Neil Turoks Stunningly Simple Testable New Theory Of The Universe

TITLE: VlP-12yc2f8 CHANNEL: Unknown DATE: ---TRANSCRIPT--- The spirit of this talk is try to connect what we know from measurements to the big picture of the whole universe in the minimal possible way. Okay? So I’m not interested in adding new particles, adding new forces, adding extra dimensions. Sorry. Uh we’ve played that game. Uh it hasn’t read anywhere. Let’s go back to basics. And I think this is a very optimistic point of view. Okay, thank you very much. It’s wonderful to be here. Uh what an atmosphere to be in this incredible room, an institute, a new institute for germinating uh completely new ideas. Um I know what fun it is to start institutes. Uh I started one in Cape Town, the African Institute for Mathematical Sciences on a scale roughly like this. Uh and it’s incredible fun because you get to make the rules.

Um and what you realize is that conventional universities um are actually not very suboptimal. uh they’ve become sort of factories for cranking out people with standardized qualifications and that is not what you need if you want to progress cutting edge science. You need much more freedom uh much greater challenge and expectation uh and you need uh weird people. Okay? Because it’s always the weird people who really come up with new things. Um so uh yeah I’ve been very lucky to uh to start one institute and then to help build another one in uh in Canada. Um and with hindsight I think I was too conventional uh with the one in Canada. It’s now a large institution and after 10 years of being director I thought you know what if we’re going to make real progress um this needs more originality and so I escaped to Edinburgh uh I don’t have any institute now uh and I have a small group of like-minded thinking people around me and we’re basically questioning everything um and that’s great fun so I’m going to tell you about questioning everything in this talk. Uh we started off out of a sense of frustration that the field of fundamental physics has diverged from the universe. The observations of the universe point to incredible simplicity and economy in the laws of nature as I’ll explain um on both on very large scales and on very very small scales. So the most powerful microscope the large hadrron collider failed to discover anything you know that wasn’t predicted that was predicted after the 1960s. Okay. nothing new and on the large scales same story on the scales of the universe what we see is more or less exactly what was anticipated uh you know going back at least 50 years. So um whereas fundamental theoretical physics has got into a multiverse and extra dimensions and all kinds of extra particles and forces and so on and so forth. uh in my view probably something has gone wrong. Okay, we uh we ended up going down a direction and I say we because I did as well. I was working on 11dimensional M theory and so on. uh uh we tried our best but those approaches seem not to have worked just created more and more complication and zero predictions zero correct predictions. So basically the spirit of this talk which is the most important thing about it is uh that we need to revisit our fundamental assumptions and see have we gone wrong somewhere. So of course being here uh you know th this is certainly our philosophy and Faraday was a absolute visionary who and now I I don’t think this is a real quote it’s on the internet no source is given but I think it’s a paraphrase of something that is in his book in his lectures he gave here in these three years it’s not a law under which any part of the universe is governed which does not come into play and is touched upon in the chemistry of a candle. And so that is saying that you know the universe is governed by the same laws that are operating in in very mundane and everyday phenomena. And I don’t I mean this is absolutely visionary and I don’t think even he realized how visionary it was because that’s exa if you think about this it’s telling you about quantum mechanics. The color of a candle is related to the uh temperature right by plank’s constant. And uh here’s a little calculation. I won’t go through the maths, but the energy of a photon is the thermal roughly 3 * KT. And if you know the temperature of the candle and you know um uh the color or wavelength of the light, you can figure out plank’s constant. So uh of course it’s way before quantum mechanics um and and it’s absolutely true and I think uh it captures the fact that the laws of physics are absolutely universal and these discoveries I mentioned from observations especially on the very large universe what they have done is confirm that the same laws of fundamental physics which Faraday and such similar people discovered in laboratories like the one here. Those laws operate everywhere. Absolutely universal. Um and uh we’ll see many many examples of this. So for some reason we don’t know or understand the laws of nature are incredibly simple. Um the opposite of this philosophy of the multiverse which has become popular. Okay. Okay, so lambda CDM is a very good fit to the large scale universe and as I mentioned it’s really a simple phenomenological picture. There are three parameters. So, we’re sitting here. We look outwards. As we look out, we see back in time. And we’re seeing this red uh shell, which is the last scattering surface, the surface which emitted the microwave photons, which we now uh see the big radiation from the big bang. And if we go back earlier in time, uh we hit the blue circle, which is the big bang singularity. And since the universe shrinks as you go back in time, this blue circle has a proper size of zero. Um, so everything we see apparently came out of a point. Uh, and that point is is this blue circle. Uh, now this lambda CDM model which is a good fit to uh all the available data and there’s now lots of data. That’s a revolution that’s happened. Um in the last um uh 30 years or so there’s been a revolution in data but the data is extremely well fit by amazingly simple model which could have been guessed um and basically was guessed in the 1970s um the energy or or earlier the energy content the dominant one is the cosmological constant that’s uh that was guessed by Ein Einstein on the basis of no data at Einstein had the equation for gravity and he said let me make a simple model universe what kind of stuff would I put in it well let’s assume there’s a kind of stuff which is just constant doesn’t change in space doesn’t change in time um it it doesn’t define a lent frame uh it’s the simplest stuff so he put it in and that was lambda and what do you know this is 70% of what we see today so that’s another indication that you know the simplest solution solution has turned out to be the the right solution. So then uh another parameter is the density of dark matter compared to barons. This ordinary stuff we’re made of. That’s a single number. That’s a number of about value of about five. Um I’m going to explain to you a very simple model of the dark matter uh momentarily which will be checked in the next two or three years. And again the philosophy behind our model of the dark matter is let’s try the simplest thing first. And amazingly the simplest thing was overlooked and I’ll explain you why it was overlooked and this has happened again and again. The simplest possibility has very often been overlooked. A third parameter in the standard uh cosmology lambda CDM is the number of baronss per photon. That’s a num number of about 10 the minus 10. It’s a it’s a free parameter in this theory. Um and uh yeah there are very plausible explanations for that number which don’t involve anything beyond the standard model. Okay. Uh standard model I’ll describe. Um then we have two other numbers which describe the geometry of the universe. It’s extremely simple. It’s spatially flat um with very small perturbations. And the pertubations which are these structures you see here growing into galaxies as the universe expands. Perturbations have a very simple power spectrum. They are scale invariant. That’s what this DK over K means. It means equal power in each logarithmic interval of K in the uh gravitational potential or the Newtonian uh potential phi which is dimensionless. And so dimensionless number um you know if nothing else enters has to be given by a dimensionless power spectrum which is just DK over K. And that’s what we see. There’s one free parameter. Uh this number is again about 10us 10. Um, and that’s telling you when you take the square root, it’s telling telling you that the RMS fluctuation in the gravitational potential is about one part in 100,000. Um, and that tells you that the temperature anisotropies across the sky are about 10us 5 of 3° Kelvin or 30 micro kelvin. So, we look out to the sky, we look back. If we have accurate enough um uh radiometers, we can see these fluctuations of 30 microelvin across the sky. So that’s what this formula uh predicts. There’s a a a slight tilt here. Uh this NS minus one, this is just conventional cosmology cosmological terminology. And this NS minus one is about minus.04. So it’s this is a very small uh tilt. It’s saying that the fluctuations are slightly stronger at small k uh i.e. long wavelengths. Um but there are two numbers which parameterize the primordial perturbations and then the statistical character of them couldn’t be more simple. It’s just random Gaussian noise with this power spectrum and there’s no evidence for anything else. So with five numbers you explain uh you fit you don’t explain but you fit all available data. There are some discordance. People obviously are always looking for deviations from this violations of this model. Uh there always are some uh uh they come and they go uh they uh the Hubble Hubble there’s what’s called the Hubble tension. Is the Hubble constant nearby the same as it is distant? Um, you know, I I tend to take a longer term view. I don’t get too excited by a two sigma uh, you know, measurement when when and many of these measurements are very very difficult. Um, but um, but yeah, so there’s some hints of other things, but nothing is compelling. So we live in this extraordinary simple universe. I was very lucky. Um uh when I was in Princeton um we calculated the polarization of the primordial uh cosmic microwave background and here it is as a function of L. This is the spherical harmonic index leandre polomial index. So this is large angles. This is small angles. Um and this is what we calculated using equations that Chandra Seikka wrote down in 1930s uh describing the propagation of light through a hot plasma. Um and that was the prediction. Um and we made this prediction before the plank satellite was launched. In fact, I went to Queen Mary College and and explained to one of the experimentalists, you better measure this. Uh and fortunately, they did. uh they had to actually compromise their temperature measurement by putting in copper grids, wires that would eliminate one polarization. So they would get the two polarizations independently. But fortunately because this was such a clear prediction, they did that. Um they said it’s a really tough measurement because this is the this is microelvin squared. So they had to measure you know this to an accuracy of sort of um eight or nine micrlins. They had to measure the difference in temperature in the two polarizations, two orthogonal polarizations as you go across the sky. But you know this is the data and it just fits perfectly. There are no free parameters in that curve. If you fit the cosmological parameters to the temperature, this is an absolute prediction and it fits beautifully. So my conclusion of this is that the universe is utterly simple and the you the laws of physics which we learned in laboratories work perfectly. Um similar story in particle physics no deviations from the standard model up to 10TV. Many people are very disappointed. Uh many models are ruled out. I think it’s really exciting. It’s telling us that there’s the possibility that we actually do know all the laws. Uh maybe that’s it. Okay. Now, we have all kinds of contradictions in those laws. So, though they those contradictions are our best clue as to what’s happening. But the spirit of this talk is try to connect what we know from uh measurements to the big picture of the whole universe in the minimal possible way. Okay. So, I’m not interested in adding new particles, adding new forces, adding extra dimensions. Sorry. Uh, we’ve played that game. Uh, it hasn’t led anywhere. Let’s go back to basics. So, and I think there’s a very optimistic point of view. Maybe a unified theory is actually closer than we think. That that’s what I’ve come to believe. Well, it was mentioned about CPT. So CPT is the most basic known symmetry in physics. Um that uh charge conjugation parity and time reversal um is uh we don’t know of any good theory of physics which is uh consistent with relativity which violates CPT. And why? because CPT is basically a consequence of analyticity uh and um uh relativistic invariance and uh our nice nice physical laws always uh satisfy CPT. So Laam and I leam boil and I um uh noticed the following thing. So this was an extremely simple observation which is that if you take our universe and trace it back in time to the big bang and you ask how does the scale factor the s the so this is the the the scale factor is just the size of the spatial extent of the universe. How does that scale factor vary with time? And the particular time we use is conformal time uh meaning that um the the metric is just a^ squ of t multiplied by the minkovsky metric. Now that’s a very natural choice of time. So if you choose conformal time then the scale factor turns out that if you have a radiation dominated universe that’s what the hot big bang was then the scale factor just has a simple zero at t equals z. So yeah, a goes like zero. That’s very strange. The size of the universe goes to zero. Um but it goes to zero in the simplest possible way. Um and uh and when you when you ask why is it so simple, it’s because the stress tensor is traceless. Okay, stress tensor is traceless. Einstein equation implies that the Richie scaler is zero. And that implies directly that a of t goes like t. Okay. In uh in four dimensions. So we notice this point since it’s an analytic function. You can consider the analytic extension. Uh and so a of t goes like t that means I can just extrapolate to the other side. The metric goes like a squared. So you’ll find that the size of the universe touches zero and reemerges on the other side. and you get an exact mirror image universe behind the big bang. Okay. So, is that real? Is it not? Probably it’s not real. But I think most likely this is telling us that we can understand the big bag singularity using the method of images. Right? One way to impose like if I want to study light bouncing off a mirror, I can either impose the that the electric trans the electric field um parallel to the mirror is zero at the mirror, solve the equations or I can just put a mirror image of myself behind the mirror, throw the mirror away and solve the free space Maxwell equations. It gives the same answer. And this is kind of what this is telling us is that a way to understand the boundary condition at the big bang is to use the method of images. Okay, that’s a suggestion. Anyway, by the way, the analytic structure of the universe is extremely simple. We came out of a simple zero and we’re going to a simple pole. That’s that’s the lambda dominated universe, right? That the scale factor will blow up to infinity. And the way it blows up to infinity is exactly as a simple pole. So again, you know what what more clues do you want? Nature is telling us that it’s it’s described by the simplest analytic uh uh functions um non-trivial analytic functions have to have some singularities and it has the simplest possible singularity. So um so that was the idea that maybe the universe respects CPT. The CPT is this strong symmetry of the law of physics involves time reversal and um you know there are two options either the universe breaks the symmetry of its laws or it doesn’t and obviously the simplest possibility is it doesn’t and that’s the hypothesis that the universe is compatible with CPT and the boundary condition at the big bang is that uh the boundary condition respects uh CPT symmetry. uh now by the way the well I’ll talk about gen you might object to this to say this is really naive I’m just studying the scale factor what about all the pertubations and so on uh I’ll I’ll talk about a generalization in a moment this turns out to be true of a generic metric not just a special spatially homogeneous metric generic metric behaves like this um what we you want a prediction out of this. Okay. So, given that this is the universe, uh what can we predict that wasn’t predicted before? Well, we we realized that uh this picture of the big bang makes viable an explanation of the dark matter which has been sitting there waiting to be used for 50 years but hasn’t been used. What’s the explanation? Well, the obvious candidate for dark matter is a right-handed neutrino. Why? Because a right-handed nutrino has no charge. Electric, strong, weak, it’s neutral. So, it’s dark matter. Okay. The only thing it couples to is the Higs boson and gravity. And it turns out to be trivial to switch off the Hig boson coupling with a certain symmetry. So if you hit switch that off, the only thing the right-handed nutrino couples do to is gravity. Well, that means it’s the dark matter. Okay? So this was known since the 70s. Why didn’t people use it? Because they had this preconception that the way the abundances of particles were determined in the hot big bang rested on thermal equilibrium. You assume that everything is in thermal equilibrium here. Um and as the universe cools you’re left with the residue of uh you know stuff who’s so this is a way of avoiding the issue of initial conditions you just assume thermal equilibrium and then the universe cools and the stuff drops out of equilibrium at some abundance. But if this right-handed nutrino doesn’t couple to anything except gravity it was never in thermal equilibrium. Okay. And so then basically it’s an embarrassment in the standard picture. It didn’t know how to predict its abundance because it was never in thermal equilibrium. So you know what they did? They assumed it was unstable and so you wouldn’t have the problem. Okay? Honestly, literally that’s what they say. Oh, it’s an embarrassment. So we’ll just say it’s unstable. Okay. But what if it’s stable? Then it’s a dark matter. But then in this extended picture, you can ask how many right-handed nutrinos come out of the big bang. And here you get into the um the the the question of does a timed dependent metric create particles? And the answer is yes. It’s called Hawking radiation. That’s how black holes make uh stuff coming off them. And so one has to solve the time dependent equations for the right-handed nutrino through the big bang. Um and then it turns out that the the vacuum state in the quantum field theory you have a choice of vacuum state there’s one of them which is CPT symmetric. It’s a special vacuum state and you can ask in that vacuum state how many right-handed nutrinos come out of the big bang and it’s a an easy calculation. Turns out that if if one of them is stable, uh we predict the abundance just by the using the nutrino equation of motion and standard cosmology. Um and then its density matches the dark matter if its mass is this. Okay, so that’s very heavy. So it can’t and it doesn’t couple to any of the known particles. So you can’t make it in the lab. Okay, but in principle this is testable because it means the dark matter is discreet. It’s little particles. They have a gravitational field and that discreetness can in principle be measured. That’s very difficult of course but in principle can be. There’s a better prediction which is measured which is testable in in the next three or four years and that is if one right-handed nutrino is stable than the lightest neutrino. So we see three light neutrinos. It follows that if one of them is if one of the right-handed nutrinos is stable, these are the neutral ones, then the left-handed the lightest nutrino which is approximately left-handed is massless. Okay, why does that follow? I said that to make the right-handed guy stable, we had to switch off this coupling to the Higs. You do that by saying that the yukawa term which is basically new right new left higs is um is set zero by symmetry and the symmetry is just new right goes to minus new right that excludes that ukar term so we switch off that vertex but that vertex is the same as this vertex so if you switch off this vertex you switch off that vertex that means that the left-handed guy doesn’t mix at all with the right-handed guy this is if they’re only one of each it’s a little bit more complicated because there are three of each in the standard model but same mechanism works if I make one of them right-handed guys stable then one of the left-handed guys is massless and that’s a so if I switch that off I have to switch this off and that’s the prediction okay so uh we know these are the nutrino mass the mass of the nutrinos squared we know two differences from nutrino oscill ations but we don’t know the absolute scale. So we know two numbers but we have three parameters in the in the three nutrino masses to parameterize um what we know and we predict the lightest one is zero. They could be arranged in what’s called a normal hierarchy or the inverse hierarchy. This one is more or less ruled out now by data. But with the normal hierarchy, if we fix the lightest one to be zero, then we predict the sum of nutrino masses based on what we already know. So here’s the sum of nutrino masses. Uh this is um this is these are the um the the colored curves are the upper bounds coming from measurements of galaxy clustering. Okay, it’s absolutely amazing that you know if you want to measure the if you want to set a limit on the mass of of the um on the sum of masses of the nutrinos, the best way to do it is to see how efficient matter clusters in how galaxies cluster when they form big clusters because if the if the nutrinos have a mass then they cluster slightly more efficiently. If they’re massless, they just fly off. But if they have a mass, as the universe expands, it turns out they slow down and clump under gravity. Um, and by measuring the clumping, you can you can see the signal of nutrino masses. So this is the upper limit from the observations. Our predicted signature is a bump around here at the minimum level. There’s no bump in the data. Okay. Um and if this upper limit keeps coming down, we will be ruled out. Okay, which is fine. But you know, I I I’m fairly sure these are very difficult measurements. And I’m fairly it happened with the CMBB. People set upper limits and upper limits and upper limits and oops, they realized that the signal was was above. Okay, because they just got used to uh ruling things out and they like ruling things out. But we’ll see. So it could be that in three or four years a bump appears at this minimum sum of nutrino masses and that will be incredible uh confirmation. So we we’ll see. So that’s that may be the dark matter. And by the way if if the uh by the way the if there are right-handed nutrinos and um in the standard model this this is required one of them is the dark matter the other two play a very important role too because their interactions violate leptton number. Uh in the standard model leptton number can get converted into baron number and I mentioned the baron asymmetry of the universe. you can explain that as a result of the leptton number violation in the right-handed nutrinos. So uh so those numbers are in principle explained of course um there’s a free parameter involved. So it’s not a numerical prediction um except the zero you know that we’d love to have a you know that the our numerical prediction is zero in this case. We’d like we’d much prefer to have an actual number we predicted, but we we’re just relying on two measurements and then this one we predict to be zero. So yeah, you you know you have every right to remain skeptical even if this is confirmed. There many ways to predict zero. Um okay. Um so let me move on to another issue. Let’s imagine that we do believe this picture of the universe. Um people in cosmology for the last um 45 years have believed they had to explain why the universe is so big, smooth and symmetrical, right? And there’s this idea of inflation which which is that the universe started out very little and very lumpy and then underwent this incredible exponential expansion um which is possible in certain uh particle physics theories and this expansion smoothed everything out and stretched it and removed the spatial curvature. Um so that’s the theory of inflation. We don’t have inflation here. Okay. So there’s no inflation here. We’re extremely minimal. We we basically have the ingredients we know about and nothing else. Okay. How do we explain that the universe is so smooth and spatially flat and simple on very large scales. Okay. So we had to think go back to fundamentals. How do you ever explain something is homogeneous, isotropic and uh and smooth? Well, think about the gas in this room, right? We’re not surprised that the air is uniform in this room. Did we need a mechanism? No, we don’t need any mechanism. We just need statistical mechanics. We throw some molecules in a room. Uh we ask what’s a typical state for those molecules and this is what the typical state is. They distribute themselves homogeneously. Now, the universe a little bit different. You see, you’ve got to think about the foundations of statistical mechanics. Some people would say that the reason the air is smooth in this room is that even if it wasn’t smooth, if you threw them started with them all in one corner, they would have smoothed themselves out, right? They would have spread out and filled the room, have a certain energy, spread out and fill the room and become uniform, right? That’s relying on what’s called erodicity. The system explores enough of phase space to find the most likely configuration. But if you think about it, that’s completely unnecessary. Okay? If I just give you a room and I say there’s a certain number of molecules in the room and they have a certain total energy, right? What’s a typical state? I don’t need time for them to equilibrate or whatever. I just what’s a typical state? I’ve got limited information. What’s a typical state? The answer’s crystal clear. You quantize the molecules. You count the states. put in the constraints and the typical state looks like this. There is no need to equilibrate. That’s very important in the universe because we don’t really have time to equilibrate. We have the big bang and uh you know we don’t have any we don’t have to wait for the system to reach equilibrium. We just want to know what does a typical universe look like. And so for that we’re going to have to do statistical mechanics of universes. Okay, which sounds very difficult but fortunately this is exactly what Stephven Hawking and collaborators did and it works amazingly beautifully. So here are all the laws of physics that we know and these really describe everything uh which we know of if the dark matter is in here somewhere if it’s a right-handed nutrino. Um and uh so here’s gravity and what uh Hawking Gibbons and uh and other people Malcolm Perry um this was in in the heyday of Cambridge general relativity. What they did is they understood how gravity or or had suggestions how gravity is related to thermodynamics and they were mostly interested in counting the number of states of a black hole. But uh their formalism actually works perfectly well in cosmology. So the formalism is based on this very simple trick that uh you see this formula describes a transition amplitude initial state time evolution final state and this is the amplitude given as a path integral. But if I go to this formula and I say how do I get thermodynamics out of an amplitude? Well I make time imaginary. So time goes to beta actually minus i beta and h is still h it’s a Hamiltonian operator and then I sum over initial equals final and sum over all of them. So trace uh over all states will which basically means I do this path integral with periodic boundary conditions in time um in imaginary time. This gives me the partition function. Um for gravity. So the partition function. Yes. So for gravity the Hamilton is a is very formal argument because in gravity the Hamiltonian is zero on all states. The Hamiltonian has to be zero. Basically because there’s no preferred time coordinate. It wouldn’t really make any sense to have a Hamiltonian which was not zero. So this factor actually disappears. The trace becomes a trace of one. And that’s just counting all the states. Okay, you just trace over all the physical states. Uh this partition function is the uh the trace over states. It’s the exponential of the total entropy. The total entropy because the Hamiltonian zero. So this would normally be free energy but E is zero. So the total entropy is the ordinary entropy like of the radiation and then you have the gravitational entropy. So uh it turns out so people use this for black holes. Um and it works tremendously elegantly. It having said that it’s still very controversial. Okay, because nobody quite knows uh what states you’re counting. There’s this formal trick to count the states uh and nobody quite knows what those states are. Um so the hawking temperature turn gravity is special because it defines its own temperature. You don’t have any choice about the temperature. The spacetime with defined by whatever constants define it has a periodicity in imaginary time that defines the temperature. That’s the Hawking temperature and the action gravitational action calculated over one imaginary time period is the gravitational entropy. Okay, it’s a tremendously elegant uh formalism. uh as I say we’re still sort of wondering about what that means. Now these are realistic cosmologies. Here’s the line element the scale factor uh we we we will let uh space be homogeneous. It could be curved uh that that would be kappa and this is the freedman equation. So you have the expansion rate of the scale factor is fixed by the radiation the matter space curvature and lambda. So when you write down this equation you immediately realize this has very nice analytic properties. Okay this equation was solved in the 19th century uh in terms of Jacobi elliptic functions. It’s like the simplest uh simplest nonlinear problem in classical mechanics. And it turns out the solutions of this equation are periodic in imaginary time. What do you know? That means they describe a hawking temperature. That means you can calculate the entropy of any spaceime with these constant parameters. So strangely this wasn’t realized. Uh we we solve the equations. Most cosmologists you see would just put this on a computer and just solve a of t. They have to do that to calculate the cm. But this Hawking method relies on analytic continuation. So you you have to solve them analytically. So a of t is doubly periodic in the complex t plane. We came out of a simple zero. We head to a simple pole. That seems to be the real universe. If we go up the imaginary time axis, it’s uh it’s similar. We come out of the bang, we hit a pole. And then when you look in the complex t plane there’s a um fundamental domain which is in in general is is a uh a rectangle and uh and the solution is periodic um uh so you tile the plane with these rectangles which is saying that the a of t function really lives on a taurus with these opposite sides identified. Um and uh the um imaginary time direction goes around the Taurus. Um so uh so now you just integrate the action to get the entropy gravitational entropy and it’s a it’s a completely unambiguous answer. It’s a function of the cosmological parameters and it gives you a semiclassical counter counting of states. And then amazingly enough it turns out to be greatest the entropy is greatest if the universe is homogeneous isotropic and spatially flat just like what we see there more states there and if it has a small positive cosmological constant that’s also what we see okay so I’m being deliberately a little bit vague here because we actually don’t know the rules of the game okay we this is the correct statement but um you have to fix something and predict other things. In thermodynamics, I fix the volume and the energy or I fix the pressure and the temperature or I fix, you know, you always fix something and predict something else. We don’t know what to fix. So, we have a formula for the entropy and we don’t quite know what we should fix and what we should predict. But these statements are are qualitative descriptions of that formula. doesn’t it’s information theoretic doesn’t require equilibrium or eroticity and now we say why is the universe the same in two opposite directions okay well because it’s correlated that’s the most likely state you don’t need any causation you don’t need that side of the universe to have communicated with this side right that’s that’s a fallacy that um correlation implies causation no it doesn’t you don’t need a cause that’s the most likely state. Uh and that’s all. And so that solves the horizon puzzle, right? You don’t need inflation. You don’t need a mechanism. You just need to count the states. Of course, we have to believe this Hawking formula. It’s very formal. We don’t know what degrees of freedom it’s counting. Okay? Uh we don’t know what to fix and what should vary. So there is a lot to do to understand this better. But I think it’s extremely plausible that the explanation for why the universe is so simple is just that’s a typical universe. Uh there was this rather nice picture in quantum magazine. If you had a machine making universes and you just picked one at random, it would look like this. Uh I mentioned it generalizes to inhomogeneous radiation dominated cosmology. uh it turns out that half of the classical solutions are time reversal symmetric and describe a regular conformal forge geometry. So conformal means that if I pull out the factor a uh a squ of t out of front of the metric and I take the remaining formetric that’s completely regular metric with time reversal uh isometry um and so it looks like this. So uh you can actually solve the full nonlinear Einstein fluid equations in a gradient expansion that’s an a gradient in space spatial gradients um and and show that and match the gradient expansion near the big bang to the gradient expansion at future infinity. So yeah this is a very general uh statement about cosmological solutions. So if this is the right point of view then we should think about the universe like this. The universe is this incredible microscope. Okay, we live here uh 10 billion or uh 14 billion years after the big bang. But um as we look back to the big bang we can go back to we we and when I say look back we’ve got to look through the surface of last scattering. Okay. So gravitational waves for example just travel through the hot plasma without getting scattered. So in principle we can see all the way back to the plank time. Uh we will only be able to see what’s in our past light cone. So we will be seeing a patch of the hot big bang that’s about 10 microns across. Okay. And that contained all of the initial structure which gave rise to what we see. Um so when you start thinking this way uh yeah so if I take a plank length object at the plank time and I run it forwards it’s about a millimeter that’s the microwave background the cosmic micro background has millimeter wavelengths it was a plank length at the plank time now many people believe there there all kinds of strange pre preconceptions people developed one of which is that we can’t talk about what happened before the plank time. Okay, that’s a very typical statement you will say see all over physics literature. Can’t we can’t even talk about this. That’s that’s a very unthinking statement. Okay. What you should do is try to predict the geometry for example using some real calculation for example a path integral and then the question you want to ask is is the action for this part of the spaceime bigger or bigger or smaller than h bar. If the action is big compared to h bar it means there’s lots of interference. It’s very classical. Okay. And indeed that’s the case. There’s in this picture there’s no reason to stop at the plank time. Uh there are other arguments people will give. They typically argue that because the fluid wasn’t in thermal equilibrium around the plank time, one shouldn’t use the fluid equations. That’s also a wrong argument. You can use the fluid equations even if they’re no interactions at all. Why? because a stochastic pattern of waves, you know, with random orientations has an equation of state that looks like a fluid. Doesn’t need interactions. So, uh, the more I’ve thought about it, the more I’ve realized that the standard arguments have loopholes. I won’t go into them, but in principle, we may be able to look, you know, right back to uh, way earlier than the plank time. And what we’re seeing in the sky is this direct image. Okay, so we’ve got the ultimate accelerator. We just have to look at it and see what it means. So let’s dig a little deeper. So now let’s think about quantum fields and gravity. How does that work in the standard model? There’s this basic disease in coupling uh quantum fields to gravity which people have been sweeping under the rug for decades. And the person who emphasized this I think best was Bryce Dit in the 70s. He wrote a very good article on uh quantum field theory in curved spacetime and he emphasized that the really the basic rules are very troubling. Okay, why are they so troubling? Well, at some level we know that the zero point fluctuations diverge in energy, right? You just ask somebody what’s the energy in the vacuum for a photon for for electromagnetism. Well, it’s infinity plus infinity. And I’m supposed to couple gravity to that. Okay, good luck. You know, you’re trying to the source for gravity is infinity. Okay, that’s the problem you encounter. Gravity se and and so electromagnetism has infinite positive energy. Durac’s theory of the electron has infinite negative energy, right? And in the in the minimal standard model, they don’t they don’t cancel, right? So you’re left with infinity. In fact, they’re more firmians than Bzon. So, you end up with minus infinity. So, uh it’s very very worrying. Uh there you can always reormalize them away. Okay. So, what you do when you get an infinity in quantum field theory is you say, “Oh, well, I didn’t really specify the parameters correctly. I should change I should do divergent reormalization of Newton’s constant and the cosmological constant and cancel the bare cosmological constant against this infinity. You can do that but unfortunately these divergences spoil uh the local scale symmetry. You see, I should have said in this picture, uh, let’s go back to the big bang. Um, the reason this is so simple is because the stress tensor is traceless. Um and um um that is true for gauge fields at a classical level and for firmians massless firmians. They have a traceless stress tensor at a classical level. So the classical symmetries of the standard model obey this exactly. Okay, it’s very beautiful. But the trouble is that those classical symmetries are violated by quantum divergences. And this is called the trace anomaly. Uh and so if we really want that description of the big bang singularity, we need this traceless stress tensor that’s associated with local scale symmetry that I can ch it’s an amazing fact about radiation that if I change the scale the wavelength of the photons nothing changes the equations are invariant right we know an X-ray is the same as a as a radio wave right why because of the scale symmetry but it’s actually much more than that you can change the scale locally. You can stretch and expand spaceime locally in an arbitrary way and the Maxwell’s equations are invariant. So there’s this very deep symmetry which which ensures that the trace is zero and these divergences spoil that symmetry. Um, another way to to to to see this is that gravity couples to the stress tensor. And so a very naive thing you can do is say, okay, imagine I’ve got a spacetime and I put some quantum fields on the spacetime and now I calculate the stress tensor in those quantum fields on a spacetime. Well, of course, it’s infinity. And in a typical quantum field theory, all moments of the stress tensor are infinite. They’re all divergent. Okay, it’s really telling you that the stress tense is not a well- definfined operator in quantum field theory. Okay, I I mean you can, as I say, you can reormalize and so on, but then you you you lose you lose intuition about what really is going on. So all of these in a typical quantum field theory, the stress tensor correlators are all divergent. Looks like a terrible problem, but there’s a very nice trick which is you put the quantum field theory on a curved background and then calculate the stress tensor this way. So what happens is that the effective action for quantum fields in the gravitational background. So this is I I integrate out all the quantum fields and I’m left with this effective action. And then all of the divergences in these correlators are actually captured in divergences in this effective action. And there only a limited number of terms. Okay. So now you can vary this action and figure out all the correlators. It strictly only gives you the UV divergent parts of all the correlators. But these counter terms encode all of the divergences and stress energy correlators. This is a very powerful way of sort of capturing these divergences. So we want to try to get rid of those divergences. Okay. Um and we have a clue. We look at the sky. Okay. Sky is telling us that there are scale invariant fluctuations coming out of the big bang. The simplest hypothesis would be that those scale invariant fluctuations are just a picture of the vacuum fluctuations of something. Okay. And what could it be? What kind of field has fluctuations in the vacuum of exactly the character we see? And when you ask the question, the answer is obvious. There’s only one field. It’s a four derivative field because four derivatives cancel the d4x in the action. So phi is dimensionless. If dimensionless, its power spectrum has to be one over k cubed. So that this is dimensionless. Okay. So dimension zero field automatically has fluctuations which look like what we see in the sky. So that’s a natural thing to look at if you want to explain those fluctuations. It turns out this field with four derivatives is called a dipole ghost. Um and until recently I thought it was invented by Heisenberg. Uh but then my PhD student uh Sam Baitman uh got very interested in the history and it turned out that um Homi Baba actually started this uh the Indian physicist. Um so he was playing around with nuclear physics model of the nucleon and so he invented this four derivative field. It has very interesting properties. It confines things so it might have held things together in a nucleus and so on. Um but it it it was called a dipole ghost field. Now okay so that’s been studied and then what we did is we just put together a number of results in the literature and and realized the following. So imagine I take a standard model which has gauge bzons chyal firmians and dimension one scalers. There’s the Higs Bzon in the standard model. It’s a dimension one scala. It has two derivatives in its action. And then let’s just throw in a bunch of dimension zero scalers and see how they change things. So can we cancel the vacuum energy? And then even better, can we cancel these conformal anomalies? If we cancel them, we’ll have a well- definfined stress energy tensor which we can then couple to gravity. Okay, so a very very naive point of view and it’s just numerology because these quantities are all just proportional to a string of integers. Okay, with strange coefficients. Okay, so now we just have to do some numerology. We’ve got three equations for four integers. Um are there any are there any solutions where where they they’re all zero? Okay, so you type this into Mathematica and you say set them all zero. That immediately implies that ns1 is zero. Okay, so now it’s very unfortunate because I have I hold the Higs chair of theoretical physics and they say there’s no Higs. Okay, it’s not allowed. But actually that’s a very good thing because the Higs Bzon comes with a whole bunch of headaches. Uh there’s the hierarchy problem. Why is its mass so much smaller than the plank mass? Um there’s a landal pole. The cortic coupling in the Higs boson means that the quantum field theory doesn’t really mean anything at high energies. There’s no UV completion. Um and so there’s some headache. So if we eliminate the Higs boson and replace it with these guys, maybe we have a chance of solving this problem. And indeed this this is the way things are looking. So let’s go ahead. Even though this is going against my philosophy of, you know, take what you see and interpret it, I’m going to be generous and say, uh, okay, I’m going to give up on the Higs for now as being fundamental. Maybe the Higs is composite. Uh, any two of these equations give that the number of firmians is four times the number of gauge bzons. That’s just a result of these funny um coefficients. And also the number of dimension zero scalers is three times the number of gauge bosons. So let’s take the standard model in which there are uh 12 gauge bzons. 8 + 3

• 1 12 gauge bzons number of firmians is

48. Okay. Well, what do you know? That’s three firmian generations each with a right-handed nutrino. Uh and then we have 36 of these scalers. Okay. So it turns out you can satisfy all these equations. Everything’s zero. Um the existence of a solution is extremely non-trivial. If you try this for SU5 or SO10, uh it doesn’t work. Okay. Uh but the standard model works without a hig boson as I emphasized. And it turns out that in this solution um it’s kind of obvious there are equal numbers of bzon fian degrees of freedom here. A four derivative scala has twice the number of degrees of freedom of a two derivative scala. That’s why there’s a two here. A vile firmian likewise has has a two. Um in the solution there are equal numbers of bzons and firmian degrees of freedom. And actually you have the same helicity content as n equals 4 super symmetry. So we weren’t looking for super symmetry but it this suggests there’s maybe another representation of super symmetry that this is pointing to. We don’t know how it works yet, but that’s quite uh tantalizing. Now, let’s try to quantize this theory. Okay, so again, my student uh Sam Baitman uh went and looked in some very deep quantum field theory books and in chapter 10 of Bogalubof’s last textbook which I highly recommend, amazing textbook, very dense. In chapter 10, you will find this theory, the dipole ghost. And he actually quantizes at the beginning of his section on gauge theories. The reason is when you quantize it, you find that the it doesn’t live in a Hilbert space. When you quantize it, the space of states is indefinite. It includes positive norm and negative norm states. Okay? and they talk a little bit about that and don’t really resolve it. But um so uh so that’s what we’ve been working on for the last couple of years trying to make sense of this fact that there are negative norm states. Now again you will hear all kinds of wrong statements about this. People say oh there are negative norm states that’s people usually call those ghosts in the quantum theory and that means you predict negative probabilities. Okay, absolutely wrong. A quantum state is just a label for a physical configuration. Okay, whether its norm is positive or negative is neither here nor there. Okay, it’s a label. The the the the misconception we had is everybody’s used to normalizing the wave function in quantum mechanics. So we think, oh, if it’s not normalizable, you know, what do we do with it? But um the point is you’ve got to generalize quantum mechanics to work in an indefinite space of states. We’re used to indefinite spaces. Minkovski space is indefinite. You’ve got timelike vectors space-like null. You know, nothing wrong with those spaces. You just have to get used to working within them. So what we’ve shown is that now the free theory is a little bit too trivial because there no interactions. But it turns out there’s a simple interacting version of this dipole ghost which is roughly speaking like a gauge theory. See in a gauge theory the action is f the lrangeian is f squared and f is linear in the gauge coupling and that means when you square it you get um cubic vertices with one power of the coupling and quadratic vertices with two powers. And this this theory we call this the perfect square theory and it’s it’s the analog of a gauge theory but it’s much simpler than a gauge theory. There are no no indices here. This is just a scalar field and it’s dimensionless. Um there was a couple of very nice papers by Bob Holde studying the general for derivative scalar theory dimension zero theory invariant under shifts of the field. You see all the field itself doesn’t occur in the lrangeian just gradients. So it’s invariance under shifting of field and he did a a general study of them and noticed that this one for example is asmtotically free meaning it has a UV completion okay this is a continuum a theory with a genuine continuum limit a very nice theory he also calculated the scattering cross-section 2 to2 in this theory and found it was positive okay even though you’re in this indefinite space of states the transition probability which is the only thing you care about is positive. Um and so we have recently proven that all transition probabilities are positive unitary causal uh and this theory obeys analyticity. It’s it’s a perfectly sensible theory. Now our result rests on generalizing Q ofT from Hilbert spaces. The assumption in a Hilbert space is that the inner product is positive. Okay. So many people say oh when you look at a four derivative theory doesn’t live in a Hilbert space therefore it is nonunitary. Okay. This is complete nonsense. Okay you can have a unitary you know there’s unitar there’s unitary theory there’s a pseudounitary theory. The only thing that matters is that the probabilities um the sum of the probabilities the probabilities are positive. They add up to one and um uh and the one is conserved. Okay? And that’s that’s unitarity. So the fact you have a negative negative norm states doesn’t tell you anything. You’ve just got to work within these indefinite spaces. Now there’s a whole mathematics of generalizations of Hilbert spaces to what’s called crime spaces. And I just learned that crime was Ukrainian which is great because Bogalof also did most of his work in uh Ukraine. There’s a Bogalubof institute there too. So um crime spaces. So what is a crime space? A crime space is a space of states can be infinite um infinite dimensional which uh is decomposed into positive and negative norm spaces by a crime operator. So there’s some operator that’s plus one on the positive norm and minus one on the negative norm. uh you can use that operator to define the topology of the space because using kappa you actually have a definite inner product you can use to define the topology you don’t want to use that inner product it turns out be uh because this kapper is not covariant in the lorenian sense so there’s a subtlety in there but anyway there is this operator uh the perfect square theory that’s this one uh has a non-perturbative grind symmetry. Okay. So there’s a hidden discrete symmetry sitting in this theory which which under which half of the states are positive and half of them are negative. Okay, that’s very important. So not every four derivative theory makes sense. You have to have this crime symmetry. I’ll show you what it is in a moment and ask if you would have guessed it. Okay. Now, now then you have to generalize the B rule. You see the normal Bourne rule, you normalize the wave function. Uh you you you deal with it deals with normalized wave functions. You can’t do that here because some states have zero norm. Okay. So instead, but there’s a very nice alternative which reduces to the standard picture in the case of a Hilbert space which is the probability of going from initial to final state is the trace trace of the following operator. This is a projection operator. You see a crime space is uh not degenerate. So there are projection operators and and the so these obey P ^2 equals P. Sum of the P’s is one. So this projects you onto the initial state. You then evolve with the scattering matrix and then you project onto the final state, multiply it by s dagger and take the trace. So that that reproduces the usual formula, you know, mod mod of the amplitude squared. And if you have this crime symmetry, if these operators are invariant under crime symmetry, you’re guaranteed that these probabilities are all positive. Okay? So you sum over all the states without prejudice. I just project onto my initial state, final state, use the scattering matrix and uh and everything’s fine. And we show in our paper this is completely consistent with analyticity and the optical theorem and and so on and so forth. Now how do we see the crime symmetry? So so we want the way to see the discrete symmetry is to embed this theory into a bigger framework where that symmetry is obvious. Okay. A very often trick that we use becomes obvious if we embed it in a larger theory. The larger theory has two fields and only two derivatives and it has 011 symmetry. Okay. So this theory has shift symmetry a one parameter continuous symmetry. This guy has SO11 which is a continuous symmetry but it also has Z2 cross Z2. This is just a usual statement that the Lorent group in four dimensions has four components. Uh well this is the internal Lorent group in two dimensions and again has four components. So this theory which is the host theory. It’s not really a theory. It’s actually a sick framework but it has a absolutely well- definfined perturbation expansion. This theory has obvious symmetry under u goes to V. And then if I take this theory and I integrate out the V, notice the V is only quadratic here. I can do the Gaussian integral. If you integrate out V, you get this theory. Okay. So you embed the theory you’re interested. This is really a theory. This has a positive ukidian action. It’s it’s a good theory. This is just a framework for perturbation theory. But this has an explicit um uh symmetry. And it turns out this symmetry is minus1 on negative norm states and plus one on positive norm states. That’s easy to see from the kinetic term. Um if you go back and ask what is that symmetry in terms of your original field, this is what it is. It’s a it’s a a terrible mess. Okay. So phi prime goes to minus five then inverse powers of lambda. So this is a symmetry which which doesn’t which involves all powers of lambda and it’s a real mess if you try to use this in pertabbation theory. This symmetry is just u goes to v. So you calculate in pertabbation theory here and the symmetry is obvious. Okay. So we use this symmetry to prove the crime symmetry of of this theory. Uh but nevertheless this is really an onshell symmetry of this action. you can work out the equations of motion, check them against the symmetry, and they’re exactly satisfied. So, um, now I think I’m I’m maybe running over time. So, I think I’m going to wind up because I really want to allow questions. Is Is that Can I have uh three minutes? Is that okay?

Yeah. Okay. Um, and I’m happy to talk more about this. This is very recent stuff which we’re very excited about. Uh my student uh Megan Anderson, that’s uh her right at the beginning was reading uh I haven’t even mentioned her. That’s terrible. Okay, sorry. My student Megan Anderson um was studying the beta functions for this theory and was also reading about four derivative gravity theories and she noticed that the beta function in this theory corresponds exactly to the beta function in four derivative gravity theory. Okay? And I’ll explain why. So it’s a very clever observation and that put us on the track that maybe this this field actually has something to do with gravity. It’s not only good at cancelling anomalies, maybe it’s really part of gravity. Okay, so how does that work? Again, this is underemphasized that there is a reormalizable theory of quantum gravity. Okay, people will usually say uh quantum gravity is not reormalizable. Okay, so we need string theory or super gravity or something. Okay, that’s a little bit too fast. Quantum gravity is reormalizable if you add terms quadratic in the remanum tensor. Okay, so this was shown by Kelly Stell. Kelly Stell very sadly passed away uh not long ago. So he was at Imperial for a long long time. So Kelly Stell pointed out that this action is perfectly reormalizable. Okay. And the reason is just the usual argument in reormalization. If you have dimensionless couplings um and uh soft couplings and the positive mass dimension couplings, the theory is reormalizable. Okay, the only divergences are logs and uh just by dimensions and this is perfectly reormalizable. Not only is it reormalizable, it’s asmtotically free. Okay, wouldn’t you know? uh gravity is very similar to young mils theory in this sense and this was shown by these people 1985 there two dimensionless couplings kai and gamma and in the far UV these terms dominate over those and the UV flow uh kai and gamma both flow to zero okay provided they’re positive uh which you need for I I’ve written the ukidian action here. So, uh, so quantum gravity may have a really simple answer. Okay, just add the four derivative terms. The reason this didn’t work is because of ghosts, negative norm states. But now, now we know how to deal with those. At least in this very simple theory, we know how to deal with negative norm states. We generalize the Bourne rule. Okay. And um let’s look at this theory in the far uv. Now in particular there’s and this is what Megan noticed there’s a uh there’s a particular limit if gamma goes to zero that very naively forces the vile tensor to zero. Right? Because this would have infinite ukidian action. If if c is non zero everything’s positive here. Oops. What happened? something went to zero. Um so so there’s a limit of quadratic gravity in which uh there we go. This part of the ukidian action is positive. So there’s a limit of quadratic gravity in which uh where gamma goes to zero where c is forced to be zero. That’s a little bit too naive actually. What happens is that in that limit you take the con the c nonzero modes which include gravitons and you uh you renormalize the kinetic terms to absorb the gamma and then you find all the interactions vanish in the limit gamma goes to zero. So those modes just decouple, right? Those modes are just have a Gaussian path integral. You can just integrate them out. The only interesting modes come from this R squar term. And the clue is in the fact it’s a square. Okay. So here we’ve got a perfect square action. It’s a Richie scala squared. It’s a scalar and it’s squared. Well, what do you know? It turns out it’s exactly this action, right? it. If we know the vile tensor is zero, the metric is conformal to flat space. Plug this back into this action, you get this action which is scale invariant four derivatives. Now with this substitution, that action turns into this. Okay, so quadratic gravity in the limit of zero gamma is precisely the perfect square theory. Okay. And we know how to deal with it. We know how to get uh consistent quantum probabilities. It’s asmtoically free. So it has a continuum limit. It’s a really good theory of gravity. It’s a great theory of gravity but without any gravitons. Okay? Because the v tense is zero. But it turns out you know the scale factor of the universe is the conformal factor. So we can study that and we can study even inhomogeneous propagating modes in the scale factor which turn out they do exist in this in this limit as gamma goes to zero. So uh and then furthermore we’ve recently this theory as simple as it is r 2 gravity with a conformal metric has ditter space as a solution that’s a classical solution and the theory is scale invariant so actually ditter spacetime with arbitrary ditter length is also a solution um and we’ve recently pro proven all of those solutions are stable okay so this removes another objection to four derivative theories called the Ostrogradsky instability. I don’t know if Ostrogradsky was Ukrainian. It’s a famous Russian theorem from 1850 that any theory involving more than two derivatives in its equations of motion. In classical mechanics, any such lranianbased theory with more than two derivatives in equation of motion has a Hamiltonian which is unbounded below. And typically that means the theory is unstable. So yeah, this is unstable. This is the scale factor of the universe. It is unstable. It has a simple pole. I showed you that. And and that solution uh Ostraardsky might say, “Oh, it’s unstable.” But that’s a real universe. Gravity is unstable. Um what we’ve shown is that the dissa background is actually classically stable. So it circumvents this instability by just reinterpreting it by saying no this isn’t a field living on flat spacetime. It is actually the dynamics of the spacetime. uh there’s a very powerful three-way correspondence quantum gravity and this limit uh or this perfect square embeds into that uh the perfect square theory embeds it turns out it embeds into good old ph to the fourth uh you know we always learn ph of the fourth scalar field theory as the most elementary example of a QFT um this UV theory is actually just ph to the fourth this theory okay it’s got a quartic potential. If I think of u as being fi star and v is phi, this is just the aelian higs model right or o2 invariant scalar field theory. Uh and and and this is the theory that’s corresponds to our theory and has a perfectly sensible expansion. People have worked out this fight of the fourth. It doesn’t make sense of the field theory with positive coupling at negative. It only really we only use it as a framework for pertabbation theory makes perfect sense there even at negative coupling and ph to the fourth theory is asmtoically free at negative coupling that and these things correspond perfectly this is known to seven loops now I it’s largely Russians who do these calculations okay I’m not quite sure why but they have calculated to seven loops uh this we my student Megan Anderson has done three loops these correspond perfectly exactly. Uh quantum gravity in this limit is only known at one loop. So now we have a prediction of quantum gravity in this limit to seven loops. Okay. Uh and good luck if you have an AI maybe it can do that calculation. Um so I want to end I mean these are very baby steps. We don’t know how to describe the graviton yet. But now there’s a clue that maybe gravity is after all rather simple. You’ve got to find some hidden symmetry within quadratic gravity which will eliminate the ghosts. Okay. And that’s all you have to do because this theory is just waiting there to be used to describe gravity. So I think I’m finished. Thank you. Thank you Neil for the wonderful glowquin.