 So, this is work done in collaboration with, okay, with Irene Valenzuela, Fernando Marchesano, Francisco Pedro, and Sean Billiman, and the title is Historic Inflation and Stream Theory. So, let me start by recalling the issue of Fundamental Scholar in Physics. We all know that scalars are a bit special in field theory, they are hard to maintain light. Here are the most famous scalars in particle theory. The Higgs, which is supposed to give masses to fermions and gauge bosons. The Inflaton, which is a very efficient way to understand many aspects of cosmology. A little bit more in-depth is the action. But there is an important difference between these three objects, which is that this one has been observed. So, on the other hand, well, this is completing the standard model, the consistency of the standard model, but it's hard to believe that this is the end of the story. In particular, it's known that if one just extrapolates what we know of the standard model, the self-coupling of the standard model, high in energies, the potential seems to become stable. The vacuum becomes at least metastable at a scale in between 10 to 11 and the 14 GB. Of course, there are errors in this estimation, but it seems so. And some people say that there is an instability problem. So, there should be some new physics turning on at these large scales. And possibly, one of the simplest possibilities would be that about that scale, we have a high-scale supersymmetry. So, supersymmetry appears in those large scales, as I guess it was first proposed by some people in the audience. And the idea is simple. Above that scale, the potential becomes just positive definite. So, the scalar potential of the standard model becomes stable. And, okay, now the supersymmetry breaking scale is then 10 to 11 to the 13 GB. There is an additional motivation, because one could say, well, supersymmetry will introduce to solve the hierarchy problem. So, why don't we get rid of it altogether? Within string theory, there are additional motivations. Supersymmetry is a fundamental symmetry in string theory. It's there. And also, you need it, even if you have such a large scale for supersymmetry breaking, it is hard to build models which are vacuum-free if the theory is not supersymmetric. So, having supersymmetry is a nice thing, an expected thing in string theory. However, not necessarily all the way down to the low scale. So, in certain cases supersymmetry would be needed not to solve the hierarchy problem, but to stabilize the standard model, which would require that the scale of supersymmetry breaking is smaller than 10 to 11, 10 to 13 GB. So that the potential is all the time positive definite. When I talk about the scale of supersymmetry breaking MSS, I'm referring to the mass of the soft terms, not the real scale of supersymmetry breaking. That's the size of the soft terms. So, then the solution of the hierarchy problem will have to be fine-tuning. I'm sorry about that. So, possibly a landscape type of idea, although I'm not going to elaborate in that direction. So, let us consider for simplicity the most MSSM and that there is the most general MSSM is mass structure, which is this one. We have a diagonal masses and then the diagonal B term you wish there. And then there is a fine-tuning which is taking the determinant of this matrix equal to zero. And then at that, if you do that, at that scale, 10 to 11 to the 13 GB, you get a mass less doublet, which is this particular combination of HU and HD in the MSSM. So, that would be identified with the peaks of the standard model. Here, tangent beta is not the ratio of any band. It's the ratio of these soft masses here. And then there is the orthogonal guy, which is massive. Another doublet, which appears in the MSSM. If you look at the scalar potential of those energies, you have the potential of the massive field, which will decouple below that large scale. And we will be left with his potential, which is going to be just this piece. We know that at that scale, the potential seems to be almost vanishing. So, that suggests that tangent beta is close to 1, because tangent beta is close to 1, cosines to be close to 0. Then at that scale, you have a mass less, as I said, the Higgs field, which would be this combination. And this combination, when tangent beta is close to 1, this guy would be massive. And then the potential is close to 0 at that scale. And then you know that then almost automatically, the mass of the Higgs layer of certain mass at low energy is going to be around 126. In fact, you can obtain this plot if you just allow free the scale of supersymmetry breaking. You can compute the Higgs mass in terms of the quartic coupling. And if you just assume that the two Higgs masses are equal at some unification scale, strength scale, combatification scale, whatever, it doesn't make much difference. Then you find that barine, the value of the muter, different ways, above the scale of 10 to the 10 dB, essentially the mass you obtain for the Higgs mass is around 126. By the way, these kind of plots should have been computed before LAC finding the Higgs, because it would have been a very nice prediction. Unfortunately, it was pictured after. Anyway, so now let's go to the other topic, that of inflation within string theory. We have learned some things already from the talk of Gary. So inflation before March the 17th of 2014 looked like this. Some quartic inflation model like the quartic was almost close to its exclusion. So models with a small r were very popular and suddenly came this data from this that you already saw indicating that r could be in between 0.1 or 0.2. Within the chaotic type of inflation, which is this polynomial potential with these powers, you obtain those values for inflating excursions large in between 11 to 20 times the planned scale. So you need a good favor of large field inflation. We have learned that the data, in fact, are compatible with just dust, although still there is room for relatively large values so far, it's more than 0.12. So still large field models are well alive. We will have to wait probably one or two years to settle the question. Still as Gary said, it is interesting to explore what if these large values of r are found. So if such a large values are there, that would indicate the scale of inflation that you see in GEV, Hubble parameter 10 to the 14 GEV, and then inflaton scale of 10 to the 13 GEV. And now the bell rings, could that be related to this large scale of sushi breaking we were mentioning before? It could be. So I repeat that the sushi breaking scale here is the size of the software. So that's the idea we would explore. Then the structure of scales would be like this. We had the inflaton at 10 to the 13 GEV, inflation scales at 16 GEV, and the value of the inflaton traveling above the previous plan scale. So we need, as usual, that the inflaton must be stable under corrections. This is the eta problem. We need that the field, the inflaton can have a large field range. And then we need stability under corrections for when the value of the inflaton is large compared to the plan scale. So the tradition is that 1 and 3 could be cured if there is some shift symmetry, a simple way to obtain large ranges for the value of the cakes wheel is that there is some periodicity in the inflaton. So within string theory, large inflation can be accommodated in a variety of ways, identifying the inflaton either with an action, a Wilson line, or a deep brain position. In fact, these things are somehow related under the dualities, ns dualities, depending on the case. But this is in Dorfield's law for large transplucking scarcians. So that's something which is found often in the string theory, in principle. And there could be gauge symmetries in a standard sense. I'm not talking about you and gauge symmetry, for example. Of Dorfield's, make the potential stable against corrections to this potential. So this is the idea underlying this monotherm inflation that Gary mentioned. But first, considered by Silverstein Westphalm, there has been a lot of work, particularly last year, after this sort of discovery by Bicep. So I'm going to talk about a variety of this, which goes under the name Higgs-Ottock inflation. It has this peculiar name because it is the Higgs-Poo, it's going to be the inflaton and Otock because this is sort of caotic type inflation. The idea is simple. Why using the Higgs as the inflaton? Well, it's within the context of string theory, which is, I think, a reasonable context. Or I would say in any field theory context, having light-scaled light is not that easy. So it is already amazing that we have a Higgs so light. So introducing another fundamental field, which is also light to get inflation, would be an additional miracle. So it would be interesting to try to combine both. In addition, the Higgs has been observed, so it would be nice if both things could be combined. This, in fact, of course, is a very old idea. Many people have written papers and models with Higgs inflation. One of the most popular ones recently is one in which you have a non-canonical coupling of gravity to the Higgs, but with some parameter, the group of Shapposnikov et al. Should say that this, that's OK for me, no problem. But I don't think it's easy to embed this into string theory. So in any event, I'm not going to talk about that. But I want something simpler, as far as I can see. As I said, at the scale 10 to 11, 10 to the 12 GB, the potential of the Higgs in the standard model is close to zero. But there is another massive guy with a mass of order 10 to the 12 GB also. So again, it brings the bell. So perhaps you can use this heavy guy for producing chaotic inflation with H the inflator. We will see it is a bit more complicated than that. It's not a light Higgs and a massive Higgs is something more sophisticated. But this is the essential idea. So still you need that the large inflatons pressure should be possible and the potentials should be stable. So what we are going to do is look for a string implementation with some sort of monodrome inflation in which the Higgs is some sort of wish-online or deep-brain position. It can be done both ways, because in fact they are T-dual and string theory. So I will concentrate in the case in which the Higgs is correspond to deep-brain positions. By the way, I will not address here at this stage full modular stabilization, because here I'm going to isolate the sector of the theater associated with the Higgs. It would be a more complex problem still to be addressed. Okay, so let me consider how you get the Higgs MSSM-like type of fields in maybe obtaining type 2 orienting force or in heterotic. Here it's a standard model, toy model test of type 2B orienting force. You have these seven brains, in particular a set of six, these seven brains, sitting locally in a geometry of this form with two torus in the third complex plane and this is a C2 with a singularity which is set 4 and here is the action of the set 4 in the three complex coordinates and the corresponding channel patterns. You don't need to understand the details. You get a gauge group which is U3 because U2 because U1, there will be, if you have a compact model there will be some heated sector, etc., but we are interested only in this sector. And what is interesting is that you have fields which are precisely the behavior and the coupling constants and the structure of the Higgs of the MSSM. So schematically you have these six, these seven brains in this singularity, when one these seven brain goes away from this point to the bulk, well there is a mirror because this is an orientable, it has a mirror, then the symmetry, this geometrical movement corresponds to the gauging of the standard model symmetry down to electromagnetism and QCT. So the inflaton breaks the standard model of gauging symmetry and there is a D-flat direction is U equals HD, parametric by the parameter, real parameter sigma and then the relative phase theta. So these are going to be our two parameters. So within string theory you can see that the position of the D-brain really corresponds to beps of these Higgs fields. In particular this is the position in the third complex plane, this is the position in the tutorials and while the real part can be identified with this Higgs field and the other one with this. These are real fields now in singlets because they are defining here. So let me explain in a bit more detail the degrees of freedom here. So we have eight real scalars in the minimal set of Higgs in the MSSM. Three are scalars and become massive when there is a path. Then there are three gauging bosons but you are still left with two neutral guys, this sigma and theta that I told you, which really parametrize the position of the brain. When you are at the origin, the symmetry restored, when you are away, your symmetry is just QCD times U1 essentially. One important thing to realize is that in string theory it is not true that what is the mass of a gauged boson, is it the coupling versus times the bed? No, that's only true in the effective field theory. The mass of a vector boson here is really given by the distance in between the position of the brain and the origin. So that's because it is just given by the tension of the open string in between those two points. So the Higgs can have a very large bed and travel all this way around the torus having a much larger than the radius is still the mass of the W since it never exists in the combatification scale. Okay, so the potential is flat up to now. It was a flat direction but in general you have in this combatification fluxes which are present. It is well known this type to be oriented for. You have these Raman fluxes and Nevespar fluxes which combine in this way in rise to a complex free form and depending on the tensorial structure, you have this tensorial structure, they give rise to supersymmetric breaking, give rise to non-super symmetric soft turns, do you wish? And then with this other tensor combination you get supersymmetric turns, essentially new turns. So we are going to assume that we are in the presence of this type of fluxes and then we know the Lagrangian, the local Lagrangian for the deep brains and has the influx that is given by the Dirac-Born infill action and the Chelsimian action of the D7 brain. So here is the expression of the Dirac-Born infill action. This is the pullback and E is the sum of the metric and two in the centrosymmetric tensor. And well here you have the B2, C6, C8. You need to know much about those. These are the Raman and Nevespar fluxes which appear in type to be. What is interesting is that in the presence of these backgrounds, the values of these fields depend on the value of the adjoint of U6, the gauge symmetries. So this is the guy which is, you wish, parameterizes the full movement of the Higgs, in particular the components in here, but they are contained in a 6 by 6 matrix. So, okay, doing the full exercise, putting these fluxes inside the Dirac-Born infill and Chelsimian action, in fact you find that they give the same contribution with sums and you get something of this form for the Lagrangian. You get a potential and you get something which is important. You get a non-canonical genetic term which is proportional. There is a correction, it's not just one, but there is this correction which is proportional to the potential itself. And this is non-parameter in terms of the compactification volume and the tension of the seven brain. And the potential is something which is just a quadratic potential in terms of the fluxes G and S. And okay, when the G is equal to S, when both Susie and non-Susie fluxes are equal, you get, as you can see here, a massless Higgs field. This is the associated to the standard model, and this is the heavy guy. And well, one way to parametrize. So the particular size depends on the relative size of the Susie breakings and fluxes. So one can define this parameter A which measures that. It's in between 0 and 1. And if you want to obtain a massless Higgs at some which should be identified with a standard model of Higgs, A should be equal close to 1. If you take into account that there is a running in between 10 to 11, 10 to 12 GB and the unification scale, it is not equal to 1, but the choice of fluxes should be more closer to 0.83. Okay, so in angular coordinates in these parameters sigma and theta, this is the way the potential has, which this A parameter which is close to 0.83, you want to consider the massless guy associated to the standard model Higgs. Sigma, which is the distance to the origin and theta, the angle, the relative phase in between these two fields. So while there is essentially in principle two free parameters, this g tilde which is associated to the size of the fluxes. So it is associated to the scale of supersymmetry breaking. And the parameter A, but we know that A is close to 0.83. And one can estimate the g tilde in this, putting all the parameters in here and assuming there is a sort of isotropic modification. You can estimate that the g tilde is always of order one over the plant scale times the factor which could be 3 or 0.3 or whatever, but it's always around one over the plant scale. So okay, we are left with a very specific potential. There is this interesting point that the kinetic term is not canonical and it has a very special form in this non-canonical kinetic term. For example, if I take the A equals one limit, which is close to the reality of A, 0.83, you can see what the potential is essentially just a quadratic piece for the heavy Higgs. Then you can compute the canonical normalized Higgs in terms of an integral which you can perform analytically. And you find that the potential, instead of being quadratic, at the larger values of the canonical normalized field is really linear. So it is linear for large inflaton. This is built in. It's nothing that I did to lower the power of the inflaton potential. It is there. This is something which in general you have to do numerically. You cannot do analytically. So in the end, you're left with a two-field inflaton model in which you have a metric in field space which has this form. It's diagonal, but still it's not trivial. It's curved. So in terms of two-field sigma and tau, and you can study, of course, the evolution of your inflaton fields. One of the questions one would ask is that we are in a two-field inflaton model. What happens with isochromatic perturbations? There are two large isochromatic perturbations. They are very much bounded by plant data. So here is the form of the potential. And here is the theta. It is the relative phase of HUNHD. And this is sigma, which is essentially the size of the wave of the Higgs. So the dynamics depends on which region you start with. This is theta and sigma again. And these are several examples of trajectories which you'll find. And it is true in general when the inflaton starts evolving, not only you have adiabatic perturbations along the way, but there is perturbations in the normal direction. And they interact. And there is a transition. There are isochromatic perturbations which contribute to the curvature of perturbations. So you have to perform a full analysis. And you find that this is the ratio of isochromatic perturbations. So really, 10 to the minus 20, 10 to the minus 20. They are really very much suppressed. And this is for 50 and 60 e-folds. However, one effect which is present is that curvature of perturbations so R decreases due to the isochromatic or curvature conversion. So this number here is the ratio of the curvature perturbations compared with ignoring the effect of isochromatic perturbations. So you can get enhancements of order 2, in fact. So this is why the experimental data has disappeared. You obtain, this is depending on 50 or 60 e-folds, a value of R in the region 0.07, 0.12, depending on your initial conditions in the potential. But it's always like that. Here you can see, well, the results you would get that is for some particular set of angles you would get the very large R. If you ignore the two field effects, but we shouldn't do that, so this is the right answer. And for NS, this is what you get. This is structured in here. So most common plot, this is R versus NS. And the colors mean this is for a variety of initial conditions. You get for most of the initial conditions, you end up in the region close to 0.08, 0.09, or the red point is more abundant. This is rarely you end up in this region. And this is, by the way, what you get. If you ignore the two field effects, you would get also this kind of funny structure, which is not there, in fact. So many people are not used to using the Dirac-Borninfeld action for computing scalar potential, and are more used to a supergravity description. Here is a scalar potential, which gives rise to some of the dynamics I showed, which is this scalar potential in this way. This is the complex structure of the two torus in which this is where it is traveling. This is the complex dilaton. And these are the his fields. This is the kind of scalar potential that you get in this type of model. Well, of course, there are other pieces. But the sector, which is interesting for us, then assuming that there is a constant potential and a new term, and you just compute the potential, there is no scale type of cancellation, and the residual potential you are left with is this. If you assume that the supersymmetry braking simply comes from an embarrassing auxiliary field for the modulus, this is the quadratic structure that we showed. But if you use this kind of, if you try to use this supergravity description, you are going to fail in the sense that you are not going to get flattened. I mean, this is going to be quadratic forever. You should include all alpha prime corrections to this supergravity lagrangian to be able to describe the flattening effect, to get the real potential for last field. One thing which is interesting is that in this supergravity approach, you can see that there are duality symmetries. In particular, the complex structure fills under this duality transformation. The dilaton gets shifted, but also the hits transform. And the color potential is not invariant. It is not the color potential which is invariant. It is the full potential which is invariant. The potential is invariant, or the color potential is not. So you expect that the alpha prime corrections should be powers of the potential in order to preserve this, which this symmetry would be broken only spontaneously. This is consistent with what we obtained from DBI and Placere-Simon expansion. If you do an expansion for small field, this is the kind of power that you obtain. I don't have time to explain it, but you can also understand the stability of this potential in terms of this caloper sorbo structure in terms of four forms that I'm not going to describe. Just a few words. Data problem, let us know that data problem here in the Higgs tuning problem, they are not independent. You need an inflaton mass of 4 to 10 to 13 GB, but that's also the scale you need to break supersimilar to get a lag Higgs, which is 126 GB, well, to get a lag Higgs. So there are not things that you can separate. The large inflaton range comes from the multiple winding around one cycle, which is the existence of these cycles. It's common in stream theory. One important point is there is this generic flattening of the potential for large inflaton, which is something you cannot capture using supergravity potentials. I think we are lacking at the moment the technology to use large alpha prime, to sum up the alpha prime corrections in the supergravity and in supergravity, because if not, I think we are going to miss important information in the potential inflaton potentials. Reheating is quite high and it's still compatible with leptogenesis. So let me come to the conclusions. Well, the surface mass leads to a stable or metastable vacuum at a scale in between 10 to 10, 10 to 13, 10 to 14 GB. And one elegant way to re-obtain stability is that supersimilatory is found at all scales. In fact, that range is consistent with Higgs mass around 126 GB. And then, of course, minimality. Economy suggests to study whether the SUZI Higgs sector with supersimilatory broken at that scale can give rise to inflation. So what we find is that the MSSM Higgs system may work in using two field inflation. The Higgs degree of freedom inflaton may be realized as a decision position. Of course, there are varieties in which you can realize the Higgs in terms of a DC domain position or Wilson line. That depends on your model building abilities. And fluxes, which are genetic in these compactifications, then induce a potential, which can be computed in terms of the Dirac border interaction and the chance of an action. And what you obtain at the end is a variant of a two field chaotic inflation with, essentially, something you have to perform. In the original case, it's something you kind of do analytically, you have to do it numerically. But essentially, you get something which is linear-like type of behavior. There's a coverage of perturbations on mass suppress in one of 10 values of R in this range and also for details, which hopefully will soon be tested. So one of the virtues of this approach is probably that in one year or two, it could be ruled out or in. Thank you. Questions? So I don't know if I understood correctly. But did you mention that you break the electric symmetry at the high scale, at the 10 to the 13? No, no, no, well, I mean, the inflaton is the Higgs. So it's broken at the scale. The minimum of the potential after inflation, the baby's 0. What is broken at that scale is supersymmetry, not the. It's like usually in any Higgs inflation model, the Higgs has a baby. So the electric symmetry breaking is broken. But at the minimum of the potential is 0. And it's recorded. Yeah. I think there was a question in the back. Hello. So as far as I understood, you started from the point that our vacuum is not stable. Actually, this point is very discussive one. I see many reviews about it. And it could be stable or metastable and up to plan scales. So my question is the following. If you proposed to use it at the scale of 10 to 11 GV, how would you solve problem of the proton decay, for example, because we have already measured that proton decay will lead to the much more higher energy scales? Well, that depends on the details of the scales. What is important is the unification scale can be large, can be 10 to 15, 16, 17. So there is no, the only problem from proton decay could be the scalar triplets, where below 10 to 10, 10 to 11 GV. But if it is 10 to 12, it's perfectly consistent with proton decay. OK. And another question is, will the loop correction give additional mass to the infantron, not to the infantron, to our hicks? Will the loop correction form such a high scale? Well, this is protected. The hicks and the inflaton is protected in several different ways. First, you recover supersymmetry. So that counts as some of the corrections. But there is this built-in symmetry, which protects your potential, which tells you that any correction cannot come, it has to come in powers of the potential, essentially. So it should be, the potential itself is very small, because it's an inflaton scale over plant scale to the full. So any correction would be very, very small to the potential. So there are different ways to see this. You can see in this particular model, you can see it also because of the built-in duality symmetries, also because the built-in caliper sorbo symmetries, they are all related. But this is something which is really stable. I think in string theory, the scalar potencies are always stable. It's not my model. By the way, all the action models in string theory, although people don't say it, they are monodromy models. Because the monodromy story is something which is built in string theory. It's not up to you. You don't have actions of other kind. All actions in string theory have a monodromy behavior. So they are stable. You mentioned that the reheating temperature was something like 10 to the power of 213 because your influx is. Well, this is just perturbative. This is something which we have to do. We haven't done a serious analysis of. That will be in conflict with the gravitino. You could have gravitino problem, no? This is very model dependent. So I cannot answer to you. It depends on how you do your cosmology. It depends on the rest of your spectrum. Be concentrated. But your inflaton is heavy, right? Is it like 10, 12, 10, 13 GB? So you want to produce it thermally. So that's why you want the reheating temperature to be something like that. A repeat again is that's very model dependent. Depends what I do. If I preserve our parity and things, many things. I have one more quick question here. How about non-gaussianity model? What? Non-gaussianity. Non-gaussianity? Yes, well, it's something which we are considering now. We don't expect there are very similar two field inflation models, which is very, very typically these non-gaussianities are proportional to powers of the epsilon and eta. So we would like to find some effect, in fact. But we don't expect the sizable non-gaussianities, unfortunately. The inflation ends just at the end of the inflation end with the violation of the total parameter, in this case. I'm asking that if this model of inflation ends with the violation of the total parameter of the overall condition. Violation of the overall condition. Slow-roll condition. Ah, small-roll condition. We haven't studied how the end of inflation takes place, so cannot tell you. Not yet. So we're OK. Let's thank Luis Sabanez again.