's because space is three dimensional, that it's three times the pressure So rho plus three p, where rho is the energy density, p is the pressure, that's the number that comes into the acceleration equation in general relativity for the acceleration of the universe. The problem with that explanation, I mean, it's perfectly true, mathematically, Ro plus three p is negative if you have a cosmodologial constant because for the cosmologial constant, T equals minus ro pressure is precisely minus the energy density. And therefore rad plus three p is minus two row So if you have a positive energy density in the vacuum, you have a negative amount of energy density plus three times the pressure. And that's what pushes the universe apart. The problem with that as an explanation Is that Where do I get any intuition for the claim that rhow plus three p is appearing on the right hand side of my equation? It's just magic, right? unless you've actually gone through the math. You're not actually explaining anyone anything to anybody. So I don't like that explanation There's another way of explaining it, which is the following. the equation that cosmologists actually solve for the expansion rate of the universe. And this is all done post Einstein. Like Einstein had the idea that The universe could be a three dimensional sphere, but then other people like Robertson and Walker And then followed by Friedman and Lem Metre and others, really generalized that idea to all sorts of different possibilities. And they got a very general equation, now known as the Friedman equation And the Friedmann equation in factors several Friedmann equations but the one that everyone solves sets the expansion rate of the universe, which is given by the Hubble parameter, right We now call the Hubble parameter because Hubble measured it in Hubble's plot of velocity times distance, velocity versus distance, his equation says that they're proportional Velvelocity is a constant times distance for a distant galaxy, and that constant is known as the Hubble parameter And so that same constant appears in the cosmological version of Einstein's equation in the Friedman equation And it's a way of judging how fast the universe is expanding So the Friedman equation says that the Hubble constant squared proportional to the energy densityity of the universe. Maybe if you also have a term for the curvature of space, if you want to include that, Th days we know that the curvature of space is close to zero, so we don't need to keep talking about that for today's purposes. So anyway H squared, H is the hubble constant. We square it, it is proportional to the energy density. That's it, That's the equation. okay? There's no appearance of pressure in there. and you say, well, How do I get the difference between accelerating and decelerating universe out of that equation And the answer is how the energy density changes with time matters So imagine a universe that has nothing but vacuum energy in it, nothing but cosmontrical constant, okay No matter to worry about makes our lives easy. That says that rho, the energy density is just a constant That says that h is a constant because h squared is proportional to ro. H is proportional to the square root of ro, and if rho is a constant, so is the square root of rho So what the equation is telling you is just h is a constant. the expansion rate of the universe is a constant. and you might Now get confused for a different reason. You might say, wait a minute. You were telling me that this means the universe is accelerating And now you're telling me it means the expansion rate is a constant. That doesn't sound like accelerating to me And that's because you haven't grown up with non nucleide in geometry. Sorry about that. You're thinking of expansion rate is somehow a velocity but it's clearly not In an expanding universe, if you look at a galaxy, using Hubble's law, a galaxy a billion light years away is moving apart an apparent velocity of some number Whereas a galaxy twice that far away is moving away twice as fast different velocities for different galaxies. so the expansion rate of the universe cannot possibly be thought of as a velocity Okay. What it is is a rate of expansion Basically the answer to the question Ely does the universe double in size, right? In fact, the Hubble time, which is one over the Hubble constant is almost exactly that. doubling time for the universe And so to say that H is a constant, which is what you get for vacuum energy, says that the A amount of time in which the universe doubles in size is a constant So in other words, from any one size of the universe, it can double in size and then double again and then double again and double again. So it goes from its initial size to twice that to four times that to eight times that to sixteen times that and so on That is what we call exponential expansion because you keep multiplying by two at every time step They told two friends and they told two friends, etcetera So a constant energy density leads to a constant expansion rate which shows up as an exponential expansion to the universe, which is obviously accelerating So that chain of logic is longer than the negative pressure business, but it actually makes sense unlike the negative pressure business. The negative pressure business is, like I said, it's not wrong. It's completely true. It's just sort of making it sound easier than it really is Okay, sorry, I gott to get off my chest because I'm trying to all the mistakes that I hear out there in the world. There's probably too many mistakes out there for me to fix all of them, but I can do my little part Okay, so that's the state of play in the nineteen thirties. Einstein had come up with his equations He had come up with the idea of a cosmological constant. Lemetra interpreted the cosmological constant as an energy density of the vacuum. But Lemetra wasn't doing quantum mechanics. This is all still perfectly classical, okay makeake sure that we distinguish different ideas in our head. So the metro is just pointing out that this number Einstein had invented could be interpreted as what is the energy density in empty space? If I take a cubic centimeter of space And I remove all the stuff. so there's no There's no radiation, There' no dark matter, as we would now say,' just truly empty You can ask yourself how much energy is in that empty cubic centimeter of space. and according to Einstein and Lemetra That's a new constant of nature. That's not something you can just say, oh, it should be zero because it's empty, right? It's something you have to go out there and measure Everyone talks about summer like it's supposed to be care free If this season brings up money stress, body stress, family stress, or social stress, that's real too therapy can help with that Whether it's your first time in therapy or your fiftieth, GroO makes it easier to find a therapist who fits you, not the other way around. They connect you with thousands of independent licensed therapists across the US, offering both virtual and in person visits nights and weekends. You can search by what matters, like insurance, specialty, identity, or availability and get started in as little as two days. And if something comes up, you can cancel up to twenty four hours in advance at no cost There are no subscriptions, no long term commitments. You just pay per session Rro helps you find therapy on your time Whatever challenges you're facing, growth therapy is here to help Gro accepts over one hundred insurance plans, including Medicaid in some states. Sessions average about twenty one dollars with insurance, and some pay as little as zero dollars depending on their plan Visit growthraapy. com slash book now to get started growththerraapy. com slash book now. growrthraapy. com slash book now Availability and coverage by state and inssurance Pl Hey everyone, it's Cal Penn. I'm the host of EarsSay Audible and IHart Audioobook Cub. This week on the podcast, I amm sitting down with Ray Porter, the narrator of Andy Weir's audiobobook project Hail Mary, Massive sci fi adventure about survival and science. And what happens when you wake up alone very far from Eth? I really had to make the decision because I caught myself getting that frog in my throat and starting to get teary as I'm narrating some of these sections and it's like, okay, yo, yeo, yo is this indulgent? And I really thought about it. I was like, No, at this point, it would kind of be betraying the trust the author and the listener have in telling this story if I don't Go through it. There's places in this book that deeply emotionally affected me And I left it on the mic. That's great 'cause it served the story. People will say like, oh my Godd, I cried at the end. It's like, yeah, dude me too. Listen to EarsSay, the Audible and I Heart Audioobook Cub the IrHart Radio app or wherever you get your podcasts Now at the era, the nineteen thirties and so forth, like I said, a lot of the excitement in physics was in quantum mechanics, particle physics, things like that. People knew and loved general relativity, but they didn't think about it too much. front end center in the minds of leading theoretical physicists. People did know about it. Wolfgang Pauli wrote a whole textbook on general relativity when he was preposterously young It wasn't what they were thinking about on a day to day circumstances, they were thinking about quantum field theory and quantum mechanics. And guess what The idea of vacuum energy rears its head in a different way in quantum field theory And this is again something that people get wrong a little bit. So let me try to explain it the best I can Forget for the moment about quantum buildield theory. We'll get back to that. Think about the simplest physical system we can think of the simple harmonic oscillator, okay? So literally A weight on a spring attached to a wall bouncing back and forth, simple harmonic motion In physics, we describe this in terms of a potential energy as a function of x. if x is the location of the weight on the spring The potential energy looks like omega squared, x squared Omega is the frequency, literally the frequency of the thing bouncing back and forth And so This is a very, very simple physical system with an omega squared X squared type of potential energy and ordinary kinetic energy. It's simple because it's simple to write down, but you can solve it and it's kind of beautiful and it illustrates a lot of very basic ideas And so if you take a quantum mechanics class, like I was teaching here at Johns Hopkins last semester One of the very first things you will do and one of the things you'll keep doing at higher and higher levels of sophistication throughout your physics career is study the simple harmonic oscillator So in classical physics, what that means to study the simple harmonic oscillator is, you have a ball and it's rolling in this hill and the hill looks like a parabola, omega squared x squared. And you say, well, if I let the ball go, withs zero velocity at a certain point on the hill, can I solve its equations of motion going backward and forward? And the answer is yes And they look like sines and cosines, sinusoidal functions for the oscillation of the particle back and forth in this potential Of course, it would be very natural to do the quantum mechanical version of this What does that mean? That means you don't have a little ball moving into a potential. That means you have the Schrodinger equation, which means you have a wave function in that potential And you're going tol the Schortdinger equation in that kind of potential and see what you get And it's very, very instructive to do that. What you get by solving the Schrodinger equation in the simple harmonic oscillator potential is a series of states with constant energy You can have any energy you want But if you want a definite energy, remember in quantum mechanics, when you measure something You're not sure what answer you're going to get generically If you measure the position of a particle, there could be some uncertainty there. If you measure the energy, there could be some uncertainty there. But there's a special set of quantum states where the energy is perfectly well defined and known eigen states of energy And for the harmonic oscillator, these eigenstates are exactly exactly equally spaced in energy. So there's a lowest energy state And there's a state that has one more energy, wherey one, I mean H bar times omega Remember omega is the frequency of the harmonic oscillator. H bar is Plck's constant So H bar omega is the size of the energy step from the lowest energy state to the next energy state Also the size of the energy step from the first energy state to the second and from the second to the third, etcetera There are exactly equally separated energy amounts between the different levels, as we say, or different excited states of the simple harmonic oscillator, okay? So that's just one of the things that makes it a very, very nice system. Other kinds of systems with other kinds of potentials will also have different kinds of energy states, but they won't be equally spaced in energy between them So all that's very well known. you'll study that to death in your quantum mechanics class. But there's one thing that is kind of mysterious and it's going to depend on your professor's inclination, how much you're going to think about it, which is that the lowest energy state, if you start with ordinary simple harmonic oscillator with a potential Omega squared squared by the way it's usually one half omegaquared sared but don't worry about the hf So make a squared dex. Um What is the lowest energy state? Well, classically That's the particles just sitting there x equals zero So of zero potential energy and also zero kinetic energy. It's not moving. It's the lowest energy state to zero energy. That's how we're trarained to think when we grow up Quantum mechanically Solve Schortneiger's equation, that turns out not to be right The lowest energy state of the simple harmonic oscillator doesn't have zero energy quantum mechanically if it did classically There is a difference between the classical lowest energy and the quantum mechanical lowest energy, and that difference is one half H bar omega H borr omega is the gap between one energy state and the other. One half H borar omega is the starting point So the lowest energy state is one half H bar omega. The next one is three halves H bar omega, and then five halves h bar omega, et cetera. infinitely far into the higher energy states This phenomenon that the quantum mechanical energy of the ground state of the lowest energy state is one half H b omega is called the zero point energy of the harmonic oscillator And so like I said, it's going to depend on The predispositions of your professor, how much you're going to fret upon about that I think that the answer is you shouldn't fret too much. And the reason why is the Num, one half H bar omega is not to be interpreted as the ground state energy of the simple harmonic oscillator What it's to be interpreted as is the difference between the ground state energy of a classical harmonic oscillator and a quantum mechanical one Okay. So quantum mechanics raises the ground state energy by one half H bar omega, but it doesn't tell you what it was to begin with could have imagined starting with a simple harmonic oscillator whose potential was not onene half o meega squared X squared. but rather one half omega squared X squared minus one half h bar omega. Nothing can stop me from doing that And classically, if all you're doing is studying the rocking of a Ball in a hill or something like that Adding a constant to the overall energy makes no difference whatsoever It does not show up in any of the motions of the particle. It has no effect on the physics. It's completely irrelevant. All that matters is how the energy changes from point to point So two things. One is actctual zero point energy is completely arbitrary I can set it to be whatever I want. It's not one half H borrowing, it's whatever I choose it to be And number two, the number one half a square omega isn't even anything intrinsic to nature It's a difference between a quantum mechanical theory and a classical theory But nature is just quantum mechanical. Nature doesn't know about the classical theory. Nature says you're quantum mechanical from the start Why were you starting with a classical theory and then quantizing it? You should have just started with a quantum mechanical theory. and in that case The relevant fact is that the energies of different energy states are separated by H Bar Omega, okay Nevertheless. People kind of get hung up about this a little bit. They start thinking that, you know, Quantum mechanics tells you that there is energy density in the vacuum. Don't get me wrong, there could be Right? That's what I'm trying to say. It's a constant of nature. It's a fact about reality what is the zero point energy of the simple harmonic oscillator? It's not a fact about your quantum mechanical calculations, you can choose the vacuum energy to be whatever you want Okay So Why do we care? aboutb that? Why do we care about the simple harmonic oscillator? You know it's a very nice thing to be able to solve things precisely, but we want to get into the messy real world with electrons and protons and stuff like that So we have to upgrade our game a little bit and start thinking about quantum field theory t point, I will encourage you to read volume two of the biggest ideas in the universe quuant and fields where we talk about precisely quantum field theory. If you want to know what that means, it just means that there are fields stretch throughout all space and time and they vibrate and you quantize them. and that's what gives rise to particles and things like that. So since the nineteen thirties, at least getting into high gear the nineteen fifties, Quantum field theory has been our best attempt at understanding The world at a deep level, at least particle physics and the world other than gravity. Gravity is a special thing, but okay, that's a more difficult topic to get into, not something we understand very well Okay, so quantum field theory sounds like a very large journey away from the simple harmonic oscillator But here's the wonderful news When you start studying Cantumfield theory Just like in other areas of physics, you're going to start simple and you're going to work your way up So what does it mean to start simple? It means to start with a field that is just doing its own thing. a field that is not interacting with other fields, not even interacting with itself. And those are all very well defined statements and you can specify what they mean. So we talk about a free Field. be one that is not interacting with other fields or itself Okay That's one step. Let's think about free field theory, no interactions, just make our lives easy. Then we'll put in the interactions later It's ancient move. It goes back to Galileo, saying, let's ignore air resistance. we can put it back in later, right? We're saying, let's ignore interactions between fields, we can put them back in later. The second move, which is something that is less ancient, but is absolutely always what you do when you study fields is you start thinking about waves and that means you start thinking about waves of definite wavelength, what we call modes of the field. And again, I'm not going to get into details if you haven't read the book. If you have read the book, this is all perfectly transparent But you can think about what is happening in a vibrating quantum field rather than thinking about what's happening at each point in space You can think about what's happening at each wavelength. And this is not a weird thing. This is called Fourier analysis. and it's literally what your ears do when you hear sounds, you hear different pitches because your ears are saying, well, how much vibration is there at this frequency and how much is there at that frequency and so forth So let's do that rather than focusing on the behavior of the quantum field at one point. let's focus on the behavior of a single mode with a fixed wavelength everywhere. of this quantum field, okay Guess what happens, miraculously Each mode of a free quantum field obeys an equation which is exactly the same as the equation of a simple harmonic oscillator That's why we're doing all this. That's why I was wasting my time telling you about the simple harmonic oscillator because Three non interacting quantum fields very naturally behave like a collection of an infinite number of simple harmonic oscillators. Not one at every point in space, but one at every wavelength. indndeed, one at every wave vector, we say, because a wgth a mode of the field has both a wavelength but also a direction in space. That's the way vector. So every way vector is a mode and every mode acts like a sy harmonic oscillator for a free field theory And that means everyvery mode of the harmonic oscillle of the quantum field has the same kind of zero point energy contribution that the regular harmonic oscillator has And everything that we just said about the quantum mechanical harmonic oscillator really is still true in quantum field theory. That is to say it's both true that if you start with zero energy in the classical theory and then you quantize it You get a new addition to the energy of the vacuum, which is one half H bar omega, now there's every value of omega. okay? So you don't just because there's different wavelength modes of the field, they're all have their own vibrations And what that means is that you don't just have energy density in empty space of one half H bar omega. You have the sum or the integral if you like all possible omegas of one half H bar omega And what does that equal that equals infinity So This is one of the famous infinities of quantum buildield theory. This is perhaps the most basic. infinity of quantum field theory, the energy of empty space, the vacuum energy is infinity You're very, very naive about quantum field theory But before you get too excited about that Everything I said about the quantum mechanical oscillator is still true. I could choose the vacuum energy to be whatever I want. It doesn't need to be infinity. I can just choose it to be zero. okay U This is one of the steps in what we call the renormalization of the quantum field theory It's perfectly legitimate No one forced me to have a certain value of the vacumentergy to begin with, okay So the lesson is not that there's an infinite amount of energy in empty space in quantum field theory, the lesson is that there's an arbitrary amount of energy in empty space in quantum field theory. And guess what? That's just the lesson of The vacuum energy that La Metra had talked about, there's a new constant of nature, the vacuum energy and we have to go measure it, okay So Like it's a very delicate back and forth kind of thing Quantum field theory says, Okay, there can be vacuum energy in empty space. It does not say what it has to be. But there's another level that says, well, maybe it lets you have a guess as to what it could be Maybe it lets you sort of estimate a natural value. L there's nothing natural about zero. You could set it to zero. You' say, I'm just going to say there's ero energy in the vacuum. You're allowed to do that There's no reason to do that from the point of view of quantum field theory. It's some number And you can wave your hands and you can say like, okay, I have sort of natural guesses for how big that number should be So the first person to go down this road was Jakov Zeldovich, who was a physicist, a Russian physicist. And in the nineteen sixties, he made this point very clear that the vacuum energy of quantum field theory is precisely what goes into the vacuum energy of relativity, the cosmological constant. And this is the beginning of the connections between quantum field theory and the vacuum energy There were some precursors there. I shouldn't jump right ahead to Zeldovich. if there's again, it's a fascinating story because peoplee don't know what's going on. so they like they cling to certain beliefs and they get rid of others and you they learn something, but don't put it in the right context and all this stuff Um You know, Richard Fynman, of course, became famous for Feynman diagrams in quantum field theory and Feyman diagrams are little pictures of particles moving But they're one hundred percent derived from quantum field theory, okay? They're not derived from thinking about particles, The particles come out of quantum field theory as predictions once you quantize these fields But these ideas don't come out of a vacuum, if you'll excuse the pun. And Feynman had this previous idea with John Wheeler, who was his advisor at Princeton, the Wheeler Feynman Asorber Theory of radiation. You may have heard of this This is of the package of ideas where Wheeler came up with the idea that maybe positrons, which are anti particles of electrons, are just electrons moving backward in time. and therefore there's only one electron anywhere that sort of moves forward and backward in time and goes through the whole universe People love this idea. It's not right It was a good guess. It was a fun idea. But these days, we know, no, that's not right. What's actually right is quantum field theory. The reason why all electrons are the same It's not because they're the same electrons, because they're all vibrations in the same underlying quantum field. Hey everyone, it's Cal Penn. I'm the host of EarsSay The Audible and IHart Audioobook Club. This week on the podcast, I amm sitting down with Ray Porter, the narrator of Andy Weir's audiobook project Hail Mary, Massive sci fi adventure about survival and science. And what happens when you wake up alone very far from Eth? I really had to make the decision because I caught myself getting that frog in my throat and starting to get teary As I'm narrating some of these sections and it's like, okay, yo, yeo, yo is this indulgent? And I really thought about it. I was like, No, at this point, it would kind of be betraying the trust the author and the listener have in telling this story if I don't Go through it. There's places in this book that that deeply emotionally affected me And I left it on the mic. That's great 'cause it served the story. People will say like, oh my Godd, I cried at the end. It's like, yeah, dude me too. Listen to EarsSay, the Audible and I heart audioobook club On the ArHartt Radio apppp or wherever youre getting your podcasts. Beachbum's June Jackpot is dealing out winners all week long. sccore seven dollarars Sn or sppray tans, seven dollars Red lightight or sauna, seven dollar lotions, and more. Feeling lucky? G buy one, get one seventy percent off packages. No gamble, just glow. The odds are in your favor, and these seven dollar deals are your ticket to a golden summer. Beachbum's June jackpot sale is live through june seventh. Don't miss it at Beachbum Tanning. Your glow up starts now. Head to beachbum dot com and stay tan and tasty all summer long But okay, they didn't know that. They weren't sure. they were trying new things. That's what physicists do. And so Wheeler and Fenman, and their absorber theory really tried to think of electrons as particles, not as fields, even though quantum field theory already existed at the time, they were open to changing that. And one of the things in the back of their minds was they knew about this vacuum energy. business. They didn't know was the cosmological constant. They didn't know as far as I know They didn't know it had anything to do with gravity or anything like that, but they were just kind of worried about the fact that when you quantize theory, you get an infinite contribution to the energy again, I think that a more correct attitude is to say Infinity is not the energy It's the difference in energy between the classical theory and the quantum theory, and it's the quantum theory that is right So who cares about the classical theory? but still they were a little bit worried And so they thought if they could replace quantum field theory with a theory of particles, that would make this vacuum energy problem go away. It didn't work know that was part of their motivation. and eventually led to Fyman diagrams, which is pretty good. The other example is Phil Anderson, Phil Anderson, a Nobel Prize winning condensed matter physicist who arguably was the first person to really propose what we now call the Higgs mechanism The Higgs mechanism says if you have some scalar fields, you have some field with no directionality in space or anything like that.s just a number at every point in space. And imagine that it couples in a certain way to other fields, like electrons and photons and stuff And this field that is now called the Higgs field, which Anderson thinks it should have been called the Anderson field Imagine that this field gets a non zero value in empty space. So what your imagine is that this field, the scalar field, which we now call the Higgs field has some potential energy function. which says how much energy is in the field simply as a virtue of its value As opposed to fields have kinetic energy if they're changing in time and they have gradient energy if they're changing in space The potential energy is just how much energy they have because they have a value So if the minimum energy is not at zero field value, which is no reason why it should be, this is the famous Mexican hat potential. Then the field will roll down to the minimum, which is not at zero, and it will sit there and it will affect other fields. And Anderson knew this and he sort of mentions it in words in one of his papers, but he didn't pursue the idea. That's why he doesn't really get credit. He doesn't get his name on it for the Higgs mechanism Why didn't he pursue the idea? Part of it was because he was really a coens matter physicist, not a particle physicist. That's where his interests lay Um but also because I think, this is my impression, he knew that there would be a tremendous energy density. associated with that field, changing its value in empty space. So you're proposing that there's a field pervading the universe that carries an enormous amount of energy And no one has ever noticed it before I'm not sure that he ever again, connected it to gravity or the cosmodial constant, but it bugged him So he moved on to do other things. That's okay. He won the Nobel Prize for other things Anyway, this all of which is to say like by the nineteen sixties and Zeldavit, people had put the story together If you just care about the zero point energy of the quantum field, it doesn't matter. You can make it whatever you want. It's a constant of nature. And if all you're doing is particle physics, it's not even an observable constant of nature. It's just like the ball rolling back and forth in the quadratic potential and the parabolic potential, the harmonic oscillator. If I lift the potential up and down by adding a number to it, it doesn't change the behavior of the particle Likewise, if I just change the energy density of empty space, it doesn't change particle physics in any way does change his gravity Gravity cares about the total amount of energy in the universe and Zeldevicich appreciated that. So he pointed out, you know what? we have a problem becausecause there is a number, the energy density of empty space. We have no idea what it is. We have no idea what it should be, I should say. But you can sort of wave your hands about natural energy scales, blah bl, blah, and Zeldovich points out the natural scale for this number is much bigger than it can possibly be given the observations we're talking about an enormous discrepancy. So let's like skip ahead to the modern way of thinking about these things Um, The modern way of thinking about these things actually puts some meat on the bones of all this talk about natural values and stuff like that And that framework that we're talking about here is effective field theory. In the effective field theory framework, you admit you don't understand everything You say, look, I don't know the theory of everything. I don't know whether it's string theory or something else. I don't know what's going on. at very, very high energies, which in quantum field theory corresponds to very, very short distances in spaceet timee. say, I don't know what's going on Hily, quantum field theory has this feature that even if you don't know, what's going on at very short distances, you can still find an effective theory that only includes particles and fields and phenomena at low energies and long distances It's called the infrared theory because you think about infrared things as long distances, long wavelengths ultraviolet things as short distances, short wavelengths So following Ken Wilson and others, you say, I have an ultraviolet cutoff. basically the shortest distance that I'm claiming to understand I don't know what goes on at even shorter distances But I'm going to bundle all those effects up. and ask what they do in my infrared theory Okay And then there's some rules for how big you expect parameters in the infrared theory to be etcetera, etcera And basically, some parameters in the infrared theory are what's called relevant They get more and more important as you go to longer distances and more in the infrared Some are irrelevant. They're not that important And the cosmosologial constant, the vacuum energy, is super duper relevant very much shows up. in the infrared. And you can use these techniques of effective field theory to say, okay How big do we expect the cosmological constant to be And the answer is hilariously bigger. than it can be. and I say this even knowing that the nineteen sixties, you know our cosmological observations were not nearly as precise as they are today They didn't need to be. The difference, the discrepancy between the effective field theory prediction for the vacuum energy, And what you actually observe it to be is just so hilariously large that you don't need very precise observations The most dramatic way of saying it is if You run your effective field theory you put your ultra rather cut offff all the way up at the Pank scale And you compare it to our limitations, let's say in the nineteen eighties before we actually found the vacuum energy how much bigger is the predicted vacuum energy then the limit The answer is the famous factor of ten to one hundred and twenty two times bigger One followed by one hundred and twenty two zeros, okay? So not the number, one hundred and twenty two. That would be easy. We could deal with that One followed by one hundred and twenty two zeros. That's ten of the one hundred and twenty two. It's a very, very big Discrepancy, okay Um, that discrepancy is known as the cosmological constant Problem And again, as I keep emphasizing, you're one hundred percent allowed to solve the cosmological constant problem in the following way Just say that's the way it is But the Cuse Marsal constant In the infrared, the measurable quantity is something we measure Okay. I mean, maybe you had an expectation for what it should be. Your expectation was wrong, Tough cookies You know U and that's an attitude that you can have and you can get away with it it's completely compatible with the data. Maybe that's just how things are. Sometimes physics is like that I think a lot of theoretical physicists are going to want to say Maybe that's true Maybe it's not. But maybe this huge discrepancy between our expected value for the vacuum energy in effective field theory and the observed value is a clue to some new physics that we don't yet understand. So even though it's intellectually allowed for you to say the cosmologrial constant just is what it is. I measure it that I got all with my life Maybe you're missing an important clue that nature is trying to give you to develop a better theory. I think that's what a lot of physicists these days would think So came about in the nineteen sixties and by the nineteen eighties, once we'd put the standard model of particle physics Please peopleople began turning their attention to gravity and cosmology, okay? The nineteen eighties were when the first supersting revolution happened And it also was the time when people really began thinking about the cosmetologrical constant problem, very hard. becausecause they'd solve all the problems in experimental particle physics, they were moving on to the universe. And so why is the observed vacuum energy? So just to make it super duper clear? If the cosmosule constant or the vacuum energy were anywhere close to its natural value as far as particle physics is concerned The universe would have exploded apart into nothingness in a tiny fraction of a second After the big bang expansion rate of the universe driven by such a vacuum energy would be so big that you couldn't make an atom much less a molecule or a planet or a star or anything like that. So it's not like you have to do some delicate cosmological measurements and maybe you have error bars on those and maybe you're wrong about this The discrepancy is just so big that it's absolutely overwhelmingly obvious Furthermore, you don't even know whether the cosmological constant is positive or negative theoretically, right? You're not making prediction for its sign you're making a prediction for its absolute magnitude, if anything, it's just a guessestimate more than a prediction It could be negative and that would mean it would make the universe recollapse in a tiny, tiny fraction of a second, and that's also ruled out by the data since the universe is around fourteen billion years since the Big Bang. So By the nineteen eighties Theoretical physicists had started thinking seriously about this cosmologrical constant problem And I say this because I entered graduate school in nineteen eighty eight and now from the rest of this podcast, solo podcast, and for the entirety of the next one on dynamical Dark Energy, it's going to be a very Sawn centric view of all these problems, not because not because I am central to the story of dark energy in the accelerating universe, but dark energy in the accelerating universe are central to me because I did a lot of work on it and wrote a lot of papers on it and things like that. So I'm not going to try to give you a completely unbiased view of anything. I'm to tell you what was happening around me when I was thinking about these things because I'm not doing a lot of research for these solo podcasts, sorry about this, but I do have some experience that I can share with you here So there's a bunch of things in the late nineteen eighties, early nineteen nineties, where people were thinking about the cosmologial constant problem And I'm going to mention For ideas, for attitudes, for Let's say strategies you can take. to address the cosmologial constant problem. One of them is a little bit anachronistic. it came along later, but it gives you a feeling for what's going on None of them are very good Okay, none of them are like obvious slam dunks. That's why it's still an interesting problem Um One, that got an enormous amount of attention. is supersymmetry Supersymmetry in the nineteen eighties, especially was incredibly popular. It really just had grown popular in particle physics in the seventies and in the eighties, people were still very excited about grand unification, And also connections of supymmetry with string theory. So it's like the hot topic in theoretical particle physics circles And supersymmetry, unlike other symmetries does have something to say about the cosmologule constant. So what do I mean by that rememember The absolute value of the vacuum energy, as we're talking about for just the harmonic oscillator, it doesn't matter, the absolute value, right? All it matters is how it changes from place to place Except when gravity comes into the game So for the rest of particle physics, for the standard model of particle physics, for the Electric weak force and the strong force and the Higgs mechanism and all that stuff. You can ignore gravity and you'll only need to workry about the cosmological constant Supersymmetry is different because supersymmetry is a mixture of a spacetime symmetry or it's a way of mixing spacetime symmetries with what we call internal symmetries Um Supersymmetry is sort of a unique way of having a nont trivial interaction between spacetime symmetries and things like gauge invariants that you get in the standard model of particle physics So supymmetry because it relates Particles of different spins, right? spin zero and spin one half particles, for example Bin is a spaceetime feature It's a spacetime property of the quantum mechanical field So supymmetry in some very rough sense knows about spaceet timee. If you talk to like supersymmetry experts, they will start telling you things like, The superymmetry transformation is the square root of momentum or something like that. And I'm not sure if that's very enlightening or not, but the point is it is related to spacet timee, supersymmetry, okay? So it's related to both particle physics and to gravity. That's very exciting all by itself And because it's related to spaceet timee, supersymmetry knows something about the vacuum energy, by which I mean In a given theory of supymmetry, the vacuum energy is not arbitrary anymore. In regular old quantum field theory, it's arbitrary. It's of constant nature, the vacuum energy, you're going to measure it or whatever And a superymmetric theory it' determined by what is going on in the rest of the model And people very quickly realized that there were certain versions of supersymmetry where the vacuum energy would be exactly zero You could actually solve the puzzle of why the vacuum energy is small if you had perfect supersymmetry But they also realized you could have negative vacuum energy, which seemed weird, but okay, at the time they didn't bother that with that too much We did though instantly realize a problem with this, which is that supersymmetry is not exact in the real world as we know it If it were There would be an electron with a certain mass in charge, and there would also be a spin zero partner of the electron with the same mass in charge. No such particle exists. This we called the selectron by supersymmetry aicionados It hasn't been found This is not a huge puzzle. This is just because probably supersymmetry is broken. If it exists. Broken symmetries are super easy to have. In particle physics, that's what the Higgs mechanism does That was something that particle physists understood very well. So you have supertersymetry and then you break it. And you could even estimate the energy scale at which it had to be broken and things like that. The problem there is that again, if you break supersymmetry, it does care about the vacuum energy and you generally not only do not get zero for the vacuum energy, but you do get a number that is incompatible with the data So supersymmetry was intriguing for the cosmological constant problem because it seemed to have implications for it But the implications seemed to be bad It seemed to take away your freedom to cuse martial constant whatever you wanted Now, that's not necessarily a sign that you're on the wrong track. mayaybe just haven't filled in all the details yet. And so people put a lot of work into seeing could they come up with a supersymmetric model that explained the small value of the cosmologruical constant? And the answer was No, they haven't been able to do that quite yet. So that was one avenue Another avenue is wormholes and Euclidean quantum gravity. and I mentioned this because This was one of those ideas in physics that it got very popular for a very brief period of time and then it went away And the person who really put it together was Siddney Coleman, who's a professor at Harvard, who was my quantum field theory professor and was on my thesis commommittee. And it was a great guy, a brilliant scientist And usually it's very funny, and Siddney himself was a little bit chagrined about this. Like his style as a theoretical physicist. The reason why he's not as famous, as Stehven Weinberger, Sheldon Glashow, his colleagues at the time was just that he was very cautious. He was doing well established calculations in quantum field theory. He was not speculating about some crazy model And then the one time that he did a little speculating about some crazy model was this cosmartial constant stuff. and it got him a lot of publicity. But it wasn't really well grounded because it was just speculating. ultimately it went away. But I gott to tell you about it because Even though it went away, and even though people don't really think it's the right answer, it it's really brilliant. I mean, it really worked and if it had worked, it didn't really work. If it had worked, it would sort of offer an explanation in the super intellectually satisfying way. which is kind of intriguing. So here is the idea Um People like I said, were beginning to think about gravity as well as particle physics And what is the simplest way to get there? I didn't really plan out this part of the episode that deeply, Maybe I should have planed it out more deeply. but One of the ways you can do quantum gravity, we know that you don't have an exact theory of quantum gravity, right? We don't know all the details, but we know a lot about quantum mechanics, we know a lot about gravity You can make some reasonable statements that you think are telling you something about quantum gravity And that was done by people like Stephen Hawking and Jim Hardle and others And they did it via what is called the path integral. to quantum gravity. So basically The first thing you do and this is already a suspicious step, but You think of spaceet timee, but instead of four dimensional spaceet time, You just think of four dimensional space. This is called doing Euclidean quantum gravity. So four dimensional space, that is to say all the four dimensions are the same. There's not one picked out to be time and three picked out to be space And by a path integral, you say, you calculate the quantum mechanical probability of the universe being in a certain state By adding up all of the different ways you can get there. This is one of Feynmann's ideas, the Path integral formulation of quantum mechanics And so in gravity, since gravity is the theory of four dimensional spaceetime The proposal from Hawking and others was that you could calculate the wave function of the universe byy summing over all of the four dimensional spaces have a boundary that is the universe that you're looking at right now. And it was just a mathematical trick. It wasn't the universe is not really Euclidean. It was just supposed to be a way of calculating the wave function of the universe. So people hadad this idea, all right, let's sum over all the four dimensional geometries and calculate the wavef function of the universe, right? It's a good way to spend your time while you're waiting for the particle accelerators to actually give you useful information And they realized, okay, what's the first thing you do? What's the simplest thing you do Well, you're thinking of how to approximate Integral were a sum over all four dimensional geometries That sounds hard. But let's look at what we're summing up and it's Einstein's equation, right? It's Einstein's expression for what we call the action of general relativity is the number you can attach to every four dimensional geometry. And in well I'm not going to go into all the details, but you want to find a saddle point or an extreme of the action, that's the classical equations of motion And so what they found was the simplest solution is just a big speere, a big four dimensional speere. okay? That's a simple contribution to the path integral of quantum gravity Fine. That's easy. We can do that But then what about like the next simplest thing And some genius, I don't know who it was, but someone said, lookook If I have not one sphere, Tw spheres So they're both very smooth. the idea being that if you wiggle the spear, it gets less and less of a good solution to Einstein's equation and therefore less and less important in the quantum mechanical. calculation This person says if I have two spheres, I could connect them by a tiny wormhole And that tiny wormhole would have almost no contribution to the action because it's this tiny wormhole, right So two spheres are almost as good of a contribution to Euclidee and quantum gravity as one sphere is And then once you say that, well, okay, I have three spears or I could have two spears with two wormholes connecting them, et cetera. So there's an infinite number of things I can add up. and this was exactly the kind of thing that Coleman was really good at So he and others, Steve Gittings, Andandy Strhminger and other people worked on this, Joe Polchinsky They thought about, how they calculate the wave function of the universe as a sum over spheres connected by all these wormholes And people realize that this was a huge problem, actually, because if you have a wormhole connecting two big spears It's not just gravity that gets involved. What if an electron falls down the wormhole What if it goes from one spirere to another, right And this is a lot of I'm going to try to cut this short because we could get out of pay. And likeike I said, it didn't really pay off anyway The point is it would seem that this was worrisome for real world particle physics. It would seem like in the real world, you might be able to have processes where like a photon goes down a wormhole and disappears, and that would be bad Coleman was able to figure out was that in fact, that's not the observable impact of these wormholes In fact, what happens is you can't just have an electron go down the wormole because it would look like charge is disappearing in the universe and that's bad, okay What you could have is an electron and a positron going down the wormole and a photon coming out So that would conserve charge and energy and everything like that And that wormhole therefore looks from far away where you don't know it's a wormhole, it looks just like an ordinary particle physics interaction. So really, Coleman says, the effect of these wormholes is not to swallow up particles and make them disappear. It's to contribute to all of the existing parameters of particle physics like the fine structure constant that tells you how strong the electromagnetic interaction is like the Higgs mas, like all these other things. and like The vacuum energy. Okaykay. So in other words, Coleman says these wormholes add a new contribution to the vacuum energy. So you have whatever classical contribution you have, you have the zero point energy, you have the Higgs field, and now you have the wormhole contribution to the vacuum energy. and what he showed by a calculation was D. The contribution of the wormholes was exactly to cancel out the contribution of everything else It was truly beautiful. It was very, very convincing and provocative when it first appeared. And this is late eighties, about when I arrived in grad school Sadly, the whole thing never lasted because as Coleman himself said very, very clearly, he was not bombastic about it. he says, Look, this is a house doubly built on sand. Okay? because we're talking about euclating quantum gravity and wormholes. These are things we don't understand very well at all And the more and more people looked at it, the less and less sensible and reproducible, it all appeared So it didn't burn out, but it faded away. know the idea that wormholes provided the successful resolution of the cosmologial constant problem. There were enough obstacles to it really working. like some people said, it actually doesn't make the cosmatricconsin small, makes it big. It was very hard to figure these things out because no one knows what the rules are, so that kind of went away. But again, I'm trying to give you a flavor kinds of ideas were being bandied about at the time. Another idea I wanted to mention, which came out much later ten or fifteen years later. There's something called self tuning. and this is interesting because I did have a little I wrote a little paper about this I didn't invent it. O people invented the idea This is once the idea had come along in the two thousands that maybe we'd live on a brain. B our ANE brain, right? notot B our AIN brain So a brain is like a three dimensional, there's different dimensionality of brain. Let's say's three dimensional surface embedded in higher dimensions. So if you have higher dimensions, extra dimensions of space, like you do in string theory, maybe we don't live in all of them. Maybe we live on a three dimensional brain embedded in them And by specially picking the way in which the brain interacts with the rest of the world, you can find parameters or you can find dynamics, I should say, that will cancel the vacuum energy on the brain So basically, if you have like, let's say, a cosmological phase transition where you have a change of physics from one phase to another, ordinarily that would be associated with a change in the vacuum energy, like a change in The average energy in water and ice is different. That's why ice c is float The same thing is true for space time and quantum fields, when there's a phase transition, the energy Changes And so this self tuning idea, what they were able to do, was to show that they could pick setet of fields, et cetera, with the property that when you had a phase transition on the brain, It would not change the vacuum energy vacuum energy or would not change the effective observed value of the vacuum energy that you would measure by doing cosmological experiments. And this is called self tuning. The documenterary sort of goes away, okay And now this turns out again, it didn't work. In the dustbin of history, it was a good idea, like many good ideas don't quite work I remember when I gave a talk on it at the University of Texas and Stehen Weinberg was in the audience and Weinberg was an expert on the cosmological constant, he had written an extremely influential review article in the late eighties. where he went through all the different ways of solving the cosmos toical constant problem that had been proposed at the time, and he actually proved a theorem that said basically, you can't just invent some new fields and solve the cosmological constant problem. There will always be some fine tuning involved, at least in the context of ordinary quantum field theory And so when I explained in my seminar, I was explaining the idea of self tuning, which again I didn't invent, but I'll tell you what I did about it in a second And he's asking questions. He's like, where do you know how do to do this? And like I thought I had to fearum and said this couldn't be done. And I eventually explained it to him. And he goes, that's not self tuning. You tuned it And he was completely correct in the sense that you had to choose other parameters of the theory, not the vacuum energy, but other parameters of the theory very carefully so that the vacuum energy would cancel in a certain way My paper with Laura Merscini, which I wrote when I was a beginning professor at Chicago, was not about whether or not it was fine tuned or not. I thought it was fine tuned from the start, but I thought it was interesting because I wanted to know like We have the Friedman equation, right? We have this equation that says the expansion rate of the universe feels the total energy density of the universe. It doesn't just feel the energy density of matter and radiation How does it know to feel the energy density of radiation, but not the energy density of vacuum energy. How does that work And what we showed was, I sort of guessed this ahead of time and then we showed that it was true effectively what was going on was that the self tuning mechanism had replaced the energy density in the Freedman equation The energy entity is given the letter ro, the Greek letter rho I don't know why, for historical reasons, with the combination rho plus p where row is the energy density and p is the pressure Now remember U For the vacuum energy, ro plus p is zero because p equals minus rho, the pressure is exactly minus the energy density ordinary matter, there's no pressure So cosmologically, you could get an ordinary acting universe at late times where we're dominated by matter density And then the vacuum energy would just disappear from the equation The problem with that is that there's also radiation In the early universe, the universe's radiation dominated in fact. radiation is more important than matter And at the moment of B Bang nucleosynthesis, when we are fusing protons and neutrons into helium and other light elements, the universe is actually more radiation than matter. And if you change the Friedman equation by replacing rho with rho plus p Radiation has pressure as positive pressure in the case of Radiation, the pressure is one third of the energy density So you're replacing row with something like four thirds row And that's not allowed experimentally. I remember Shammit Katru, the string theorist was one of the people who first proposed the self tuning idea and I gave a talk at Stanford. and he was in the audience and he said, You're telling me that I've made a prediction about something that can be experimentally ruled out. That's awesome and it was experimentally ruled out, but it was also theoretically attractive, so again, it went away, but I'm trying to give you a feeling for what was what was attempted those days And I'll give you one last one, one last attempt at solving the cosmatial constant problem. Of course, you know this one It's the anthropic principle. And this was suggested by a number of people, but it was Stehen Weinberg who really did it carefully and he showed that if you live in a multiverse differenterent parts of the multiverse, having different values of the cosmartial constant, but everything else the same then you would naturally not get a big cosmologial constant in those parts of the universe that were hospitable to life For exactly the reason we talked about, if the cosmetric constant is too big, it blows galaxies apart. If it's negative, it collapses the universe very quickly So there's a small window relatively speaking And to his eternal credit, he made these predictions in the nineteen eighties before the cosmological constant was discovered And he said, look, the natural expectation, if this anthropic principle is on the right track is that there is a non zero value the cosmological constant that we will eventually discover because there's no reason, no symmetry for it to be Exactly zero It turned out to be right and he was more or less in the ballpark of the correct answer That doesn't mean the Athropic principle is right, but it does mean that compared to those other things that I was telling you about it did a better job of making a prediction and coming out right. Okay, so there we were. In know CirCca in nineteen ninety, we had the idea of the cosmarthial constant. We related it to the vacuum energy. tried to explain why it was small without a lot of progress Now I come into the game because Bill Press, who was a professor at Harvard at the time, is at the University of Texas now, he was in the astronomy department, and he was a very well respected theoretical cosmologist, and he had been invited by Alan Sandage, who was the editor of a journal called Annual Reviews of Astronomy and Astrophysics Bill was invited by Sandich to write a review article about the cosmontule constant I have no idea why It was not like a particle physics review article. That's Weeinberg had already done that. This was the astronomy version of the review article And okay, so Bill for some reason said yes. And then for some reason, I was a grad student in the Astronomy department at the time and Bill asked me to collaborate with him. I mean, I know why that happened because Bill didn't want to write anything about supersymmetry or wormholes or anything. and he knew that That was important to the story. So He was going to do some cosmology. He was going to like make some plots. He was a very numerical guy. He was one of the authors of numerical recipes, which was at the time before you could ask LLMs to do all your coding for you, numerical recipes was a very helpful way to do scientific computation And so Bill did a wonderful job at figuring out what the effect of the cosmosial constant would be on Cosmological observations, growth of large scale structure, a million different things. He actually didn't just do numerical calculations, he derived formulas and semialytical approximations and things like that that were super useful for working cosmologists. Um And then we eventually realized that neither he nor I were an expert in the observational side of things. So we asked Ed Turner who is a professor Princeton, an astronomer to help us with that. And here's where it gets a little embarrassing because what Ed was really an expert in. was a technique called statistics of strong gravitational lensing The idea is that if you have a very farw away galaxy or quasar, it can be gravitationally lensed by an intermediate distance galaxy orquasar. The probability of that happening is something you can calculate And you can calculate how that probability changes as a function of the cusemartial constant If you have a nonzero cosmological constant, that can change the statistics how frequently you willll get lensed quasars and galaxies in the background. And when we started writing our article around nineteen ninety, this was thought to be the best way to constrain the cosmosu constant. Like ever since Einstein come up with the idea peopleeople were trying to measure the value of the cosmonologrial constant, they had not done so historically and notoriously, it was very difficult to get precision measurements in cosmology This gravitational lensing story was thought to be a promising way forward Now as it turned out Within ten or fifteen years after we wrote our article, there were two ods that were really useful for measuring the cosmartial constant. One was suuper Noveae distances And the other one was anisotropies in the cosmic microwave background We didn't mention either one of these in our review article. This is what happens when you're in the right place at the wrong time. We were a little bit too early to be able to do that. So we were superseded by later articles, but you know in the meantime, we were useful for quite a time there So my job was to write about the theory of the cosmologrual constant. I wrote both about U All these things I've just been telling you about, the anthropic principle and wormholes and stuff like that But also I just tried to explain The Issues with naturalness and fine tuning with the cosmologrual constant. So There is The idea that the value of the cosmologrical constant is mysterious. Why is it so small? That's the cosmologrical constant problem But there's also the idea, well, what if it's not exactly zero? So this is nineteen ninety We didn't know that it was not exactly zero, but we were open to the possibility. We thought it probably was zero, honestly In the back where everyone's mind, all the theoretical businesses anyway, there was this idea, look I don't know why the cosmologrical continant is so small But in the space of all possible theories that I haven't yet thought of More of them make it exactly zero then make it ten to the minus one hundred and twenty two times its natural value, but not ten to the minus one hundred and twenty three, times its natural value. Like maybe there's some symmetry or some dynamics or some mechanism or something like that that makes the cosmetric constant zero canan't imagine that it's just beyond the scope of detectability right now. Of course, the one big counor example to that was the anthropic principle What if you had detected? So I and others were saying, you know back there in nineteen ninety, what if we do detect the cosmologial constant there was one thing that everyone recognized, which is that If you know how fast the universe is expanding, if you know the Hubble constant, then there's a certain amount of energy density in the universe. that would be compatible with the universe being spatially flat So remember Einstein, ever since Einstein, you can think of the three dimensional geometry of space changing through time in a cosmological setting And that three dimensional geometry of space could be flat You could be positively curved like a sphere or negatively curved like a saddle And that zero curvature option right in the middle is sort of the special point, right? It's the middle point between the other two things, it's what's called the critical density of the universe. The critical density is the amount of energy you need to satisfy Einstein's equation with a flat universe So you might like on the basis of theoretical pretiness, prefer the critical density And in the early nineteen eighties, we had the idea of the inflationary universe scenario From Alan Guth and others, we had the idea that you could explain why the universe is so smooth and homogeneous and isotropic Um, because you can imagine that the universe underwent a period of super fast expansion very early on that basically smoothed all the wrinkles and flattened everything out And at the time, nineteen ninety, inflation didn't make a lot of predictions other than critical density should be the density of the universe. The universe should be spatially flat Meanwhile, astronomers had looked for the density of the universe. they'd tried to measure it. they measured the gravitational density of galaxies and clusters and whatever They couldn't find it They kept getting numbers that were close to zero point three times the critical density. So a lot of astronomers just thought the universe was not spatially black It was negatively curved So one of the motivations astronomically for taking the cosmological constant seriously is, you know Nickly Maybe the universe has the critical density, but point three of it is matter And point seven of it is the Cos Marthial constant We knew in nineteen ninety that that would be allowed byy the data, it would be a little bit convenient. It would be a good story for inflation. It would be weird. I'll tell you the reason why I'd be weird, it's something which we call the coincidence problem The point is that the universe has been expanding for a long time, since the Big Bang, fourteen billion years. And as the universe expands, matter and radiation, which we know exist in the universe Dilute away, right? The density of matter and radiation goes away as the universe gets bigger and bigger Whereas the vacuum energy does not dilute away its energy density stays exactly fixed. So just to compare it to matter, By matter, cosmologists just mean any collection of slowly moving particles slow compared to the speed of light So dark matter is matter, but stars are matter, galaxies are matter, etcetera Matter scales away as the volume of space increases, right? Because the number of galaxies stays the same, but the volume of space goes up. So the amount of galactic matter per volume goes down Meanwhile, the vacuum energy remains constant. So if you compare the value of the backacuum energy and matter today to what they were in the early universe Whatever they are today, There was an enormously bigger amount of matter, an enormously smaller amount of vacuum energy in the early universe because the Matter has to have declined ever since And in the future, it will be almost all vacuum energy. So if the vacuum energy is of the same order of magnitude within a factor of ten, of the matter density in the universe today. That means it was completely invisible in the early universe and will be completely dominant in the late universe in the future. And we just happen coincidentally to live in the one time in the history of the universe when these two numbers are comparable So this is called the coincidence problem. And I was really convinced in this coincidence problem. I made some plots that were gotten into the paper that explained how hilariously unlikely it would be for the cosmologrical constant to actually be of the same order of magnitude as the matter density It doesn't matter how much theoretical uncomfortableness you have. Eventually you're going to have to go look at the data and that's what people did. So in nineteen ninety two, The Kobe satellite discovered the anisotropies in the cosmic microwave background. So the cosmic microwave background radiation left over from the Big Bang was discovered in the sixties, but between the sixties and the nineties Whenever you measured it, it was the same temperature, the same intensity in every direction of the sky. It looked perfectly smooth. We all knew that it couldn't be perfectly smooth because we knew there was galaxies in the current universe. those galaxies had to come from somewhere And that implied there must have been tiny ripples in the universe at early times, which is what the microwave background is reflecting So eventually we're going to find them, and the Kobe satellite did find them. A, Nobel prizes all around That was in nineteen ninety two. And it was I remember it vividly that this was one of the first times in my life that I got to feel like an insider because Bill Press, who was an insider and also an inveerate gossip, so he knew before the official announcement Kobe had found these antisotropies. and he told everyone at lunch And then I got to tell people in the physics department, like Sidney Coleman and others that yeah, Kobe had discovered the temperature anesotopies and microwave background. Everyone knew that was a huge deal. and I got to like be the bearer of news and feel like I was a little bit ahead of the game. I'm not above feeling good because of those kinds of things, even though they're pretty meaningless in the ultimate standard of things But anyway, it was again, a kind of an interesting historical moment because People knew prospect of finding anisotropies in the micrate background Jim Pebles and others, and Zeldovic and others had worked out all the math in the seventies and the sixties for that matter for what those anesotropies should look like, but People hadn't really thought it through. like the rest of the community hadn't really absorbed. So what can we do this data that's going to come in. okay? We're going to we have this telescope, the Kobe satellite, which have didid the existence? of these MIS entropies, but it was very primitive. It only just found that they're there. didn't really do a great job of the details. It was not a very highly in focused image or anything like that. So we knew that future telescopes would be bringing us enormously richer data about the microwave background and is entropies And soon it was figured out that indeed, these data that were going to come in would be very, very informative about cosmological parameters Like the Hubble constant, like the cosmologrical constant, like the dark matter density, all of those things. turned out to be true, it took another ten years between Kobe and other ways of measuring the microwave background before we really started to squeeze information out of it, but it was clear even in nineteen ninety two that that was going to be coming soon The other thing, of course, that was data oriented, which turned out to be decisive was measuring the Hubble expansion rate, the Hubble diagram. That is to say velocity of distant things versus their redsifts No, that's not true. Velocity redshift the same thing. distance of distant things versus their redshifts in a new way, namely using type one A supernovae So I had nothing to do with that except I was plugged in. again, I was in the right place or the right time and my friends were very involved with this So the idea here is that there's different kinds of supernovae. understand all the different classifications. That's real astronomy There are type two s and type ones and the type ones have subdivisions, type one A, type one B, etcetera. Office made Client Schmidt who was a graduate student of Robert Kirner, who was a professor at the Harvard Astromy Department. He might have been the chair at that time. He was certainly a chair at some point Bob Kirushner And Bob was like the guy in observational supernova cosmology Back in those days, you know, you don't remember, you kids are too young, but we didn't have that many supernove, right? They were hard to find in a big galaxy You might be able to see one supernova per century. And so if you don't look at many, many, many galaxies, you're not going to see any unless you're very lucky or they're very close So you could there had been a couple. there had been a few supern Noova that had been found, more than a few, but it was not a systematic procedure for finding them And Brian Schmidt my office mate. worked as his thesis project on type two peronovee and measuring the hubble constant. using what's called the expanding phhotosphere method. Basically you model the expanding type two supernova and you use geometry and black body radiation and physics to compare the brightness versus the distance and things like And it was pretty good as a method for measuring the Hubble constant, but it was not quite good enough There's just too many uncertainties in the sort of sphericity of a tyype two supernova and things like that The other thing you could do is type one A supernova There the physics was a little bit less understood. mayaybe still is. I don't even I'm not really up on it, but for some reason, It seemed as if Type one A suupernovae were almost Standard candles That is to say, almost every type one A supernova is approximately the same brightness There is an understanding for why this is true. A type one A superova, well, sorry, let let's go backward. The type two supernova happens when a red Giant star runs out of fuel, collapses and bounces. And different red giants are different. So that's going to be different for different type two supernovae. A Tai one supernoa, type one A supernova is supposed to be when a white dwarf has a companion star that is gradually dribbling mass onto it and eventually it hits the Chandra Skar limit It collapses and blows up and that's a type one unlike did Red Giant explosions when they give out their nuclear fuel, the Chanders Sakar limit is universal. All the white dwarfves have this same Chandersakar limit So you can kind of see why type one A supernovae should be the same brightness And they're very bright. That's the good thing Now they're not exactly the same brightness, and that's an important thing. I'll talk about that in a second, but they're approximately. So that means you can go approximately how far away they are Right at least relative to other tyype one A supernova. And if you find a type one A supernova in a galaxy that you know the distance to already, you can figure out what that absolute brightness is So in Bob's mind, Bob worked on Tpe one A supernova Supernobvi also, Bob Kirsner. And the graduate student who he put on that task was Adam Reh, who was not my office mate, but was in the floor below us So Harvard and you where I was as a grad student was like the center for cosmological supernova observations at that time. But the focus was on measuring the Hubble constant, not the cosmological constant. the Hubble constant is a natural first thing to try to measure There was an idea though What if We didn't wait around to find Spernove by accident But we made a dedicated program to go look for them And this idea it's very, very telling historically, it's a very good lesson in the history of science It wasn't the astronomers who had that idea It was the particle physicists Saul Prmoter in particular was a particle physicist who said like why are you just waiting around for these supernove to happen? Like let's get a big telescope, look at a lot of galaxies and let's in a deterministic No headable way find a bunch of supernovae and measure their distances. That would be the better way to do it Particle physists think big, right? They don't w want to like take pictures of galaxies and hope something interesting happens. They want to be systematic and go over the whole sky. And I remember having a long phone conversation with Saul and Ariel Gubar, who was his co author on one of the very early papers where they talk about could we measure the cosmologrial constant doing this? because I was still a grad student at the time and a nobody, but I had been an author on this review article with Bill Presson Ed Turner that they knew about So I became friends with Saul, etcetera. And of course I was also friends with Bob and Brian and Adam and everything And there's I still think there's a good history of science book to be written. This would not be by me, but by somebody everything that went down in that time because basically Saul and his collaborators Fm the high sorryies formed the supernova cosmology proroject, the SCP, That's what they call it And they were largely ex particle physicists who said, Damn the torpedoes, we're gonna do this And they you know had the ability to get a lot of money from the Department of Energy and they had, you know good expertise at computer programming to reduce the data and things like that. they just went out and did it The astronomers, including Bob Kirschner, very noticeably, were very skeptical that it would ever work. Because for good reasons, not for battery. they weren't just protecting their turf They knew the pitfalls. They knew the possible ways everything could go wrong. They knew that not all the Type one A suupernovae were the same. They had data saying that There was a method that Bob and others actually pioneered and Adam was involved with it. and I think Bill Press was involved with it. tried to standardize the candles. So not all tyype one A suupernovae are exactly the same brightness. But if you plot the amount of time it takes for them to get brighter and dimmer, that's related to their abstute brightness. This is the Phillips relation after Mark Phillips And so they they were trying to figure out how to reduce a heterogeneous sample of many supernovae down to a homogeneous sample and make them all behave the same. Then they would be actually acting as standard candles. So they're standardizable candles, even though they're not standard And the point was they were so impressed with all the difficulties that they thought that you know, this pro motor thing was never going to work And my understanding is, my understanding is very incomplete because it's just from my own knowledge. It was Nick, Sunsef and Brian Schmidt. Brian and Adam had both by this point graduated and moved on other things And they said, you know what? I think we can do it. In fact, I think that these of astronomers saying, I think we can catch up because we know astronomy better than those particle physicists do. And so Saul and his group started first, but needed to learn the astronomy Brian and Nick and their group, which eventually became known as the H Z suupernova team Z is for Redshif. so high zper H Rdsift superova teine U startarted later, but caught up Okay, And they were very good at reducing the data. And whatever And so Adam and Bob and many other people joined that group as well And what happened is they were both right Soaul was absolutely right in saying that it could be done and starting it. And Brian and Adam and Bob and Nick and all those other people were also writing that you need to be careful and get it right and do it correctly And they were plugging away. And I remember very it's a very cute story. I remember getting in the mail a list a set of papers that the Astronomy group had written the highZ suuperova team And so they were advertising their work. So they like we didn't have the archive. I guess we did have the archive back then, but still people would mail papers to each other So they had put a bunch of the papers they had written into like a spiral notebook and mailed it to people who they thought might be interested. And the title page was, the H Z supernova project measuring the deceleration of the universe The irony being that what they actually ended up measuring was the accelervation of the universe, but no one expected that. At the time, they thought they would measure the Hubble constant and maybe they could measure the critical density or the density, I should say, the density parameter of the universe, which would tell us did we have the critical density or not? And so It was in nineteen ninety eight that both teams came out with their results. But let me tell you one more thing about nineteen ninety seven In nineteen ninety seven I was a postdoc at the Institute for Theoretical Physics in Santa Barbara And I was doing, you know some crazy things with topological defects and extra dimensions and stuff like that. you know, who knows what I was working on at the time? But Phil Lubin is an observational cosmologist, a microw background guy who's a professor in Santa Barbara. and he organized a little workshop December nineteen ninety seven. and basically it was on determining cosmological parameters, likeike I said, the Hubble constant, cosmological constant, etcet. from the cosmic microwave background. They didn't have the data to do that in nineteen ninety seven, but they were working on how to do it So they had a workshop to do that And Phil asked me I give a talk at the workshop. I knew nothing about how to extract cosmological parameters from the microwave background but he said Could you do us a favor and give a talk on measuring cosmological parameters in all the ways that are not the cosmic microwave background. So from galaxies and supernova and things like that So I said, sure and I did that. and I you know I gave this talk And it was only because I was forced to do it because I was giving the talk, but I went through an enormous amount of papers on modern observational cosmology from very different es and it was super informative because Over and over again So this is nineteen ninety seven. the The favorite Theorist's model of the universe was the critical density of matter, the good old cosmatui universe The observer's favorite universe was an open universe with only.zo point three the critical density of matter And over and over again, there were from different angles, things in the data saying The theorist's favorite universe can't be right We didn't know what it was. I gave a talk and I said, lookook, I don't know what's wrong, but there's enough data here already in nineteen ninety seven to say that the theorist's favorite model of Omega equals one, as we would say, the density pameters universe is exactly the critical density And it's all made of ordinary matter, and that's what inflation predicts and things like that, that model can't be right Maybe it's because the universe is open, there's not enough matter to make the critical density. Maybe it's because there's a cosmological constant. Maybe it's because dark matter is warm or mixed rather than cold, or maybe there's a tilt in the spectrum of things like. There's a whole bunch of different possibilities. I didn't know which one it was, but I knew that something was going on And that was the mood in cosmology at the time. So in February nineteen ninety eight, when the Heisi suupernova team led byaper a paper that Adam Reese was the first author on. said, you know what? We did our measurements it looks like there's a nonzero cosmodological constant.