 All right. Thank you very much. So, the standard model has a hierarchy problem, as everyone knows. The Higgs mass and 7 model is sensitive to physics of the ultraviolet. If you have some mass scale is very heavy, 7 Higgs particles coupled to them, the mass gets pushed up. And so far there have been essentially two broad classes of ways in which people have tried to address this. One is either through the introduction of either new symmetries or new dynamics at the electroweak scale. This is supersymmetry composite Higgs or say models of extra dimensions or something where field theory itself ends at the weak scale. All of these ways of solving this problem predict lots of new physics at the weak scale. And so far we haven't seen any evidence for any of that. The other approach has largely been an entropic kind of approach where we just say, well, you know, it's okay for some parameters in the world to be fine tuned because our existence is very dependent on them. And that is something that you can realize in context like the multiverse where there is a huge class of solutions possible. Here in the stock, I'm going to pursue a different line of inquiry to see if that might make sense. The idea basically is that the Higgs mass squared is not assumed always to be small. So, we would think that in the very early universe, the Higgs mass square is very, very different. It's some in particular very large value. And over time, the field changes and acquires a small value. And once it acquires that small value, it stays small for a long period of time, not for eternity, but for a long enough period of time that that's where we will actually end up. So this is kind of a dynamical solution as we like to call it, where the Higgs mass square is picked cosmologically rather than either tuning or through a symmetry. So if you wanted to do that, what would you have to do? The first thing you have to do is to make the Higgs mass square depend on a field, so it can actually change. It can't just be some constant value in the Lagrangian. Something must be able to change it. That field has to evolve in time in the early universe. And the basic idea is that the actual mass square will become eventually a small negative value. And when it becomes a small negative value, let's say from a large positive value, something interesting happens. There's an electromagnetic symmetry that actually breaks, and the Higgs mass square becomes slightly negative. And we're going to use the fact that the Higgs mass square, that the Higgs acquires of F, that the electromagnetic symmetry breaks, to essentially create a back reaction that prevents the field from changing anymore, right? And the change is sufficiently drastic that the weak scale is fixed until today. So the key point here is the following. Normally when you think about a scalar mass square, the point where the scalar mass goes to zero is not a point that is special from the point of view of symmetry, right? The mass being zero doesn't really give you extra symmetry. That's why you can't protect it with just extra symmetries. However, the mass going to zero is a point that is special from the point of view of dynamics because when the mass square is positive, that's a place where the scalar field has no VEV, while when the mass square becomes negative, that's a place where the scalar field acquires a VEV. So the fact that you acquire a VEV can be used to dynamically back react and thereby prevent the change of the field. So that's the basic idea. Now I'll present the caveats for what the solution is so far and what it's not. The solution so far is only technically natural. So there are small numbers in the problem that we will explicitly put by hand, but these small numbers are technically natural in that we don't know of anything that radiatively makes them big, right? But we haven't explained where the small numbers come from. They're just technically natural numbers. The solution will require large field excursions. They're going to be larger than the scale that cuts off the loops, okay? That's something that's an intrinsic part of our model and we will still work in the field, in a regime where the effective field theory is still valid and we will define that shortly how that happens. In this particular model that I'm talking about, this entire scanning, the place where the Higgs mass square changes will occur during a very long period of inflation, right? So all of this is happening during inflation when the field is acquiring this very small value. I'll comment later on whether or not this is really necessary. But for this particular model, all of the action is happening during inflation. Of course, it's not directly coupled to inflation. Inflation is sort of just its own sector, but the scanning occurs sort of during that period. And in the particular class of models that I'll talk about today, we can only push the cutoff up to about 10 to the 8 GeV, okay? So I'm not going to tell you what the theory is above that, but at least until 10 to the 8 GeV, we don't really have a whole lot of new physics at the LHC, right? The standard model, more or less. So here's the simplest model that we have. Our claim is that if you just have a standard model and to it you add the QCD axion and also a long period of inflation, we claim that is sufficient to solve the hierarchy problem through this cosmological mechanism. How does that work? So here's the Lagrangian and here's your standard Higgs. And you're going to assume the Higgs as a gigantic M, right? This mass M is not at the weak scale. It's at the cutoff of the theory, okay, where we think something else happens. So that M is some big scale. And then we add the QCD axion to this theory, which is just a standard like, you know, phi over f gg dual coupling. This is just the gluons of QCD. And of course, just a Higgs mass squared and a standard coupling of the QCD axion will not really solve the hierarchy problem. What we're going to do instead is that we're going to couple the axion field to the Higgs itself, the Higgs mass squared itself. So once you have this coupling, the value of the axion field determines or rather contributes to the mass of the Higgs squared itself, right? So the axion field is changing, then the Higgs mass square will change. That's a natural way to do this. So in terms of symmetries, the way you want to think about this is that this coupling of the axion preserves a continuous shift symmetry of the axion field. Of course, that continuous shift symmetry is broken completely by this parameter g, right? So any other term that I add here that involves breaking of the shift symmetry will always be proportional to g. That's the way of doing this period on counting. And importantly, this is not the standard axion, the PQ axion, which only has a finite field range. Here we will assume that the axion is a non-compact field. It's just some scalar field that can take a large field value. But with these sort of shift symmetries that are discreetly broken, that are broken only by this small coupling g. All right. So once I turn on this breaking of the shift symmetry by this coupling, that will of course automatically generate other terms. So in particular, I can close the Higgs loop and get a term that goes as g phi m squared, right? That's the cutoff of the theory again where the Higgs loops get cut off and additional terms like g squared, phi squared, etc, etc. So all those terms will be added as well. Not just this term, but everything else that is radiatively induced by it and things that you expect to be there. And of course, once QCD confines, the continuous shift symmetry of phi is broken into a discreet shift symmetry by non-perturbative effects. So that's still sitting right there, but you still have a discreet shift symmetry that is quite independent of the fact that that is completely broken by this small coupling g. So one can ask how big of a field value can you really expect in this theory before the effective field theory breaks down? And the answer to that question is that field values as big as m squared over g are okay, right? Basically, because if you have a continuous shift symmetry or even a discreet shift symmetry, the field value by itself doesn't mean anything, right? It's sort of a deliberately coupled field. It can take whatever value it wants. As long as energy densities are not gigantic, that's totally fine from the effective field theory point of view. But however, once you have, once you break that discreet shift symmetry, then by this explicit coupling g, obviously for a very big field value, that will start blowing up. And the conservative regime is where phi is less than or equal to m squared over g. And you can see that basically because you can add this effective potential for phi parameterized in terms of g phi, and you want this term to be order one or smaller. And that's where you get that from, okay? So all of that makes sense. And notice that when phi is order m squared over g, it is sufficiently large that it can cancel this large m squared contribution. So potentially making the Higgs mass squared itself tiny, right? And so both those things are required and sort of consistent in the effective field theory. So here's the chronology, okay? How does this model actually work? So what we're going to assume is that at the very beginning of time during inflation, right? The, I mean, there's something that's causing inflation. And we take some initial field value for phi that is big, not tuned or anything, just some large value, such that the Higgs mass squared is positive, okay? So the Higgs mass squared is positive, it's got no VEV. So, okay, that's what happens. Then the field phi, because I gave it these terms of the form g phi m squared, like there's a slope to the field, obviously, like which are, you know, these terms, they give it a tilted potential to phi. So because of those terms, the field phi will be rolling down slowly. And as it's slowly rolling, it'll be scanning the physical Higgs mass, right? As the, as the field value changes, the Higgs mass will be changing. Eventually, it'll come to a point where the Higgs mass squared will go from being positive to being negative, okay? The point where it crosses zero. And that's a point where electric week symmetry breaks. And our claim is that with the QCD axion, that is sufficient to turn on barriers to turn on another potential for phi, okay? And that is this part of the story. And so what happens is that phi keeps rolling and it starts hitting these barriers and eventually stops because the barriers are too powerful to prevent the field from rolling anymore. That's the basic idea. All of this, of course, happening during inflation, okay? And that's a central idea here, is that the value of these barriers depends upon the Higgs VEV. And we're going to claim that in the case of the QCD axion, this is automatic. How does that happen? Okay? So this is just standard QCD stuff. We all know that if you have, you know, like in QCD, when the quark masses vanish, there is no mass for the axion, right? That's an explicit statement. Here, of course, what happens is not that the quark masses vanish, is that you still have the Yuccava couplings. But when the Higgs VEV is zero, right, the quark, I mean, there is no quark mass. So this potential actually is very small. So it doesn't do very much. However, once the Higgs acquires a VEV, the standard VEV that it acquires, the quarks get a mass and that props the potential up. The potential goes up. And the key point is that the barrier height, okay, how big this value is depends upon the Higgs VEV itself. So the larger the Higgs VEV, the barrier keeps getting bigger and bigger and bigger, okay? And the Higgs VEV is zero, that doesn't happen. So the barriers don't exist. So the field will keep rolling until the barriers are big enough to prevent the field from rolling anymore. And you can calculate where that is. This is just simply the standard statement that, you know, if you have two competing forces, this is a slope that is causing the field to roll, and this is the size of the barrier, it'll roll until the slope actually cancels. And the rough condition where the thing stops is basically given by this kind of scaling, GM squared F, it should be order lambda to the fourth, but this lambda is basically lambda QCD, which is the value that the barrier has when the Higgs is at the weak scale, okay? So if you look at this relation, it's pretty interesting. GM squared and F, these are fixed parameters in the Lagrangian. They always exist, right? Like they're not changing in time. What's happening is that as the field five rolls, the barriers keep increasing. This parameter lambda is something that changes with the Higgs VEV. So once the Higgs VEV acquires the right value, the barrier is big enough to prevent this from actually rolling, okay? That's the central idea. So there are requirements in these parameters. One can ask, you know, what's preventing us from making these parameters arbitrarily big or arbitrarily small. And this is where the cosmology really appears. So the key point to note is that as the field five is rolling, right, is changing over a large range of order m squared over g, the vacuum energy in just the five sector, okay, the sector of the axion will be changing. And it changes by an order m to the fourth, okay? That's what you get when you roll by an order m squared over g, okay? So we want all of this to happen during inflation, so it better be the case that the energy density during inflation itself is larger than m to the fourth. Otherwise, the motion of five will back react on inflation itself. So we don't quite want to do that, okay? So we will therefore require that the Hubble scale during inflation is larger than m squared over m plonk, okay, implying that it's dominated by something else. For the moment, we will also assume that the rolling of five is dominated by classical physics. That is the quantum perturbations, you know, the phi is rolling, it will indeed have quantum jumps back and forth. And for now, we will just assume that the field just rolls classically, that quantum mechanics is not too important. Of course, we'll shortly relax that constraint and then I'll tell you why we sort of really like this. But for now, let's just imagine that the field, that the rolling of the field is dominated by classical physics. And that gives you a condition that g m squared is bigger than Hubble cube. This is just standard slow roll inflation conditions. So now we can go back to the previous slide that I had where I was telling you what values of g is and then impose these two requirements on the Hubble scale during inflation. And there is some constraint equation that tells you what is the largest value of m, what can actually get, right? So the basic reason why you cannot push m all the way to the cutoff is the fact that I mean, all the way to the gut scale or some gigantic scale is that as m becomes larger, right, we would require a larger vacuum energy here. And as the vacuum energy starts going up, these quantum perturbations become larger and larger, right? So if this condition was relaxed, one can immediately see that the larger the value of m over here, it's easier to satisfy this condition. So to get this constraint, it was crucial to use the fact that we're still living in a regime where classical rolling dominates. That's really what enforces this constraint. So one can put in the numbers and basically one sees that in this theory, one can push the cutoff up to about 10 of the 7 GeV before something new needs to happen. And that's just a theory where you've got just QCD, a long period of inflation, and that's it, nothing else. No new physics of the LHC, but the cosmological evolution of the field will naturally get us to a point where the Higgs is at the weak scale for a long period of time. And this theory, unfortunately, makes a very striking prediction that is ruled out, which is that if you look at where we end up in, we end up in a situation where we end up predicting the theta QCD is order one. Why does that occur? When you have this coupling G of the axion field to the Higgs that actually contributes to the axion potential, obviously, and as you all know, if you contribute to the axion potential and that contribution is comparable to the potential that comes from QCD, then you ruin your ability to solve the strong CP problem. And in this particular solution, the contributions are both order the same, they have to be, that's where they actually stop. So in this case, even though you're using the axion to solve the hierarchy problem, you basically ruin the solution that the axion provides to the strong CP problem. So you're automatically in a situation where theta QCD is pretty close to pi over two. And this obviously means that you predict a gigantic nuclear on EDM, which should have been seen in 1951. So this particular model has a problem. So we've got two ways of fixing that problem and I'll present both of them. The key thing to note here is that the usual solutions to the strong CP problem don't quite work. So one standard solution that you would want to use is sort of setting the up quark mass to zero. Of course, that is in contradiction to some experimental results. But even that doesn't quite do it for you. Basically, because if the up quark mass vanishes, then the QCD axion has no barrier at all. So for our whole story to work, it was necessary that as the Higgs have turned on, the barriers had to show up. But if the up quark mass was zero, then even if the Higgs have turned on, the barrier still wouldn't show up. So that solution doesn't quite work. So one basically requires a new class of sort of solutions to the strong CP problem if this is what you want to do. And here's the kind of a dumb way in which we did it. I think there are actually probably much better ideas out there. We just haven't explored all of them. So one very simple idea is the following. The key problem with solving the strong CP problem was that we could not make this parameter G too big. Because if G was too big, it actually contributes to the QCD axion potential. And so it better be the case that G is small so that you don't ruin the solution with strong CP. But if G is small, we're also losing the slope over here that we were always using to move the field phi down. And that's really where the tension came from. So the kind of a dumb solution is that you can make this field phi, the axion, also depend upon the inflow down itself through this coupling like this. Kappa sigma squared phi. Kappa will again be a very small number, right? It's still something that breaks the shift symmetry in this case. So it'll again be small. We've checked that it's sort of technically natural. So the key point here is that during inflation, the field sigma has a big web. And at the end of inflation, that web disappears. So during inflation, we have a slope for phi and where we solve the hierarchy problem. And later on, the sigma field disappears, removing the potential contribution for phi from that coupling. And so you recover the strong, your solution to the strong CP problem, which of course is a solution that you only care about today, not during inflation itself. So that's some dumb way of doing it. And you can go through various constraints, very similar to what we did before. And in that case, one can actually go through the algebra and you realize that the cutoff can only be about 30 TeV. We can't really push it too high, like in that particular class. Although it sort of only depends upon this parameter theta for the one quarter power. So the smaller the value of theta, the harder it is for us to solve the strong CP problem because we really cannot contribute a whole lot to the QCD potential. But it doesn't hurt you that much. It's just about a one quarter. But there's a slight modification of the story, which actually makes the cutoff much bigger. And that's what I want to discuss right now, which is that one of the ways that we got the cutoff was because we actually put in some constraint about classical rolling, right? We said that the field phi had to dominantly roll classically. And that's something that we actually require to get this bound. The reason why we put the classical condition was because if the field phi was rolling and the quantum mechanics was still important, then what would happen is that even if you arranged for parameters such that most of phi was ending up here, there would still be a small amount of phi that sits way up there where it can have a large vacuum energy. And if you end up in that kind of universe, essentially if the quantum rolling is important, then you could sort of eternally inflate on this side. Because that's a place where some part of the universe will have values of phi that get stuck there. And one can undergo eternal inflation. And even if there's only a tiny fraction that's stuck over there, one has to talk about things like measures, et cetera, to really address that properly. So we didn't just want to deal with that, which is why we imposed that constraint. However, when we have this technology where we just drop the slope, this large slope exists only during inflation. So at the end of inflation, the slope can drop, which just means that it is possible that if you pick the right sign, the slope drop puts you in a situation where most of these patches end up with sort of negative energy density, which means there's just some tiny fraction that are stuck in ADS. So those just disappear. So when you have the slope dropping going on, what can indeed basically relax that condition that classical rolling dominates and allow some quantum transitions to occur as well. So if you go through the algebra there, the primary constraint in the story simply comes from requiring that the Hubble scale during inflation is less than the QCD scale. That's basically because the Hubble scale is bigger than that. There'll be a too large of a visited temperature, so QCD will not confine. So we won't quite have our barriers. So that greatly relaxes where the bound lies. And in that case, you can go through the numbers again. One finds that you can push the cutoff up to about 1,000 TeV. So that is one possible way in which you can solve the strong CP problem by the slope drop technology and still have a pretty large cutoff for new physics. Another way is sort of just a simple model building exercise. There's no particular reason why we have to use QCD. One could indeed just put in another gauge group in the theory. All that was really required was that the field phi had to be like an axion. So one can basically make phi couple to gg-tilt of some other gauge group G. Now of course, to make the whole story work, we would still require a back reaction. As the field phi is rolling, we would still require some way that once the Higgs web turns on, the field has to stop rolling. So we still have to create the back reaction. And to create the back reaction, what we do is we just add some new fermions that have electroweak charges, but are charged under the new gauge group. So this Su3 is not color. This is just some other Su3 that confines. And we have some new electroweak doublets over there. And the way we make the electroweak doublets care about the Higgs web is to simply give them yukawa couplings. So here is sort of the sample Lagrangian. These new doublets have some vector-like masses and they also have these yukawa couplings. So when the Higgs gets a web, the masses for these guys get changed. So that's the way in which you can make the back reaction work. And the point of course is the following, is that when the Higgs web turns on, this field phi will acquire a barrier due to its coupling to gg-tilt. And the value of that barrier will depend upon the mass of this part of the N, in this case, the right-hand neutrino. So there are various sort of naturalness constraints and LHC bounds. I don't quite have the time to go into those. But roughly there is about a parameter space of a few hundred gEV where this whole solution will work, but it's sort of currently experimentally allowed, but also still solves the hierarchy problem. So in this case, you can go through the cut-off, the same kind of arguments about where the cut-off should be, and one figures out that the cut-off can be as high as 310 of the 8gEV. And there are various sort of bounds and various things that I'm happy to discuss offline, but there's a pretty large healthy parameter space where this actually works right now. So let's discuss the cosmology one more time and see where we are. So the story is that in the beginning, when the field phi is rolling, there's classical evolution. The field is mostly just rolling down classically. Then the barriers start sort of appearing. As the barriers start appearing, there's a decrease in the slope of the field. So that's a region where there's both classical plus quantum fluctuations being important. You're doing both. But you're still dominated by classical rolling. Eventually you come to a point where the barriers are big enough, and you're sort of in a situation where quantum fluctuations are the dominant story. But these barriers are still not that big, so one can still quantum mechanically fluctuate and go back and forth. And eventually you'll get to a situation where the barriers are large enough that it takes an enormous amount of time for you to go from one barrier to another. And that is basically where the actual universe lives. So here in this particular story, it will turn out that the amount of inflation we need is very long. It's much longer than the actual age of the universe today. So the moment you're stuck in one of these barriers that outlasts inflation, you're automatically guaranteed that you were living in an era during our current 18 second lifetime, the Higgs web doesn't change too much. So what do we need about inflation? There's just an example model. We haven't really created an actual model of inflation that fits all observed data and things of that sort. This is just proving that it can last long enough. So why do I say that we need a long period of inflation? Basically this field phi has to roll a long time. It has to basically roll over m squared over g. That's the field range it needs to have to be able to tune the Higgs potential. If you look at that, one can calculate how many e-foldings of inflation that is. And essentially, this is standard formula, red phi dot over h inflation is the amount of time it changes, is the amount of field space it covers during one e-folding, and then n is the total number of e-foldings you need to cover this big region. And the key point here is that the slope is very small because g will eventually turn out to be a tiny number. And so that is a reason why it takes a large amount of time to roll all the way down. So typically, we require something like 10 to the 48 or about 10 to the 37 e-foldings of inflation depending upon which model that you really require. One can ask, is that possible? So the kind of question we are basically asking is, can you have a long period of inflation and still have enough energy density to reheat the universe? That's basically our only point that we have checked so far. If it takes a long amount of time for something, you might worry, well, you may end up with an empty universe. And here we're just showing that's not really necessary. It's possible that you can have a lot of inflation and still have enough energy density to reheat. So what does one need to have a long period of inflation? You just require a very flat potential. If you have a very flat potential, the field can roll for a long time without really losing too much energy density. And that's something that we can just construct explicitly, even with a single field model. It's just an example model. So it's m squared, phi squared potential. And one can take m to be very small. It's a standard story that the fact that phi essentially has a shift symmetry that's only broken by tiny couplings to the mass. And one can go through the calculation requiring classical rolling for the field, et cetera, et cetera. And there are indeed ranges of parameters where one can get sufficiently large e-foldings of inflation as they require. Of course, to get the observable, this particular model by itself doesn't quite work because this model itself will have a lot of energy density at the end, but it doesn't really quite reproduce things like deltoir over row, spectrum things of that sort. So one has to hack on hybrid inflation or whatever to make that story more consistent with what we've seen. But at least this just proves that you can have enough energy density during the period when we're actually scanning the Higgs VEV. And then you have to tack on different solutions to inflation. Cool. So let's move on to observables. How would we know if this is how the world actually works? So the QCD Axion, in a sense, we have a relatively small parameter space, right? I mean, about 1,000 TV. So a couple of important things is that we do, in this story, predict and, well, favor an observable neutron EDM, right? That sort of getting to 10 to the minus 10 did cost us a fair bit in our ability to solve both the hierarchy problem and the strong CP problem. So we would be quite happy if the sort of neutron EDM was sort of around the corner. But the crucial thing that really would sort of prove that this mechanism is how the world works is the fact that for this whole story to work, the field phi or the axion has to couple to the Higgs with a scalar coupling. And that means we do predict that there is a new force mediated by this very light field to standard model particles. And that is something potentially observable in new force experiments, for example. Furthermore, if this field phi happens with a dark matter, then there's a very light field. So it's kind of a coherent field that's oscillating, much like the standard axion story. All of that still works. So as this field oscillates back and forth in time, it will in fact create oscillation standard model mass scales, okay? So that is something that one can actually potentially observe perhaps with some effort. Secondly, we also predict that inflation in this story is at rather low scale. So we don't really predict the existence of primordial to tensor modes or whatever. Also, we're also predicting a gigantic amount of inflation. So there should be no curvature. So if you see either of those two hints, right, if you're really convinced that you've seen primordial tensor modes in the CMB, or you've really measured curvature, then we'll at least falsify this class of models, okay? For the case of the non-QCD model, most of the phenomenology, more or less, carries over. There will still be new force experiments and oscillation standard model mass scales, and the inflation story also more or less goes through. But very importantly, we do predict the existence of fermions with electroweak quantum numbers, right? We said due to sort of radiative naturalness, they can't be much above a few hundred GEV. So at the LIC, you could indeed go and look for electroweak particles that are sort of strongly coupled under some other gauge group. And that is something that is quite essential in the story to work. So let me quickly move to my conclusions. So, you know, we presented essentially a model, right? So I would like to think of it more as a general class of ideas. It's not that I'm super convinced that this exact model is how the world actually works. You know, it was kind of telling you, here's what you would need if you thought a cosmological solution was what you required the hierarchy problem, not some tuning mechanic, I mean, not some new symmetry or anthropics, right? If you wanted something that was sort of dynamical occurring cosmologically, here's what you would need. So I believe all of these points are essential for any such solution that you would need. Very importantly, the model always requires dissipation, right? So the reason why you need dissipation is because as the field phi is changing, right, over time, its vacuum energy will change. So if you had a very conservative Lagrangian only, right, no dynamics, then the problem is that the field phi changes to get to its correct value, that vacuum energy change has to go somewhere and that has to be absorbed into something. And that is why we need dissipation. So as the field is sort of relaxing to where it wants to go, all that energy density needs to disappear. And this particular model, we use Hubble friction as a simple way of doing it, as the expansion of the universe automatically dissipates its energy. A very important point is the fact that we use something like an axion, which has something like a self-similar potential. And this is actually pretty crucial, because if you think about it, the field phi keeps changing, right? And the moment the Higgs gets the right value, it needs to be able to stop right there and stay stuck, okay? That is pretty crucial to this whole story. And for the, if you didn't have such a potential where the field phi could get stuck anywhere, then one would have to sort of come up with fine-tuning mechanisms to say that a point that was a special point with the Higgs potential is also a special point for the phi potential, where the two of them can both be at a minimum, right? And that's a non-trivial step. So here, the fact that the axion has a continuous sort of shift symmetry where it can stop anywhere means that stopping the axion was very trivial. All we had to do was stop the Higgs at the right point. And I think that is a pretty crucial part of the story. It's obviously important that there is some kind of back-reaction mechanism that knows that the Higgs web changed from being positive to being negative. And we use Yukawa couplings to do that, to basically back-react and stop this. And in this particular model, of course, in all of these models, there would be some time that is required for this mechanism to occur. And we use inflation here as a long, to provide a period in the early universe where you could do some tuning and not use, and not lose energy density, okay? So in our model, all of these are kind of hooked together in some way. So if you were, say, unhappy with the field values that we require or how much time it requires, things of that sort, I would suggest that the key things to change would basically be dissipation, right? That's basically what controls the time scales in this problem. Because we use Hubble friction, which is a very, very slow way in which we are dissipating energy. So if you had a much more rapid way to dissipate energy, then this value of g could be much bigger, right? So you would be moving much more quickly. And as you move much more quickly, if you had a quick dissipation mechanism, all that energy density would be quickly disappeared away. But then that would, like, for example, decrease the amount of time you need to solve the problem. Furthermore, the field ranges that we require, which are order m squared over g, also depend upon g. So if g becomes big, the field ranges you need also become small. I mean, these are things that people who have heard about this model before have worried about. And, you know, I acknowledge their worries, of course. But I think these are natural ways in which you can make progress if you choose to follow this line of inquiry. So there's a lot of things to do, in my opinion. And I don't want to go through every one of these things. But, like, really, for me, what is most exciting about this kind of thought is that in our field, we have been thinking for a long time that to solve naturalness, the only way to do that is to add a lot of new particles at higher and higher energies, right? And that is basically how we've been orienting both our theoretical thought as well as our experimental ways to solve the problem. However, as they all know, that argument breaks completely when you think about the cosmological constant, right? There's nothing at the milli-EV scale that would explain why the CC is where it is. And, increasingly, it does appear that the Higgs could also be in a very similar state. And in this class of models, the interesting thing is that all of the, I mean, there is a natural solution, of course, that occurs over here. But the way you find it is not at high energy, really. It's sort of more at really low energies and a really low weak coupling, right? So it motivates both a different way of thinking about it in terms of theory as well as a different way of thinking about it in terms of experiment. So with that, I'll stop. And we'll take, we have time for two questions. Okay. Thank you for the talk. Very interesting. May I ask some questions? Am I right that in your theories there are at least two scalar fields during the inflation, in photon and Higgs field? Higgs and relaxion, yes. Yes. And even axion. Yeah. So usually when you have more than one scalar field during inflation, there will be either curvature modes in the primordial fluctuation. So how do you think to solve this problem? The scale of inflation here is really low, right? Like we're talking about really low Hubble scales. So this is really not a big deal. Okay. Thank you. Another question? I think it's minor comment or small. And in a particular model, I totally understand you don't want to go to the regime of eternal, slow, or eternal inflation measure thing. But suppose you do, okay? And suppose you take a local picture, say, for example, as I was doing, okay? And you don't need to worry about the slow, or eternal inflation because probably you're popping up is small and you don't care volume increase beyond the horizon. Then that may reduce the constraint the most. Yeah. I mean, I totally agree. Like, you know, we just didn't want to deal with that problem. That's why we did it. But I agree. If that can be solved in a consistent way, that would definitely open up parameter space. Yes. No question. Probably the biggest, right? Yeah. Sure. All right. So let's thank Surjeet and move on to the last talk of the afternoon.