 Okay, good afternoon everybody. Okay. Good afternoon. I Think we can get started now so it's a Pleasure for me to welcome the speaker for today Professor Raman Sundaram This colloquium is being held in conjunction with the Summer school on sorry on the summer school on particle physics For which all of you many of you are here and it's really nice to see I was told that there are hundred and eighty participants from 50 countries So it's really wonderful to see all of you, especially after the covid time. It's good to see full full house Let me say a few words about Raman he's the John told chair and distinguished university professor of physics at the University of Maryland College Park He's also the director of the Maryland Center for Fundamental Physics He works on theoretical particle physics Primarily the structure of fundamental forces and their connections with possible extensions including supersymmetry and extra dimensions He also studies their Implications for early universe very very early universe So I would see that his research kind of provides theoretical templates for a broad range of Experiments from the Sun Hadron Collider to precision cosmological measurements Raman is a fellow of the American physical Society as well as the American Association for the Advancement of Science is a Distinguished visiting chair at perimeter and he was formerly the Moore fellow at Caltech In 2019 he was awarded the Sakurai Prize for theoretical particle physics of the APS together with his former collaborator Lisa Randall from Harvard for their pioneering work, which is now known as a Randall Sundaram Models of higher dimensional space time and I will just quickly read the citation for you For creative contributions to physics beyond the standard model in particular the discovery that warped extra dimensions of space can solve the hierarchy puzzle Which has had a tremendous impact on searches at the large Hadron Collider So today's talk will be on cosmology and unification Welcome Raman, and it will be moderated by my colleague Professor Giovanni Vallabra. Thank you. Thank you. Thank you You can hear the mic right? Okay So let me start So this is a talk which is at the intersection of doing extreme cosmological measurements and learning about cosmology in the in extreme circumstances basically inflationary cosmology as well as particle physics in a certain extreme sense that I'll make clear and really that's just pointing to the excuse that the experiments that are relevant to this intersection are extremely challenging and The kind of thing that will get done on the decade or decades long time scale not next year Okay, so that that one has to be patient and stay in shape Okay, so I Guess this is an obligatory set of I didn't none of this means anything to you So I will I'm gonna skip the outline so So so again because I was assuming a diverse audience and not necessarily everybody is part of our school I just wanted to start with the basics here this is a picture of relativistic space time with space in the horizontal direction time in the vertical direction and These are the world lines of typical particles that you're familiar with So I've done everything in the right units light seconds for distance and seconds for time So that a light ray travels at the speed of light and so it has a trajectory in space time that looks like this 45 degree line Everything else travels slower massive particles travel slower And so this is a picture of two massive particles which have some force they bounce off each other and then travel off in this way and Of course relativistic space time mixes space and time in some way And so you can ask when things can go backward and forward in space why they can't go backward and forward in time and Indeed that would look like this. Okay So there is something that stops this from happening without quantum mechanics and that is yeah relativity does make space and time but if you look at this Proposed trajectory where this this particle bounces off this particle and bounces back in time And this one comes from the future and bounces forward in time You see that Somewhere you have to you have to go faster than the speed of light. Okay somewhere here I would have to violate the rules that I just gave you on the previous slide and Indeed the only way that could happen is if the concept of these trajectories these very classical-looking world lines Stop making sense and indeed because of Heisenberg's uncertainty principle on in regions of space time of order this size This concept of these particle trajectories with well-defined velocity and position that allows me to draw the picture Breaks down and so that's the one place the one region where you can suddenly blur the rules and And actually execute what I'm drawing. Okay, and indeed it's not just that it can happen It does happen whatever can happen in quantum mechanics must happen. Okay And so in quantum mechanics and quantum field theory you can create new particles. It's alchemy Okay, it's you can create you can smash together boring particles like electrons and positrons or protons and antiproton You can create completely new things. Okay, and the only price tag is that you have to be able to afford the The the mass of these particles the the mass of the exotic particles that you might produce You have to put in e equals mc squared and speed of light is a big number So these are costly in energy But on the other hand it can be done and therefore of course it should be done and it is done at the large Hadron collider the latest and the greatest of the particle colliders that humans have built the Hadron being in particular the proton and So far underground Across the Franco-Swiss border. We are scattering Where's my pointer there it is We are we are scattering protons. We are colliding protons and inside the protons are gluons and the the energy of the large Hadron collider the LHC is 14,000 times larger than the rest energy of the proton the mass of the proton and so there's a big budget in Terms of energy and using it we can produce things like top quarks and these top quarks going backward in time Are there antiparticles or antitop quarks? And so we are producing top quarks and antitop quarks with huge masses but easily affordable at the large Hadron collider and And and doing exotic physics in this way in particular Most famously These top quarks by being created and then even being destroyed and annihilating each other or basically a circle in space time Can can then spit off things like the Higgs boson which was discovered a decade ago by this kind of process and here is one of the CMS detector with a candidate event of this kind of scattering where there's a very messy set of Byproducts, but sitting in there is one of as the one of the decay products of the Higgs boson into two photons Okay, which are these these arms? And the Higgs boson is of course a not just a new particle not a random new particle It's really the missing link in the unification of electromagnetism in the weak nuclear force into the electroweak theory So it's one of the great discoveries in science And the LHC is continuing of course It is looking for things like as exotic Targets like dark matter particles or the particles that determine why we have more matter than antimatter in the universe or Exitations of new dimensions or of space-time or super symmetry Okay, so there are all these exotic things that particle physicists are excited and to hunt for Which can be pursued with this Mantra of E equals mc squared Okay Give me lots of energy concentrate it in a small region inside that region where Heisenberg's uncertainty principle doesn't stop particles from going backward in time And see what you can create in a strange way you're bringing from the future what you want Okay, and and so it is magic Now as all I don't know what your backgrounds are but everybody who has some Ancestry which has a you know ancient mythology will know that all the forces of nature are secretly gods and all of the gods are Related, okay, and and and that turns out to be exactly true Okay, so this is the family tree of the fundamental forces of physics and Time is going down this way and if you want temperature is going up this way and the Big Bang started at some point and If you want energy is going up this way, okay, or temperature however you wish And like all family trees there may be some relatives that you've forgotten you had or you've or you'd rather forget and And so so in this very logarithmic scale you see the energy the vast huge energy of the LHC is down here and yet our Ambitions go all the way to the so-called Planck scale which is made out of these fundamental constants and in particular Newton's constant of gravity And it's the dividing line between particle physics down here And if you go to particles that were more massive than that they would really be essentially black holes, okay? So this is the entire map of particle physics as it possibly could be and like all family trees We are very clear about maybe our own selves and our close relatives and other says a little unclear about Distant relatives and and less clear about exactly our ancestry so most of what you see down the bottom is Well known we like we think we are it and we we know who our relatives are and some of these other things Get more speculative as I go in the vertical direction. So it's not like we actually know all of this It's just like all myth, you know all great, you know kings and queens They create their own mythological ancestry to make it sound impressive well This is the one that vaguely fits what we think we know, but it's more speculative up here So you'd really like to do experiments, but here we are stuck with the LHC down here, okay? and There's an interesting arena where Gravitational wave cosmology, which I'll mention at the end of the talk Can probe to even higher energy scales than the LHC, but in a very indirect way But I will be talking about this possibility of cosmological collider physics Using the energies that were available in the very early universe to do the magic of equals mc2 and To probe super high energies, okay in this family tree and see what we can find can we find more of our ancestors? directly And and I want to explain the plot by which we can do that, okay? It'll take some luck, but the fact that it could even be contemplated as an experimental setup is to me absolutely mind-blowing, okay? Okay, so here's a picture of the expanding universe Here's time and space the way I've depicted that I've made space a little more spacious by Extending it in the horizontal direction There are my picture of galaxies and Of course the arrows tell you that they are getting further away from each other The universe of space is expanding this rubber sheet of space is expanding. That's the expanding universe Here if it's expanding meaning the galaxies are getting further away tomorrow Then if you go back in time Everything is getting crushed and at some point Everything is merging together all the empty space between galaxies and the space between stars It's all getting smushed together and you end up with an incredibly dense and incredibly hot Cosmic soup of elementary particles and that's what I've drawn here And then if you keep using the laws of general relativity which tell you about how this universe expands But you go in the reverse direction to look at our past You find that you hit a mathematical singularity where you no longer know how to trust the laws that we've seen Where the densities and energies and temperatures they all go to infinity and that's roughly what we mean by the big bang But before we get to the big bang. We really don't know what we're talking about. Okay, so that's what the big bang represents This mysterious dawn of time Okay, so But you'd like to know what happened at the beginning of the universe you'd like to know something more about it and indeed It's not just a philosophical question. There's a kind of scientific question associated with it Which is we can take photographs like actually the universe took a selfie at The 400,000 years after it was born 400,000 years after the big bang the universe took a selfie. How did it do it? Okay Well the cosmic soup at some point got cool enough That ionized particles in the atom in the plasma ionized at very high temperature electrons and proton Eventually form neutral atoms and once they form neutral atoms the cosmic soup became transparent to light And so the photons in this soup suddenly started to travel in straight lines And that means that at that juncture around 400,000 years after the big bang the light rays Started to travel in straight lines and we can directly get a photograph of this Now I've drawn it as a circle, but of course it's really a sphere, right? It's the celestial sphere and we get a photograph going back there of these photons which after red-shifting today Are coming to us in the microwave and this is if I take the four-pi map of the universe and put it on the screen This is the cosmic the famous cosmic microwave background photograph of the Infant universe, okay, it's a selfie in that sense And I have not doctored the image So if you have got another image in your head put it away. This is this is the actual thing, okay? Great so we have this picture where interesting structure has emerged Galaxies you me stars voids all this interesting stuff to emerge a universe is clearly a very differentiated place today But in the early universe it seems like an undifferentiated blob And I somehow I sometimes liken this to this question in biology of the Development of the embryo the so-called differentiation of the embryo that this blob like baby Has to turn into you know the hands and the feet and the and there's a question. How does it? Who makes those calls? Okay, so we have that kind of question here And yet our attempt to answer of what's going on in the initial conditions is is is barred by the big bang by this Mathematical singularity and physical singularity where we've completely lost control of all the laws of nature Okay, so we'd like a theory of initial conditions and part of what's driving the big bang when you go in reverse is all the matter and radiation itself When done in reverse is what is making general relativity? curve space infinitely at a finite time and Screwing up our chances of a theory of initial conditions So if only as we go back in time, could we just get rid of the matter and radiation? Then we wouldn't have to have that big bang. Okay, so is that possible? Well, we just discovered I just told you that matter and radiation matter and radiation But in particular I showed you matter can get created Right, so maybe if we go in reverse we can uncreate it and and then avoid this big bang and indeed you can and And that's related to this famous paradigm called inflation Okay, which is not though. I haven't explained the word inflation yet I just want to draw what is the hope the hope for plot line Okay, the plot line is that at this at even even before we had all the Cosmic soup of elementary particles Before that these particles didn't exist or at least they didn't exist in large numbers and were created By some by equals mc squared. There was actually a moment or time of creation where you were creating all the stuff Okay, and and therefore before that since it's not there you can dodge the big bang singularity and still have control oops you can still have control over Studying general relativity in this regime and and hopefully come up with a theory of the origin of Stuff and and and structure In particular we'd like to describe this process, okay, but of course to create these particles you need E equals mc squared who is providing the energy if you want to do all this creation So here is the simple plot line of the inflationary theory or paradigm It's in an analogy to this very simple picture in ordinary space Where this is space and this is sort of I don't know a cliff edge Okay, your wall a ball is rolling along a gently inclined cliff. Oh, sorry plateau and it rolls slowly Not much seems to be happening and then it falls off the cliff and that gives a tons of a kinetic energy It's converted its potential energy into kinetic energy now. We've got lots of energy great Okay, you can actually have colliders built like this just roll boulders off cliffs and have them collide So we want to do that, but we want to do it throughout the universe. So instead of thinking of x as Some actual direction in space think of it as some direction in some abstract space so called field space Which I'll just call Phi and yet there is the same kind of potential That we're contemplating where everywhere Phi is everywhere Okay, it's some other abstract quantity which falls off a cliff in this abstract space and the kinetic energy It picks up gives the energy that so-called reheats the universe reheating meaning it produces It creates three equals MC squared all the particles that you and I are made of and the radiation as well, okay? Great so Uh What did I want? Yeah, I just want to point down here. So this Phi the rolling the slowly rolling of this Phi is Like a clock and while it's slowly rolling in a sense the universe is asleep. Okay but then it Falls it has violent energy the energy of this equals MC squared can and must create particles and The universe begins. Okay, that fills in what really was behind the Big Bang And in that sense metaphorically the universe wakes up, okay? But this clock Phi of t in relativity. There's no such thing as a rigid object This this idea of a clock that's extended over all of space and it's absolutely Synchronized it doesn't exist in relativity everything has to happen locally Nothing should travel fast in the speed of light There's no rigid object where I do this and the other end moves automatically everything has to happen through the speed of light Which means that this clock must be a field it must depend on both space and time in other words It's not like there's a single clock for the entire universe It's not like there's a single clock for the entire universe there must be clocks Everywhere in the universe and at best we could say that we hope they're approximately synchronized so that the universe initially looks about as Homogeneous and boring as can be very much like the picture of the CMB. Okay So Yeah So what does the universe look like in this Sleeping time, okay where the universe is is Not yet produced all of the particles that we see well There is still something in the universe, which is the energy on the plateau. Okay, the plateau has a big energy everywhere in space and And that gravitates all forms of energy gravitate including that potential energy and the Way that it gravitates is that it creates a certain particular kind of expanding universe namely this famous type of Thing where the ordinary sense of space, okay, the usual Pythagorean theorem is Distance is is is expanded exponentially so it's an exponential expansion as a function of time Where this H is approximately constant? The H is the Hubble parameter during inflation and it is given in terms of the energy in the plateau the potential And then these fundamental constants. Okay, so this sets up a Rapidly and accelerating expansion of the universe But but this the scale H may be very very large. We'll talk about it in a bit and This phi this clock field is called the inflaton field because the universe is said to be inflating this incredibly rapid accelerating universe is called inflation and inflationary space time and And the field that's the clock which is actually telling you when to stop Inflating is is called the inflaton field. Okay Right So here is the picture. I'm trying to show you so far what we've said is there is this clock field Which early in time is is on this plateau and just slowly creeping along and then at some point it falls off the cliff and The energy of that is used to reheat the universe in this e equals mc squared way And then we get off to the rest of the evolution of the universe, okay But what's interesting are all the quantum subtleties, okay So this By the way, the name of this space-time that this inflating space-time is approximates a famous classic solution of general relativity known as decider space-time, but You see There is an energy even during even while I'm just slowly creeping along on the plateau There is a energy given by there's a there's something moving What's moving is that the universe is expanding exponentially and this Hubble parameter Defines a rate of expansion. It has units of one over a second or something, right? So it has it it it's it's defining a rate of expansion Which secretly when a multiply by h bar defines a kind of characteristic energy It's the energy of expanding space. Maybe nothing in it But the space is expanding and it carries an energy So this is a very subtle form of energy But all energy is capable of the miracle of e equals mc squared So Secretly at least at this h bar level quantum mechanical level the universe even in this time of so-called sleeping or during inflation is secretly quantum mechanically creating particles and fluctuate or in a related language Creating quantum fluctuations in fields. Okay, so but it's got an interesting pattern, which is that you're sort of creating You're creating Quantum fluctuations and you're creating quantum particles Then the universe is expanding and diluting Exponentially and then I'm breaking it into steps like in chess, but it's all happening simultaneously And then you're creating a little bit more Fluctuations and then you're expanding and diluting and you're repeating this, okay And so you can ask what kind of pattern would that create? and the answer is a Fractal pattern, okay? Because this this way of drawing pictures is self-similar Okay, where you draw a certain kind of shape and then you stretch it out And then you draw another shape of the same side of the same shape, but then expand it out and so on But but it's a random fractal because quantum mechanics is the creative process and quantum mechanics famously has Probabilities, okay, so it's a kind of random crop fractal, but roughly speaking it looks spatially self-similar So the pattern you create in space would be something which looks like if you zoomed out and zoomed in it would look roughly the same okay, and Yeah, so we often called it that just I can read my own slides here We call it scale invariant, okay? So that's interesting that means that the picture looks more like this that This sort of trace level of quantum quantum mechanical particle creation. Well, it can create Inflatons the particle that makes up the particle that is the quantum of the inflaton field It can create those particles and there that's what I'm drawing here in green And you can think of those as quantum mechanical fluctuations of the inflaton field now the inflaton field is a set of clocks which Classically I was treating as perfectly synchronized, but these quantum fluctuations now These inflecton particles added to this classical field are now De-synchronizing the clock in a random way So the clock field is no longer perfectly synchronous across the universe in particular this reheating time when The universe wakes up is no longer happening in a perfectly Synchronous way at different places. It's happening later or earlier because of these quantum fluctuations And so this reheating surface. It's a surface. It's a three-dimensional surface in four-dimensional space time This surface at which the universe wakes up is a wrinkly surface And therefore it gives rise to a wrinkly cosmic soup with density fluctuations here and there because The reheating process has been Advanced or retarded in time, okay But what pattern do we expect well the pattern of these wrinkles should be some sort of random fractal, okay? and and we have a way of probing which is we can go to the cosmic microwave background and Just see whether if we look at this picture whether we see these kind of Fractal like wrinkles and indeed famously we do but I showed you a picture that looked like that But if I increase the contrast by a hundred thousand then we see that actually in detail There are small small small one in ten to the five level Fluctuations in what is really say the temperature of the cosmic soup. That's what you're really seeing At the in the early universe and we see they're there and roughly speaking It is a kind of fractal image in fact in particular if you undo many of the features if you can sort of Look at this in terms of angular scale You can look at what this looks like on different angular scales or just study it as a function of distance on the sky Okay, and there are features there, but these features we can understand as the late-time processing They were not originally there at the time of reheating We can understand that as a result of Newton's laws and many other pieces of physics that we do understand And in fact if you wind the movie back using the laws of nature we understand and you wind the movie back and ask What does this picture look like at the at the actual reheating time? it looks very much like a Random fractal. Okay, that's it already looks like a random fact fractals with a naked eye But in detail it really looks like a random fractal And it really looks approximately scale invariant as inflationary theory would predict And it has these sort of Gaussian or two-point correlations just correlations from the fact that I'm producing essentially free Inflatons that correlate What the clock here and the clock here how they're getting desynchronized and we can study those Correlators by just looking at temperature fluctuations in the cosmic microwave background map The data currently would say that the Hubble scale the scale of inflation could be as big as Five times ten to the thirteen gv Which to put in perspective remember it Hubble is the energy source for particle creation in during inflation And it's a but that scale there is about ten to the ten time ten orders of magnitude above the LHC energy So as a kind of energy source for particle creation It is vastly beyond anything that humans know to do currently, okay? And similarly if we go and look at galaxy distributions or the distribution of galaxy clusters in the universe and survey that Again, those are reflections on the largest scales. These are reflections of this wrinkly reheating reheating surface Okay, which were due to quantum fluctuations during inflation and again we get a kind of random fractal like Appearance and again if we wind the movie back to the reheating time that it is consistent with a kind of Reheating surface which was a random fractal which was approximately scale invariant, okay? Okay, so Here I should I've given away. I've given away the question though Here's the thing two-point functions which are scale invariant don't they're very interesting but Not super interesting, okay, there's only so much a two-point correlator can tell us But this idea that you are doing Quantum mechanical creation and then you create things and they live their little lives and die During inflation and then you create again and then they create Like the fact that you have the power to create particles at these vastly high energies says that Interesting things are going on there. Okay, we are communing with the gods right back at those times so So and and and the interesting thing is that these patterns that we are seeing today and with some precision Right these kind of random fractals hidden in their statistics is This is a kind of record of what happened during inflation What I want to put your mind on is that it is a kind of What I'll call a time hologram Meaning we see a static picture today of where the galaxies are distributed or a static picture of what this CMB looks like but within that static picture is a videotape of actual movement During the past so you can recreate time What happened not just by taking photographs, but actually getting a record of what's happened what of objects moving, okay? So it's a bit like It's a bit like So here is a picture where something is Created baby and then The and then the expansion happens the baby keeps the picture of this baby Somehow is imprinted somebody took a photograph, but the photograph keeps expanding okay, and then the baby grows into this little boy and and the From that time the little boy the picture of the little boy keeps expanding Okay, but not as much as the baby because the baby has had more time to expand and then the little boy grows into me and and and Then that continues to expand but has had less time to expand and all of this is being imprinted in What I'm about to show you will be imprinted on the fossil records that we have Okay, and and and you might say wow if I look at the false I just I just showed you pictures of the fossil record. I did not see that Okay, and and part of the difficulty is That everything that can happen just keeps happening. It's a little but it's a it's not identical But it's a little bit like many world's quantum mechanics where every quantum thing that can happen keeps on happening It's like variations here and there and so, you know Little little baby ramen is being produced later and expanding from there And it's and it's all overlaid right in this very scale invariant So when you get a scale invariant mess when you put it all together and the job is to decode that, okay? So how can how do we even see that? Okay? How do we see what's going on? and And so let me just show you a process of quantum creation So here for example is a heavy particle something with mass of order Hubble which might be ten orders of magnitude beyond the LHC ability to create that particle But it's being pair-created. It's being created by this process e equals mc squared coupled with quantum mechanics And and then it's living its life So one one arm what the particle for example, it's living its life and then decays and It decays let's say it decays into a pair of those special particles the clock particles the inflaton particles okay, so there it is it's decaying into these inflaton particles and It's anti particle is going to some different time and then it's decaying into it to another pair of inflaton particles and Now these inflaton particles are secretly fluctuations in the clocks. It's So now I'm De synchronizing the clocks in a way that's sensitive to the fact that this heavy particle was created okay, and And so the clock is getting wrinkled in a way that's showing up at these points 1 2 3 and 4 the place where these Inflatons go 1 2 3 and 4 and somehow we can study those correlations in how the map got wrinkled by studying the children of the map namely galaxy Galaxy distributions or CMB statistics we can study that by looking at these higher point correlators the so-called non Gaussian correlators Today okay, we have to do a little bit of unwinding to get the map here to look like the map here But we know how in principle we know how to do these calculations, okay? So What are you supposed to I I made a strong claim that you're reading you're not just going to get snapshots of the past You're actually going to get videotape and you can play the videotape and watch your ancestors moving around you know Dinosaurs moving around or whatever it is. Okay, so so let's see that Just to make it slightly easier I you can actually just get away with three point correlators because one of the Inflatons can just merge into the classical background in the there is a classical Inflaton field after all the synchronized field so you can always do that So this is a tiny detail, but you can get away with three point correlators Okay, so this is the subject of primordial non-Gaussianities, okay, but it's very simple. It's basically studying this three point Density correlator in whatever fossil evidence you have like the large-scale structure of galaxies Distributions or the cosmic microwave background or whatever And you're just for your transforming it because you want to take advantage of translation and variance And so these K's are just the different wave vectors associated to the three positions and that defines a kind of object F You like guess it's called a by-spectrum The words don't matter and this delta function is just keeping track of translation and variance or momentum conservation To say that k1 plus k2 plus k3 equals zero and therefore you can usefully say that the argument of this function The fossil evidence we can encode it by doing this for your transformation into functions of these triangles Okay, triangles in momentum space Which is an interesting kind of function function of triangles But actually if you have approximately scale in variance, you don't even care about the Size of the triangle. You're really just interested in the shape of the triangle So this is a very beautiful kind of function starting from very practical considerations We've ended up with a function which just depends on the shapes of triangles, okay? and So this is sort of the raw data that we would need and and this little F I just give it to you to say it's the going rate It's like what if you chose function of an equilateral triangle the function of the equilateral triangle is just some reference for what is the going rate of This kind of thing, but of course you would like to see the entire function, okay? Okay, so here's sort of the punchline of this mechanism Which I was not a pioneer of I'm not taking credit for what I'm about to say, but it is the most brilliant slide in the talk Okay, so Just a warning. I'm just going to apply it in some simple way But but here it is distance remember this expanding exponentially expanding space-time is given by sort of the nominal Coordinates you might plonk a few galaxies down and say this galaxy is at zero zero zero This is galaxy at zero zero one this galaxy, so you just plonk them down and call those the coordinates But they will expand and so the distance between them will grow like not the coordinate distance By Pythagoras's theorem, but rather with this exponential expansion and so in terms of these wave vectors, right? Which are conjugate to space? That means that the the different k's are related to different times in in in this way, okay that the basically distance is You in fact you can see it here that the if I What should I do if I double if I double all lengths and I shift the time I Would get I don't I shift the time by H log 2 or whatever I will get back the same distance. Okay, so there's an invariance between shifting of Rescaling distance and shifting time. Okay, that's a symmetry of this space time And so we can use that to say that the I can think of two two different wave numbers k1 and k3 I can say that look at some point k1 will eventually redshift to have the same length as k3 Okay, so we can infer a time in this way or if you want ratios of ratios of wave vector Magnitudes can be thought of as The exponential of the time differences. Okay, so that means that in terms of this function of The wave vectors the non-Gaussianity What you find when you do one of these quantum calculations? Let's not talk about this right now Just trust me on this factor Is that you get terms that look like this? Which is not hard to understand if you created a particle if you created this pair of particles Let's say that one decayed promptly and the other one for whatever reason traveled some amount of time delta t Then you would expect from quantum mechanics that you would get The usual phase factor for quantum evolution e to the I energy times time That's what quantum mechanics says That's what it means for the particle to walk along quantum mechanically walking or just existing is Is that given by that phase factor and here? That if the particle is approximately at rest to keep it simple then its energy is just its rest energy mc squared Okay, you can include it moving if you want to right, but But using this To to solve for time if I put delta t and solve for delta t in terms of k1 and k3. I get this Okay, so I get this funny non-analytic Dependence on the ratio k1 over k3 where the index the exponent is an imaginary exponent i times m over h Okay So that means that if I have access to this f in the data. I can look for these kind of non-analytic or oscillatory behaviors as I look as a function of k1 and k3 now looking changing k1 and k3 Of course is just equivalent to moving around an r r1 r2 r3 I just sampled the data by changing the triangles on which I look at the correlators in the data and And basically I should be able to see this if I have sufficient precision then I should be able to see this and what I'm able To see because I control this ratio is I can I can watch the wave function of this ancient particle Moving along and in particular I can measure its mass, right? I can see its existence Okay, so so in this way you can do particle propagation you can see it you can measure its mass and and indeed due to these Very famous authors right here. You can even measure its spin, okay? But there's a price tag you you've got to have You've got to have mc squared You've got to have mc squared of order h because if m is much smaller than h Then you won't even sense this exponent, which is the entire Kernel of what you want if m is much bigger than h then this factor which I haven't Haven't explained, but I'll make intuitive right now Will kill you okay if m is too much bigger than h of course. This is roughly intuitive I'll talk a little bit about it in a second, but this is roughly intuitive because I'm saying h is the energy Available to create particles of mass m in some sloppy way. Well, this is that sloppy way It says that If h is of order m or m is of order h that it is You can unsuppressedly have the energy to create Particles of mass m if if m is much bigger than h you are outside the energy budget of the universe It doesn't produce the particle. Okay, it just does it just when I it's not a yes or no question There's a smooth function. It's this exponential, okay? I Need to at least have one confession slide to say that this requires extreme precision This is why it will be an ambitious undertaking to actually realize this with real experiments and actually see These ancient particles that are moving around and so on And that's because we are calculating quantum mechanically but we only have one universe in which to make measurements and Usually quantum mechanics only tells you anything useful if you repeat the experiment over and over again Fortunately, we can repeat the experiment at least a finite many times in the following sense that for any triangle Where you want to measure? What is f of this triangle? There's an equivalent triangle by rotating it and even expanding and shrinking it because of scale invariance So in that sense you have many opportunities to effectively measure the same correlator statistically in a single universe Roughly speaking it is given by the more the sort of the larger your data set The the the the better your precision, okay? We do it you can compare to quantum mechanical calculations roughly given by this I told you what FNL is sort of the going rate So the precision on FNL can be given in this way It's useful to just see what experiments can do this are different types of experiments and this distance is sort of Radial distance from us or looking back into the universe or technically the redshift as you go out and so the CMB that I first started the talk with is sort of this two-dimensional map because it's Effectively happening at a specific time in the universe And then we have a two-dimensional maps in the celestial sphere and that's happening at this high redshift There we are entering Decade of high of high precision measurements of large scales galactic structure Where it is taken from relatively close by okay the galaxies that we can see and the late universe and Where the number of modes Dramatically increases on top of what the CMB can do like the plank data and the ultimate In this direction the ultimate sort of data set would be what's called high redshift 21 centimeter cosmology Which can probe a very three-dimensional looking? slab of Modes and where you get again a really vast improvement in principle Where you can get high precision in this FNL and the trouble the only trouble being exactly when it comes to fruition Okay, it's technically possible, but when is when do we actually do it? Keeping that in mind For a little later. I want to just give you in the last minutes an application Okay, I had to add the other word to my title unification who is worth looking for With you have this mega collider called the universe and of course I set you up I showed you the family tree and I said well, you know We want to see the gods before they gave birth to the sub gods Okay, and and so grand unification is the classic example of this For those who know particle theory. I'm talking about the simplest version. I'm currently working on Maybe the most promising version, which is supersymmetric grand unification But that takes me outside the concept of introduced. I'm going to talk about what's called non supersymmetric grand unification. Okay? So we know the three gods that we live with and are made out of namely electromagnetism the weak nuclear force and Qcd or the strong interactions and we see that they each have different types of charges There's electric charge here But already in the weak interactions there's a notion of weak iso-spin which has two kinds of charges Usually called up and down and then there is Qcd, which famously has the subtlety of three colors or three charges Refer to metaphorically at least as color red green blue. And so there are sort of these different types of colors floating around and What we see if we look at the charge assignments of the standard model particles is there's some sort of a pattern there at first sight It looks strange But if the right geniuses quickly inform you right starting from Puthi isn't salam and then going to Georgia and Glashow and so on You eventually discover that wait these are not randomly chosen charge assignments that the world has given us They seem to point to a common ancestor. It's like seeing the DNA of three different animals and saying wait I see a pattern. Okay. It's exactly like that. And so that already makes us suspect that there's a kind of common ancestor but a quantitative sign is to plot the strength the coupling strength of the three forces as We measure them in experiments and ask what happens if I look at the strength of these forces as I go to very high energies or very high temperatures where the Where they may have been, you know born from the same parent a unified parent a parent That doesn't make any distinction between its children. Okay, all the force fields are equivalent to any other force field Well in particular the strength of all the forces if that were true the strength of all the forces should should merge at some point and indeed the data Supplemented by the renormalization group for extrapolating to high energies where we haven't actually gone But mathematically extrapolating seems to show very roughly a kind of convergence definitely Bizarre to see that happen if it weren't for some sort of unification. So there's a grand target here Because the scale at which this is happening is of you know, depending on exactly how this Try, you know, this this is only an approximate merging So there must be a story behind that but whatever it is It might happen in the window of around 10 to the 13 10 to the 14 gv And maybe we can just go explore that right so If if we're lucky and the scale of inflation is that high then maybe the cosmological collider can just take us there And we can see what's going on Okay, so the simplest theory of this sort that is actually allowed by data is Is one that involves extra dimensions and in a very simple way. It's called orbithold unification and And again, the idea is that there's a higher-dimensional Grand unified theory where all force fields are equivalent There are symmetries that relate every force field to every other force It will be indistinguishable and they all live in this higher-dimensional space time But one of the dimensions is just an interval and Microscopically small interval, but if you zoom in it's an interval and it's in the it's in the higher-dimensional space that all All of the fields look equivalent, but there are boundaries at the end of the interval and These boundaries make a distinction the boundaries say you are strong. You are weak. You are electromagnet It makes those calls, okay? But in the bulk it doesn't okay, and this is sort of the simplest so so of course at very long distances or low energies or low Temperatures you don't see this unified Intermediate step in fact you don't even see the extra dimension. You're blind to it. So this is you Sandwiched in this universe at the size L, which is this L. Okay, and you're saying what extra dimension? What are you talking about unification? That's weak. This is strong this electromagnet I don't know you're very very sensitive to the boundary conditions because you are not shrinking yourself and looking at what life would be like here, okay? But we can ask what kind of predictions there are for that and and and you know is there a way to test it and And this is the the basic idea that if you whenever you're in a you know in a compact space in quantum mechanics You find a discrete set of energy levels like the hydrogen atom or the particle in a box or whatever it is and the analog of that in this problem are called colloquial excitations and The way of seeing inside this is to have the energy just look for these colloquial excitations like any wave in quantum mechanics the energy just like a photon the energy of a photon is h Speed of light divided by the wavelength, but in a box the wavelengths are quantized and so oops Wavelengths are quantized and if this theory is the theory of unification the one I just I'm telling you here quickly Then the energy quantization scale is the unification scale This 10 to the 13 gv or so that we can hope to reach with a cosmological collider So basically you get this kind of discrete spectrum of energy equals integer times, you know Hc over L right this 10 to the 13 gv and so you get a tower of States like any particle in a box problem that you could hope to see if you only have the energy to go there And and you would say well I should I should look for these extra gauge particles associated like there should be heavier Particles that reflect this unified symmetry, okay? In this talk given the very short time I have I will just talk about something a kind of attendant thing wherever there's an extra dimension of space there should also be extra general relativity general relativity is the Dynamics of space itself space time so in particular there should also be colloquial excitations of the graviton and It's easiest for for this talk to just talk about just well can we at least see the colloquial graviton? That's even more exotic than a colluzacline gauge boson. Okay, so let's let's see And indeed you can The story looks very much like the story. I showed you for the generic vanilla plot of how to see particles in cosmological collider physics by looking at the three-point correlators But you can do it in this case where you're producing colluzacline Exitations of the graviton with at energies of 10 to the 13 gv And so look it's not all squiggly pictures. You can actually do a calculation I can't my student at the time did the calculation, but but it can be done It can be done and then ordinary humans can check it and Give him his PhD But but here is here is sort of mass as a over over Hubble Okay, 10 to the 13 gv and here is the strength of the non-Gaussianities and Remember that sort of 10 to the minus 4 is like what humans what what even the best map of the universe? 21 centimeter cosmology could achieve and you can see that if we're very lucky You can be above that you can be well above that if you're very unlucky. You are you're you're killed, okay? So with some luck It's super exciting that you could suddenly see this spin-2 particle this this theta dependence Where to go there that angle theta which is that angle in the triangle theta is actually That theta dependence tells you that you're seeing a spin-2 particle Which is what we associate with gravity as opposed to spin one particles like photons or gluons, okay? So it's something you could do and a lot I'll say this very quickly a lot of the rest of my research over the last few years has been looking into various mechanisms that can make it more you where you need less luck and There are mechanisms where you can go further and so on so in a sense this this exponential Suppression that I was pointing to earlier when you do the calculations. It is an intuitive thing it's like a Boltzmann weight in in in Statistical field theory where the temperature that's associated with this Boltzmann weight is basically the Hawking temperature of Decider space okay famous temperature, which is basically Hubble So this energy that Hubble is giving you is very much like a temperature in a certain sense It is a temperature and so it doesn't allow you to produce e equals mc squared much bigger than the temperature Okay, but just like in thermodynamics. You can always Bias things by adding a chemical potential to your temperature Then you will have larger numbers of particles then you would normally be able to afford and indeed there are mechanisms That have been worked on before and then we have generalized and I think the simplest and most robust way to allow you to have Even greater particle production than what I've reviewed so far Where for example here is producing massive spin zero particles where You're able you you can go you can actually go to mc. Squared's far above Hubble for example This is 40 Hubble without having Boltzmann suppression kill you Or five Hubble and and as a function of this k1 over k3 you can see this these oscillations you're seeing here are literally this is literally Time in the old you know in the inflationary universe being but I'm plotting it on a static map of the universe Where I'm just looking at it in Fourier space, but what it is charting what you are seeing are waves propagating This is not data by the way, but this is what the data would look like it would look like Particles propagating in the ancient universe okay with masses which could be at the scale of gran unified theories So this is getting you this mechanism is getting you energies closer to 10 to the 15 gv Maximally, and you're slowly closing in on sort of the ultimate scale of particle physics, which is the so-called Planck scale I'll say the last thing quickly and because I may be only deal with it in questions we've also looked into another kind of map of the universe which happens because The cosmic soup like all soups can boil if you go to high temperatures So one possibility if you go beyond the standard model is that as you go back in time You hit a time where the cosmic soup boils and you have bubbles and these bubbles turn out to be a very efficient way of producing Gravitational waves the collisions of these bubbles and the way they stir the soup is a violent way that of which Produces gravitational waves whose sources energy Again, and these gravitational waves can be seen by future gravitational wave detectors In fact my student my former student was saying maybe we are seeing already a stochastic Well, there's a rumor about nanograph. Let me not say anything Anyway, so so these stochastic maps you would get a stochastic map of gravitational waves very Analogous to the cosmic microwave background of photons and in these that means you've got another map And so you could try to do cosmological collider physics with that and since I've totally run out of time That allows you to it turns out that allows you to probe things that are not possible with the existing maps I won't explain why in particular allows you to look for Cosmological collider physics with just two point functions You don't have to even go to three point functions in a way that would be already ruled out with the cosmic microwave background But it's alive and well with these gravitational wave maps Where and you can sort of compare and it is Possible it's possible to do these things just barely within anticipated sensitivities of future Gravitational wave detectors again requiring a heroic effort may not be the next generation But what is possible in your lifetimes at least okay? Great, so I better stop Cosmological collider physics has huge potential But it is hugely ambitious in the sense that there are a lot of challenges I barely scratch the surface of telling you the challenges it requires some luck to see some of these new incredible, you know the gods basically But exactly how much luck is still it being worked out? We're finding new mechanisms that may require less luck that are more robust And so there's much to do both experimentally to realize this To do a lot of the winding of the movie back to the reheating surface So that all the late-time effects that are not relevant to this program Removed that's a hugely difficult set of calculations and Of course to sort of develop templates and so on that can be used in a practical way, but I'll stop there. Thank you is it possible for Inflation that could be potentially explained by a UV complete top-down approach for instance like string there is it possible to like Place the brains in a certain way and obtain a certain Decisive stable background solution something like so you ask a controversial question, but indeed, I don't know 20 years ago or something there were a famous set of papers That had authors that all be I mean they all started KK something something something and so one of them was KK LMNT, okay Not to be confused with KK LT, which is related but something else So KK LMNT was doing exactly what you said and the claim was that they had enough control to strongly suggest that you could actually realize inflation from string theory with a assortment of brains in a certain way playing out in higher dimensions and I Understand the sort of general approach to Demonstrating that but I have to say there have been recent claims that some of these constructions Like that that it wasn't proof and that in some sense These are slightly out of control Calculations and and there are even recent claims that some of these Cannot be done in string theory, okay So this is goes under the the brand swamp land conjectures, okay Now where will that ultimately come out? I don't I don't know so I understand the basic idea of this sort of constructions along your lot the lines you discussed, but Whether they are completely Proven well definitely short of that and there is at least some controversy about it So you showed his graph of color the client gravitons is FNL versus M by what is what is M in that part? Those is M by its scale. Oh Is it just the mass now? Let me see so the Which this M That's the mass remember. We're identifying the mass of the colloquial and graviton with roughly speaking the scale of unification Now we don't know given the way these couplings converge. They didn't point to one particular place There's a little bit of slop there and and the theory explains why there can't be a little bit of slop, but Therefore we are sort of going to roughly the 10 to the 13 gv ballpark And but we need to scan the different possible unification scales, which are the possible masses of the Colloquial and graviton where I'm using units of Hubble so everything looks order one because I'm already dividing by Hubble assuming the maximal possible Hubble, which is 10 to the third you know a little bit a few times 10 to the 13 gv Yes, yes, there is so again you should think of The energy that's allowing you to produce particles is very much like a temperature the so-called Hawking temperature and Therefore what happens is as the mass gets bigger than Hubble, which is the temperature and masses the energy equals mc Squared when energy gets bigger than temperature the Boltzmann distribution Exponentially shuts off and that's what you're seeing there So that's absolutely what's going on and so looking for these other mechanisms that this is sort of using the vanilla Cosmological collider mechanism that I just showed you but a lot of my recent research has been looking at Mechanisms that allow you to evade such a sharp Of course if you're lucky you great you live right there boom It's okay, but but if you don't then you're unlucky and and the question is are there mechanisms in which You don't suffer that cost Hi, is there any tension with the idea that you have these massive particles Which are strongly coupled to the sufficiently strongly coupled to the inflaton To be observable, but also the stability of the inflaton potential required for Inflation yeah, so that's a good question the the kind of couplings that one is typically playing with are Ones that Are derivatives they only involve derivatives of the inflaton so if the inflaton shifts a little bit You don't notice it in the derivative of the inflaton so then radiative corrections or however you want to phrase it Do not spoil the flatness of the or the relative flatness of the inflaton potential and in particular the one that's used here is famously the coupling of gravitons to the inflaton which is absolutely fixed Equivalence principle all of that and that involves again if you is it's Derivatively coupled the the graviton derivatively couples to the inflaton if the inflaton happens to be Approximately massless or this potential is very flat then automatically gravity does the right thing right So that's all that went into this Thanks. I just have a quick question. So as we're going to cosmology for extra dimension Doesn't mean like in LHC. It's already very hard to see Yeah, so At the so the the scale at which the universe or the size of an extra dimension is in the most agnostic unbiased view Like if I were an experimentalist say then I would say It has not been fixed by any sharp consideration that we already have and so Let me look for extra dimensions where I can look for extra mention So there are certain kinds of extra dimensions which are not ruled out the so-called large extra dimension scenario where? The extra dimension could be as big as 10 microns Okay, which is almost macroscopic right and Experiments are looking for that and it's a very different kind of experiment. These are experiments that are looking for changes in Newton's law Using precision measurements of Newton's law, right? There are other Experiments so so then there are things like this where if you asked a typical string theorist, right? Where are the extra dimensions whether they say well, they're associated with string theory? I don't know exactly where that is, but it must be somewhere very high scales That would be something like this or in string unification, which is another scenario very similar to this orbital unification Then there would be extra dimensions like this at the scale of unification but there is a And of course everything in between in principle if I don't have a big theory bias, they're all allowed, but Especially in the lectures that I've been giving At the summer school there are the there's the scenario warped extra dimensions where If you tie it to particle physics problems like the hierarchy problem They would be things that would be more in the ballpark of LHC reach like there would be a theoretical reason Why they would be in that region region, but you could always just say I'm an experimentalist unless the theorist says I can prove to you that the extra dimensions are have to be this big or this big I will just look for them and off the top of it you might so the only thing to say is Should I think of extra dimensions like I think of UFOs? So obviously I should you know you could say well, there's nobody's told nobody's proved There's no aliens in fact. I recently had a journalist writing to me and asking if extra dimensions could be Explaining some of the sightings, but anyway That it could be extra like there could be UFOs let me spend all my time looking for UFOs Like that's the best thing I could do with my time is look for UFOs. Well, you'd say no, I have only one life to live Let me choose Motivated targets and so I should at least explain our extra dimensions motivated targets and I'm just gonna say my claim which is yes Extra dimensions very harmoniously tie with what we know of relativity They very tie they tie nicely with what we know of string theory They tie very much with the kind of thing I was lecturing about today, which is emergent extra dimensions extra dimensions can actually Be the result of strongly coupled theories They can be a kind of quantum mechanical illusion created by strongly coupled theories very much like protons are Created by strongly interacting quarks and gluons Whole a whole dimension can emerge in the same way So in many ways they are fascinating Enigmatic and motivated targets, so it's something to hear one question Yeah, so you already mentioned gravitational waves as a possible signature for these kind of High-energy particles. What will be the other most promising ones like? Experimental observables in for example the 21 centimeter experiments that you mentioned So among them you know here I talked about the unification of forces and You know if we look at the unification that we've already seen in experiments Which is the unification of just electromagnetism and the weak interactions into the electroweak force what you see is that at high energies the theory looks very unified all the force fields look comparable and at low energies They look like electromagnetism and weak interactions quite separate But and the particular the weak interactions look weak because their force carriers are heavy Okay, but in analogy in if a grand unified theory was true there would have to be heavier Force carriers which helped to complete the familiar force carriers to make this more symmetric and beautiful Family, okay so we can look for those so-called colluzacline gauge bosons, which are the Extra force carriers that would make the unified theory unified And we did that work the same co-author of my former student and Those are for example Targets that would also be things that one would want to see Currently Some of my current students and I are working on That's even more motivated case of super symmetric gran unified theories at even higher energies Another thing that I think is very exciting is I told you the story of the infoton somebody rolling on me and some clock Field that rolls off a cliff, but when you closely examine the dynamics of this clock field We don't actually know the dynamics. It's not like it's like the Higgs boson where we know many things by experiment it's a there are many classes of such theories of what the clock does and So you'd like to understand what is the actual dynamics where the universe wakes up the clock field, right and Many of them many plausible ones involve more than one field Okay, so there could be multiple fields and so on and indeed to get potentials that look like this right is difficult to do with one field It's it's easier to do if that is actually a shadow in a multi-dimensional field space So in if you invoke new principles new symmetries new fields to make a more realistic Story of inflation you'd like to see those particles those extra fields or extra particles associated with the dynamics of inflation In some of my work with former students Even those Can be in the right zone to be seen in cosmological collider physics So we might use cosmological collider physics to probe specific models of inflation for Associated particles not just the infleton but infleton plus some partner or partners. I have a very non-technical question So I quite like the analogy at the beginning with this particle family tree and I'd like to push a bit on this So typically I would say I know my parents and grandparents much better than my fifth cousin And so here it seemed that dark matter sort of branches off at some point But we don't really know what it is So could it be that the picture really should be extended back in dark matter branches of much earlier And there's something really much different than we say like some new fields or stuff like that Yeah, so indeed that picture that family tree I drew is was meant to be schematic It was accurate in terms of our immediate relatives like weak interaction strong interactions and things like that But indeed where I had those dark branches Yeah, these are dark branches and I put them in speculative places in the picture And we would love part of the exploration of fundamental physics today a huge part is the exploration of dark matter and in more generality dark sectors in other words all our other less known relatives and So indeed the branching off of those dark dark sector relatives can take place in a variety of ways and They're different attempts so one of the things cosmological collider physics can do is Since the creative process is happening through you know just space-time expansion everybody feels that and so Dark sectors may show up in that way right that they may Particles of dark sectors could be created in this way if they happen to couple to the infotain or any of the gent more generalized notions of This mechanism then they could also leave an imprint and we may be able to see them I should say that you can see what a vastly difficult enterprise It is by the fact that whatever you see you see a signal It doesn't come with a name tag saying I am significant. I am the particle of Granunification I am the you know, I am the particle predicted by ramen and not by xyz right so Claiming your Nobel Prize becomes hard right But it's a difficult thing to give the significant so you have like all detective work Yeah, you would have to be very lucky to get enough pieces of information to piece it together and to even understand if you were seeing a particle in the dark Sector that it was a particle in the dark sector and how it relates to us We may be lucky in certain ways that we have other ways of experimentally grappling with similar things So just as an example, you might say how could you ever have another way of getting? comparable information About this regime Unprecedented regime so just as a cute thing the first paper I wrote on this subject with the same author Shabik Shabik Kumar was to point out that even the standard model Where the masses of particles are only a thousand GV a hundred GV? Nothing like 10 to the 13 GV that during inflation There is a robust possibility that the part of the weak scale that we now say is order hundred GV At that time could well because of the curvature of space-time there could be added in fact quite robustly added corrections which raise the map the weak scale to 10 of the 13 GV in which case the particles that we are now producing at colliders Would actually be amazingly heavy in the in that time and would be Producible in this way and and there you might actually see some recognition Because while all their masses get changed the mass ratios don't so you might be able to recognize wait That mass ratio that mass ratio that way that reminds me of the standard model that I've seen at the LAC so Never say never that what this what this whole exercise taught me was that everything that you say look Ah, there's some things we'll never do we'll never get to how could we ever go up beyond thousand TV or whatever? The ingenuity of other people is a term the engineer of other people is so vast that I can never say what can't be done First just a comment I really love the the cartoons of your talk. Thank you Yeah, and I have two questions First what's the do we need a extra dimension for grand unification? Yeah, and the second questions You introduce these chemical potential To avoid suppression for this non-caucinity Do we expect I mean what's the meaning of chemical potential and do we expect it to be significant? Yeah, so two good questions First question was do we need an extra dimension? So it turns out that there's another probe a very indirect probe of grand unification in its original form when you don't have extra dimensions There in its in its original incarnations generalizing the Higgs mechanism it predicted proton decay and and But at these incredibly high energy scales of unification the prediction was the proton would be very long lived Certainly the age of the universe so none of you need to worry, but I'm made of something else, but but but But something that we can test by testing many many protons So so right now the non super symmetric grand unified theories in the standard incarnations would have already had too much proton decay for current experiments looking for proton decay and and so you definitely needed an a variant theory and these so-called orbit fold or extra dimensional theories are Able to completely avoid proton decay in a very simple way I won't explain here, but but a very simple way and they are reminiscent of what are called string unified theories where string unification Happens at the string scale where again, there's a very simple way This is sort of almost like the baby version of string unification where you completely avoid proton decay So the extra dimension is playing an important role in somehow setting that up at least that's what I would say Your second question Sorry about the chemical potential Oh, yeah, the chemical potential you see you're really looking for an energy source to do equals mc squared So the fact that space is just expanding with an energy source given by Hubble Was great, but now I want even more. I'm greedy, right? I want to go even to higher energies So it turns out that as you are In fact, it was really I gave it I gave it away with this incredibly simple formula If I throw away all the fundamental constants which looked like this Hubble squared is equal to g Newton times v of the plateau So this is Hubble G Newton is really small Okay, so that means that in order to get Hubble to be 10 of the 13 there needs to be an even bigger Energy source called this potential in other words this itself This is the gravitational back reaction to this energy and The gravitational back reaction is in a certain sense small because G Newton is small So if I could directly mine this energy myself, right then I would be in business now Unfortunately, it's like a battery. It's like a potential energy. It's just you're sitting on the plateau and it You can't just take it. However Associate this plateau cannot be exactly flat. I need a clock So it has to be rolling that means there has to be some small amount of kinetic energy but it turns out that The kinetic energy is small compared to the potential energy, but it is much bigger than Hubble Okay, so all I need is a way of mining the kinetic energy of the Inflaton So rather than relying purely on the expansion of space If I can directly couple to the Inflaton field a heavy particle not high a heavy particle If a heavy particle directly couples to the Inflaton field then there's a way of mining its kinetic energy and siphonic stealing a little bit in order to create particles in order to create the heavy particle and It shows up as a kind of chemical potential it shows up in the analogy with thinking of Hubble as a temperature It turns out that this mechanism. It's not obvious But it's true that this mechanism looks like what I was saying here very quickly as a kind of chemical potential term in the Boltzmann distribution Maybe it's time to to end here Invite to thank