 Hello, guys, and welcome to the Latin American webinar on physics. So my name is Nicolás Bernal, I'm from the University of Antonio Marino in Bogotá, Colombia. And I'm super happy to host today a webinar by Javier Rubio from the University of Helsinki. Right, so Javi, are you there? I'm here, yeah. Present. Okay. Here we go. Okay. So thanks a lot for allowing me to speak here today about the role of the Higgs field in cosmology. So the first time that I do this, so if I do any mistakes, please stop me on time. So I will be setting the screen now so you can see the slides. So it's okay? Yes. Okay. So you can see also this. So I will be talking about the role of the Higgs field in cosmology. Most of the things that I'm going to say are based on this recent review that is now published in frontiers. And also you can find the slides of the presentation already in my webpage. So I will try to answer some questions during this talk. The first one is the Higgs itself could be responsible for inflation. And in that case, which are the requirements for this kind of scenario to be self-consistent. And now, which is also the relation between the standard model parameters, those that we measure at collider experiments and the inflationary observables that we infer from CNB observations. And finally, I will discuss what happens in the case in which our vacuum becomes unstable below the scale of inflation. I will discuss the Higgs inflation is still possible in that situation. Identifying the Higgs field with the inflaton is somehow a natural possibility given the present data sets. After many years of searches, the only thing that we have found in the LA city now is a neutral boson with a mass of 125 gigalitron volts and properties that closely resembles those of the standard model Higgs field, in particular the spin and the captain of the standard model particles. And although we have been looking a lot, there is no significant deviation of the standard model found so far. The news coming from the sky also pointed to something very simple. It seems that everything is compatible with the simplest inflationary scenario based on a single field in a slow roll with no significant generation of curvature perturbations and no significant generation of non-gaussianities. So we have a scalar. We need a scalar. So I think it's rather natural to identify these two things, especially thinking into account that we don't have any hints of new physics beyond the electric scale. But also, this possibility somehow reinforced when we look at the precise value of the mass of the Higgs. The value of the mass of the Higgs is rather particular. For some people, it will be low or high, depending on whether you have been working on supersymmetry or not, but it is very particular. So in particular, it allows us to extend the standard model all the way up from the electric scale to the planet scale while extending a fully perturbative regime. The precise behavior of the self-coupling depends on the competition of self-interactions and the contribution of fermions and they play in different directions. The self-interaction of the Higgs field tries to increase the value of the self-coupling of higher energies and the contribution of loose fermions, in particular the top one, try to decrease the value of the coupling of large changes. So that is more or less what is summarizing this figure. So depending on the precise value of the top yukawa coupling, the standard model can be extended all the way up to the planet scale while remaining positive or the self-coupling can become negative as an intermediate scale that can be as low as 10 GB or so. This is also summarizing this figure. When I saw in the critical value of the top yukawa coupling as a function of the Higgs mass that separates the region of the parameter space of full stability of the standard model from the region in which the standard model vacuum is metastated. As you see there are different contours here. The field one corresponds to those values coming from the experiment with error bars, the experimental error bars and these other ellipses thus indicate which is the theoretical error coming from relating the top mass or the Monte Carlo top mass mesonic collider experiments to the value of the yukawa coupling in the standard normalization skin, MS bar for instance, the ventes in the normalization group equation. As you can see the standard model is roughly compatible with stability at one sigma although the possibility of having a metastable vacuum cannot be excluded with present data and present theoretical experiments. So in the main part of the talk I will assume that we are somehow in this region here in the region of full stability and only at the end of the talk I will discuss what happens if we finish to be in this region of metastability once the measurements of the top mass are improved. So can we make inflation with the Higgs? Well in principle there is no problem, any potential like the one of the Higgs field can get you inflation provided that you go to sufficiently large values of the field, in particular this is the useful idea of calculating inflation because in this region of large field values the friction increases. Unfortunately what happens is that the amount of primordial density perturbation that you generate is too large for the values of the cell coupling following from the previous thermalization group running. So in general the Higgs field as formulated in the standard model is not able to produce the right amount of curvature perturbations. There are many solutions to this, almost all of these are very or something simple. You can have a potential that can be as steep as you want provided that you are able to increase the friction during the epoch of inflation. So one can consider several modifications, for instance one could modify directly the friction term here by replacing it for something proportional to the fabulous scale. So this is for instance a simple way of doing this is replacing the metric gminu by the instant tensor that is proportional to h2 and that will give you some extra friction of large field values and that could in principle allow for inflation, this is what sometimes is called new Higgs inflation. The problem with that is that it usually introduces, well it's a higher dimension operator so it can introduce some dimensionful parameter suppressing this operator. So if we want to restrict our cell to dimensionless couplings not introducing additional scales, the simplest possibility to consider is a non-minimal coupling of the Higgs field to gravity. Well, this coupling is dimensionless but still we have some uncertainty here in the way with this field couplings to gravity, in particular in the usual formulation of Higgs inflation which is called the metric formulation, the rich scalar is computed to be a connection that is exactly the liberty of the connection so it's related to the metric in this way. But there is another possibility that is take on if you want to draw the choice of gravitational degrees of freedom that is choosing that this connection is different from the liberty of the connection so that the connection and the metric are independent variables. Although these two formulations are completely equivalent in general relativity when you are dealing just with the Einstein-Hilbert action, they are in general not equivalent in the presence of non-minimal couplings so they will give rise to different observance. I will focus on the main part of the talk in the metric formulation so in which the connection is identified with the leviticus connection but if you want to know something else about this palatine formulation you can either ask me at the end of the talk or you can also have a look at this recent paper that we published on the site. So let me focus on the metric case. So I'm writing here the scalar part of the action. So this is the Higgs field and the Unitary Gates. I'm neglecting the vacuum expectation value of the Higgs field because I will be always interested in field values much larger than that value and what inflation will happen always in a region with distance is dominant with respect to n-plan. And something interesting happens when this guy is dominating over the usual gravitational constant is that the action becomes scaling value so there is no dimension-full parameter in the remitting with H is much bigger than this one. So we have a kind of emergent symmetry, scale symmetry and it's a continuous symmetry so we should have this Goldstone boson so in that limit we should expect this Higgs field to become the Goldstone boson and as any other Goldstone boson should effectively decouple from the matter sector. That is what is going to happen and that is one of the key points of Higgs inflation. Well to see that this kind of modification is giving you an extra friction you can perform a bi-redefinition okay what usually people call conformal transformation I prefer to call it vile so you can make this kind of field-redefinition involving the metric and the scalar field like so here and you obtain this kind of action okay so now the gravitational part of the theory is just the Einstein-Hilbert term and all the non-linearities of the initial theory are moved now to the scalar sector. Well you see the potential is something rather simple but the most important the most interesting part is encoded in this non-canonical kinetic term. We see that there are two poles one pole happening at theta equal to one that just looking to the definition correspond to the region of the small Higgs values that is what I call the Minkowski pole because of the small Higgs values this term is negligible and there is basically no difference between the initial frame and the Einstein frame okay so we recover the lambda phi to the fourth theory there is another pole that is the most interesting one that is this quadratic pole that has a residue proportional to this parameter a that is just some particular combination of the non-minimal term well this pole has a very interesting effect so this pole is stretching the potential around theta equal to 0 so this potential due to the effect of this pole is stretching the vicinity of theta equal to 0 and this is interesting because basically the pole is erasing all the sensitivity to the details of the potential this can be seen explicitly by making this scalar field canonical so if I define a new field phi such that we can get this canonical I obtain a potential like this okay well the potential has two parts one of the small field values that is lambda phi to the fourth that is the one associated to this Minkowski pole and then we have another part that is associated to the quadratic pole and I was saying before this rise to some exponential stretching and last field values notice that all the information that appears in this potential for the canonical in my field depends on this parameter alpha depends if you want in the residue of the quadratic pole okay and notice that a large field values this potential becomes approximately constant okay this emergency symmetry a large field values is nothing else that the non-linear realization of the initial SK symmetry we started with in the initial frame okay so this flanges of the potential allows for inflation with the usual chaotic conditions and you can compare which is the amplitude of this potential to the coven normalization okay that's basically the amplitude of primordial fluctuations of temperature fluctuations and you from this relation you can obtain some relation between the non-minimal coupling the number of defaults of inflation and the self-coupling of the Higgs field well we don't know exactly which is this value because that depends on the details of the reheating process but you can see that for typical values fiducial values n equal to 60 and values of the non-minimal coupling 10 to the minus 6 or so this coupling is typically much larger than one so the quantity that I was defining in the previous slide is alpha becomes approximately equal to 1 6 in this limit of very large size okay so what is this value how we compute this value well the good point about Higgs inflation contrary to other inflationary models is that all the couplings to the standard model particles are known okay they are known experimentally the strength of the left of the scale and also the shape of the coupling okay so we can compute everything in detail a priori so how if the heating proceed in this model so once inflation is over the Higgs field will oscillate around the minimum of this potential that is what if you make some expansion this function is approximately quadratic okay so you have a feature like this one here so the Higgs field will be oscillating around the minimum of the potential since the potential is quadratic there is no production of Higgs particles in this metric formulation of Higgs inflation you could produce in principle W gauge bosons and fermions but the fermions are the production of fermions is restricted by Pauli blocking so the main production channel is going to be the production of massive gauge boson W's and set okay so they are produced at the bottom of the potential where the velocity of the field is large by violation of adiabaticity the usual adiabaticity condition so something very similar to the swinging effect so this is what usually called parametric resonance but here is everything is a bit more complicated because these primary particles are coupled to some secondary particles that are the standard model electrons and quarks okay the decay probability of these guys into electrons and quarks is proportional to the affected mass of these particles which is itself proportional to the expectation value of the Higgs field which is oscillating in this potential so upon production the mass of the W become very large and also the decay probability into electrons so that means that once produced the W's and set can decay into the standard model fermions and that will delay the usual process of parametric resonance so well the final outcome of this is that the universe reheat when the temperature was around 10 to the 14 GB so it's not instantaneous but when you translate this quantity to the number of ephoson inflation that you require you get that is around 50 around 60 so it's not instantaneous it's not close to the limit of 50 ephoson so what when you put this number together with the predictions in the previous slides you get these numbers here so we use a spectral deal around what 0.9066 and you get some tensor to a scalar ratio at the level of 10 to the minus 3 so that if you plot in this usual tensor to a scalar ratio versus primordial deep plot is precisely in the sweet spot suggested by the plan collaboration notice also that it's precisely below this line that is the usual line associated to alpha tractors and this should be clear from the presentation in terms of the poles okay so the my parameter alpha display alpha a is playing the same role as the parameter alpha in this alpha factor theories and the poles are also quadratic in those models so it's not surprising that the Higgs inflation prediction is lying precisely on top of the slide okay um well this is also always pre-level results so now I have to also be sure that this predictions so this this model are not gonna be changed with when I take into account relative corrections okay so the first thing I have to notice is that Higgs inflation is it's non-renormalizable okay this can be seen because of the non-minimal capital gravity or in the Einstein frame because I have this non-polynomial potential so I have to interpret the theory like an effective thing theory valid in some particular scale and to be complemented by some higher-dimensional operators appraise right at this scale now the question is which kind of operator should I add well the simplest possibility will be well assume that everything is valid like I was saying till the plan scale and then I had two possibilities I could add operators suppressed by this cutoff at the plan scale in the Einstein frame but in that case I had a flat potential I had polynomial operators so the corrections to the potential are gonna be large and that will probably spoil inflation okay that happens in all the large-film models of inflation okay this is the infamous cosmological problem the hierarchy problem or the data problem in the context of inflation there is another possibility I said in these operators in the Jordan frame but in that case the corrections to the potential are small are well with some coefficients that you can assume to be order one and there is a press by the value of lambda and the value of the non-minimal coupling to some power okay since this coupling is large these corrections are small so this is perfectly okay but now the question is if this is self-consistent because this is just a naive assumption that nothing happens with below the plan scale but in principle other interactions could violate unitarity below the electric escape so a certain system approach for defining the cutoff is to define it from the theory itself so basically you consider all possible reaction or possible scatterings between a standard model consequence determine the scalar which by unitarity is violated and all kind of higher dimensional operators are placed by this cutoff okay so the typical way of computing is you take the Jordan in this case the Jordan frame action you span the fields and the metric around some bathroom values since there is this non-canonical kinetic term when you make the expansion there is going to be some mixing between the trace of the metric and the scalar perturbations that you have to diagonalize okay in order to have a diagonal quadratic action before reading the higher dimensional operators so when you do that you can define new perturbations delta phi bar and h-mini bar or hat and read the cutoff for higher dimensional operators and what you see is that these cutoffs are generically field dependent okay depends on the bathroom expectation value of the field of the scalar field well I was doing this for the scalar gravity part but you can do this in the gauge sector and also in the fermion sector with the same technique and what you get in summary is this field so I'm plotting here the cutoff of gravitational interactions the cutoff of scalar interactions and the cutoff of gauge interactions and as you see at the small scales the cutoff is simply divided by the minimal coupling and at large scales it becomes field dependent and grows linearly at very large field values of the Higgs field okay so our theories should be considered as an effective theory valid to this cutoff scale and should be complemented with a higher dimensional operator suppressed by the law of this scales in particular this gauge cutoff okay the important part to notice is that all the energy scales involved in the evolution of the universe are significantly smaller than well significantly smaller in most of the region parameter space is smaller than the than the cutoff scale so this means that we can consider this theory as an effective description that is under control okay it's important to notice that I to emphasize this effective theory interpretation because now there is no single ultraviolet completion of Higgs inflation not involving a state with masses below and plan over side okay so we always need some ultraviolet completion on that scale well now we can wonder okay you have been talking about inflationary observables but how is this related to the low energy observables that we measure of the vector with scale okay in principle these two things should be related by the running but we will see now that there are some additional complications okay and the reason is again related to the fact that Higgs inflation is non-renormalizing okay so let me follow the approach that I was discussing before so let me interpret Higgs inflation like an effective field theory and add all possible higher dimensional operators suppressed by the cutoff that I was previously computing okay I will be even more conservative and I will add only those operators that are generated by the theory itself so when I compute blue corrections I will get some infinities and I will have to add some counter terms in order to subtract the divergences okay so this counter terms we had always the same structure we had some infinite part the dimensional regularization appears like a pole in one over excellent with one coefficient that is chosen in such a way that these divergences are subtracted and then I had some finite part that cannot be computed from the low energy theory and that you should interpret like a reman of the potential ultraviolet completion I was talking about okay so this kind of operator is just a subset of the previous or the many possible operators but is the minimum that I require in order to make the theory final so let me let me make an example of this so imagine I compute this loop diagram okay so this diagram will generate some divergences and I will have to complement the initial three-level potential with some counter terms in order to cancel these divergences okay you can compute explicitly which is the counter term and it looks like this and you see the structure is rather funny because it's completely different from the one present in the initial theory okay that is not surprising because we are dealing with a non-remisable theory so of course the new the new test that I had to add were not present in the original theory but it has some very funny behavior remember that the function f is a function that is linear in the field at low field values and becomes approximately constant at large field values okay so that means that the derivative of the function goes between one with respect to the field go between one and zero okay so at the small field values this quantity here becomes five to the four this quantity here becomes one and we recover up there of the form five to the four that was already present in the initial field so that means that at low energies I can always reabsorb this finite part delta lambda into the definition of my coupling okay into the definition of the self coupling of the Higgs but when I go to higher energies this function here this derivative becomes zero and the constant that I had absorbed at low energies into the definition of the self coupling eventually disappears okay just because all this thing goes to zero well this is going to give me some jumps in the running of the coupling constants okay well now note that the procedure is not close because if I follow the logic of what the user logic in quantum theory I will have to promote this quantity to a new coupling constant with its unrealization of the equation so I will have to include it back into the Lagrangian compute again the beta functions and see which are the new constants that I had to add okay so I will have to add an infinite number of counter terms so there is some restrictions that you can put in order to truncate these these infinite series of beta functions that is that the final part that this is an assumption that the final pass must be of the same order in power counting that the loop producing them okay this is satisfied there is no reason a theory why this should be satisfied you should be able to truncate this equation at one loop and well follow the usual logic okay well but this is not really necessary why because whatever the loops that you produce they're always going to involve the function f and the derivatives so there's always going to be a region in which the running coincides roughly with the standard model running and some region in which you recover what the asymptotic of the model in the absence of yams okay so all the modification of these yams will happen in some region in field space okay as you can see here is not really instantaneous but it's limited okay so this is for the one loop if you will consider multiple loops or three or collective effects this this thing in the middle could change but the asymptotics for the standard model path and these flat regions here will never change okay so let me forget for the time being about this field dependence here okay and assume that the yams are almost instantaneous okay so I arrive to some scale and I jump to the other one and let me focus on the shape of the potential in this region that is where inflation takes place so we can distinguish well around that region what the coupling is doing the following so it's decreasing it's eventually arriving to a minimum and it's increasing thereafter okay well you can parametrize this behavior with three parameters lambda zero that denotes the minimal value of the coupling q that denotes the pointing with the beta function goes to zero and then you have also this parameter b that measured basically the curvature of this of this of this meaning okay well as I said I'm putting this threshold effect so I'm assuming that this transition is instantaneous and I'm forgetting for the time being about any field dependencies coming from there okay now well it's useful to rewrite this parameter q in terms of another parameter kappa okay just for technical reasons and we can distinguish three regimes okay there is a reasoning with lambda zero is much bigger than b over 16 kappa okay in that region this logarithmic term can be neglected and the potential behaves roughly like the one of the three levels okay however there is a region with this lambda zero becomes comparable to b over 16 kappa and in that for that region of parameter values the potential develops an inflection point okay this is only possible for very fine tune values of the hicks and the top mass but it's well it's a priori a possibility no and then there is also the situation with this lambda zero becomes smaller than b over 16 kappa and in that case the potential develops a maximum okay now inflation here is still possible but not like in a plateau like here but could be possible around this maximum provided that the initial conditions are sufficiently fine tune okay so and also that you have to guarantee that you are rolling in the right direction and not in the opposite direction okay um so let me discuss how these different possibilities are shown in the inflationary observables okay so I have been here the effective potential with I have uh this is a realization with the potential so I replace the value of lambda by the one following from the running like this one here okay and then you can see the behavior of R and S as a function of kappa okay this parameter kappa and then there will always a lambda zero is always used to fix the normalize the coven normalization and psi is a parameter that is varying between 10 between 10 and 100 along these lines okay this region here the star corresponds to the region in which you have universal hicks inflation so this region here this kind of parameter space so as you see there the predictions coincide with those of the three levels so those predictions are rather robust while if you are in a region or in a situation like this in which you are close to the you are developing an inflection point so you are in this criticality scenario the value of the tensor race tensor the scalar ratio is highly dependent on the value of this parameter kappa and in particular can be rather large so the over 0.1 so and also something funny happens in that case because when you are in this critical hicks inflation the power spectrum start developing a bump around the inflection point above the scale associated to the inflection point okay and you see that this bump is larger the larger is the tensor cost scalar ratio okay arriving to max to a maximum amplitude of 10 to the minus seven or so okay well all this was assuming that the threshold effect this jumps in the coupling constant were happening instantaneously and you may wonder how this picture is modified when I take into account potential field dependence so I take into account that this jam is not instantaneous okay you can do that you can parameterize this transition by in many ways because you don't know what happens with higher loops but you can parameterize in a simple way like this where the rapidity of the transition is parameterized by this parameter delta okay so you can take this just as a phenomenological formula accounting for potential effects coming from the running of the finite parts for the running of this new coupling constant I have to introduce in the action for which I'm not computing the beta function or for higher-order operators by neglecting by truncating the dramatization group equations and as you see they had well but in this parameter delta has a strong impact on the inflationary observer so can change the the tensor to scalar ratio by order 0.1 or so okay but the most important thing is that even in the presence of field dependencies the universal region of heat inflation remains in that and coincide with the three level side okay well this change here is also reflected in the in the power spectrum as a function of the scale you see that still you get some order one modifications in the power spectrum due to this field dependence but it's very important to notice that this power spectrum even in the case in which you take into account the field dependence is well it's much larger than the one that we observe in cmv scales but is much smaller than the one typically used for producing primordial black holes okay I'm saying this because there were some speculations for some time on the possibility of generating primordial black holes in this critical heat inflation scenario okay and I'm showing here that this is this is not possible because in order to produce primordial black holes this amplitude should go up to 10 to the minus 2 10 to the minus 3 which is not the case so the way this was done in the literature was promoting this non-minimal coupling taking into account the running of this non-minimal coupling that I was omitting till now okay well you can compute which is the running following from the standard model that is rather simple because it's just well standard model couplings say order one some well loop factor and proportional to psi h so this running is typically 10 to the minus 2 okay while in those proposals of producing primordial black holes in critical heat inflation the typical value that was used was 10 to the 2 okay so there is a strong a big difference so unless you find an explanation for this very large running the conclusion is that primordial black hole generation is quite unlikely in critical heat inflation okay so well and now all this discussion was somehow assuming that the standard model vacuum was as stable all the way up till the inflationary scale but now you can go under what happens if the heat cell coupling becomes negative before below the scale well it should be clear from the previous slide that nothing dramatic happens because well there you can distinguish two possibilities you can imagine that the standard model running brings the self-capping negative of a given scale then to the 10 gb for instance but then if the threshold effects this finite part that are coming from the unknown neutralization completion at a small you will never be able to restore a coupling to positive values at the scale of inflation but a priori nothing forbids you to consider the possibility in which these couplings are not much smaller than the lander and the nominal coupling lander and the top quadruple coupling so you can imagine a situation like this with the heat coupling becomes negative below the scale of inflation and then there are these threshold corrections coming from the neutral air completion that brings the coupling back to positive values okay well but in that case we still have a problem because if I now plot the full potential effective potential for the Higgs field coming from this kind of running I get something like this okay well this is just a cartoon it's not to scale okay but I had here the letter with vacuum at some point the Higgs coupling becomes negative okay and I developed a secondary minimum and eventually the Higgs field the Higgs self-capping becomes positive and I go back to the inflationary plateau that I was commenting in my previous slides okay this situation here now it's true we can still have inflation here but now this vacuum here is much larger than the electric with vacuum okay it's much deeper and much wider so unless you fine tune completely the initial conditions most probably upon the drying of the scalar field you will finish in the wrong vacuum okay in particular you will finish in a vacuum with negative energy that will lead to the collapse of the universe okay and just a few efforts so how to avoid that okay well there is a very simple way of avoiding that rather natural that is the following so inflation is taking place around here okay some point you finish inflation and you start to oscillating around the minimum of the potential okay in that minimum of the potential you're gonna produce particles like well in a way I was describing before so this combined reheatness scenario okay now in the temperature okay the energy that you are able to deposit in these particles is sufficiently large the bar reaction into the scalar potential can be also large and you can have some kind of well thermal correction effects that can stabilize the potential in this way okay but everything depends here on the scale of on the efficiency of the reheating process so there will be a critical temperature for which this is possible and we have to require or we have to be sure that the reheating temperature is larger than this critical temperature field okay but if this restoration happens I feel the Higgs field will be able to relax towards the electro weak minimum and will stay there in present time okay so I mean it's obvious that at some point the universe will expand the temperature will decrease and this restored potential will eventually disappear in such a way that this new minimum will appear again but at that point we are already in the safe mean okay and the lifetime of this vacuum is larger you can compute it and you can show that it's large under the lifetime of the humans so we will be safe well now looking at the numbers you see that the you can compute the symmetry needed the temperature needed for thermal correction to correct the potential and this temperature is well this one here roughly or if you want this in order to make the minimum disappear it's around 10 to the 13 GB okay almost 10 to the 14 but the reheating temperature that can be completed more or less in detail is larger than the temperature so we can always use thermal corrections to restore the symmetry of the potential and allow the electro weak the Higgs field to relax to the electro weak mean so this is telling us something interesting that okay if we allow for these jumps in the coupling constants coming for deuterite completion well that is bad because somehow we are losing the connection between low energy physics and high energy physics because well everything will depend on this on these parameters that cannot be determined in accelerators but at the same time it opens an interesting arena that allows for inflation to fix inflation to take place even if the standard model vacuum is not completely stable okay so well this is more or less what I wanted to say so let me just summarize so the Higgs field can inflate the universe you can distinguish different regions but there is one region that is usually called universal or non-critical Higgs inflation in which the predictions are robust even when you take into account quantum corrections and well these predictions coincide with the three-level values okay well there is also a region that is this critical Higgs inflation in which everything becomes very dependent on the particular ultraviolet completion okay so the value of the tensor-to-skiller ratio can change a lot depending on the value of these finite parts but this is not applying to the universal case and there's something we have to live with in the lack of a ultraviolet completion that is that the relation between low energy observables so if you want the mass of the Higgs and the mass of the top at the electric week scale and high energy observables like the spectral deal or the tensor-to-skiller ratio are always these relations are always containing some theoretical uncertainty associated to the lack of this ultraviolet completion okay so this is one of the main problems of Higgs inflation finding a potential ultraviolet completion able to fix these finite parts but the nice point is that well one can in principle speculate that these finite parts could allow to have Higgs inflation even if the standard model vacuum is not completely stable okay so thanks a lot great thanks a lot Javi for this super interesting presentation so are there questions for the audience comments hello hey Javier can you hear me thank you for your talk I have a small question is there a way to see easily why if you just eat like follow a Palatine formulation you'll get like different results yeah let me just learn the differences yeah I can show you just one second setting again the slides and I can show you specifically thank you you can see here okay so the main defense between Palatine and metric formulation is that the connection is independent of the metric okay so that means that when I'm performing this conformal transformation okay or despite viral definition the only part of the action that is transforming the Palatine case is the one coming from the metric determinant okay because basically the richest scalar is not affected by this kind of transformation because depends on the connection okay well when you look at the details that translate into a modification of this kinetic term okay the most important part is that this parameter a that I including here is not this quantity here but only the non-minimal coupling so only this so this part here six times i disappears okay this is the part that is coming from the transformation of the rich scalar okay and that is action in the Palatine so you can see that a is proportional to uh to the non-minimal coupling now you just go to my next slide you see that what controls the asymptotic behavior of the potential is the value of a okay in the case of metric influx inflation this value is one over six but in Palatine this is much larger is of the order of the non-minimal coupling okay so 10 to the 7 10 to the 8 so it's very large so the potential becomes much flatter in the Palatine case and now you can simply go to the expressions but basically what happens is that um the tensor to scalar ratio is inversely proportional to this quantity okay so r goes like one over eight okay so in the Palatine in the metric case this factor six gives you this factor 12 okay but in the in the Palatine case you will get some extra suppression here proportional to the non-minimal coupling so in the Palatine case the tensor to scalar ratio is typically much smaller than um in the metric case okay but still the spectral T is not modified and that is something very generic because the behavior of the spectral T is only related to the fact that this pole is quadratic and that is always the same in metric and Palatine formulations what changes between metric and Palatine formulations is the value of the residue okay and the value of the residue is what enters in the in the tensor to scalar ratio okay more or less here control yeah yeah thank you but but then so at the end of the day which which one should I follow or or like which one is the one like I don't know if this is a well posed question but in this is like I'll get two different values for something that is controlling my results so which approach no I mean you can you can invert the questions somehow I mean yeah you don't know which are the fundamental values of freedom that I see gravitational center okay so let's go to the experiment and see oh okay and think which you can do two things okay and and it's interesting because well if you look to this paper that I was commenting here you can really see that future experiments will be able to this in principle will be able to distinguish great metric and Palatine formulations so if you want we'll be able to tell you something about the nature of gravity yeah yeah yeah because this is very interesting in GR in pure GR you get always the same results okay GR the two things are the same because when you make the variation for the connection basically thank you Javier welcome great thanks are there more questions for the audience so if not I have a couple they have to say so Javier was wondering why the cut the cutoff for not universal I mean why do they depend on the particle say again why the cutoffs are not like universal so why why do you have I think you present a plot with three different cutoffs that depends on the nature of the particles something on the spin I think well I don't know universal because the heat centers in different ways in the different interactions so basically you are changing different interactions in different ways I mean and that is just an estimate of the cutoff that is telling you where you should state violation of unitary in different channels so doesn't mean that the unitary is really violated that there could be cancellations among different channels so if you want this is the most concerned but in a stop just taking the lowest of this cutoff but okay so what one should do is that to compute all this cutoff and just take the lowest one so well that is that is what is used like that if you don't have any other maybe the reason you have different cutoffs and different interactions that are violating unitary things so the cutoff of the theory is defined like the lowest cutoff of the all possible cutoffs okay okay that's my definition the cool thing because there are cancellations you know okay thanks are there more questions well I have another one so that the very end show a plot of the running of the quarter cupping so the stutter ball running and also the kyer stutter ball running and you were showing some kinks so like some jumps so could you please come back to that slide okay sorry I'm going to come back and say no I don't really say it in my slides so I think you have to show the screen could you please do it okay I thought I was saying no I can't you know don't make me okay so what we're seeing you know your face okay well let me from read the question so you say that these kinks and jumps are like two threshold effects right yeah that's not a great slide I think it's the variant like that that one right so but at some point I can see that in the running you're going deep into the negative part of lambda who is that not problematic because then so I think you want to avoid this lambda to to to go negative at any point in the evolution why because of metastability or so please go go on table I mean there are two things so you have to ensure two things that you never finish don't want to finish here okay so that's the first reason why you don't want lambda negative because in general you could finish here but if you come with a reason in which or a mechanism to avoid finishing here and guarantee that you finish here there is a secondary question that is well which is the lifetime of of this vacuum okay and you can compute that in the standard model and well even in the for the regions that I was showing before in this plot of the mass of the hicks of the mass of the top are compatible with data the lifetime is much larger than the lifetime of the universe okay so the probability of the case almost zero in this particular case of hicks inflation if you really compute this number the probability of decay is even smaller than in the standard model case so yes I mean the coupling will be negative at a high scale but you will be here and you will not decay in the lifetime of the universe okay so so you have anytime you have to I don't think there is any any particular problem with the self-capping with an immediate scale yeah wait there's something that is allowing you to go on top of this barrier like for instituting inflation some situations or tunneling but if you the probability of that is very small that's safe okay any further questions so from yeah hello I have a very naive question uh what happens if you extend the this scalar sector well uh like very generic question to be honest I don't know in that particular realization but people has considered many many possible extensions I mean usually when you introduce new scalars you have more freedom and you can't say how play a bit with this you really your question is it really the the hicks tablet or is going beyond the hicks no in general I mean just the hicks tablet model is it's like an easiest extension well the hicks tablet is is accounted for here because I'm working in the unitary gates so this is just a choice of the gates okay so that is accounted for but now if you want to go beyond the standard model that will change things okay there's another question but now from our youtube chat by Daniel Camargo so he's asking if there's a metric independence atop for inflation so I'm not sure if I understand the question what they mean by metric independent right here yeah I'm not sure maybe Daniel if you're still there could you please straight away for me the question anyway my question probably is that I don't know so if they mean a theoretical strategy without the without a metric I don't know if he's really living in that okay are there any further questions are you from youtube or from the audience here so I maybe have a very last one so at the very beginning when you were talking about the preheating you say that the number of defaults was fixed to be 59 something like this yeah that comes from preheating that comes from preheating of course um you have to think which is the number of defaults that you need to solve the horizon problem and that depends not only the hot bit monthly but also what happens during preheating in particular if you had some kind of matter here or if you went right away into radiation nomination okay so I mean in the actual reheating there will be some matter here because this potential is basically m squared phi square okay and that would increase this value that tend to increase this value from 50 to say to 65 or so okay so in what happens here is something in between so we don't enter in radiation right away that will correspond right to 50 if also but neither enter and had a very long matter dominated data that will correspond roughly to 65 or so so we are somehow in between okay so this this number is fixed for the particular estimate on when you enter values into radiation nomination here okay there's another question from the youtube chat so is suru chidas he's asking if you could if you can explain what restricts the production of fermions by parametric resonance well the production of fermions is simply restricted by pauli blocking okay so you cannot produce more if you try to produce more fermions using some parametric resonance like that um you can never go beyond occupation under larger than one so you will do is producing thermos with higher momenta that could can be interesting for the distribution of momenta but it's not gonna give you a large depletion of the energy of the condensate well for bosons uh you have basically bosonic amplification so the number of bosons that you could use is proportional to the number of bosons that were there before like happens in a laser so the answer the sort answer is pauli blocking or fermions okay thank you can you leave the last question for the audience it doesn't seem to be the case so thank you very much how you so for this super nice talk and uh yes i wanted to remind the audience that in two weeks time from now i will have a new talk ready to inflation of dark matter by tomi tecani so we hope to to have you here to see you here again so thanks again heavy for my story thanks a lot see you guys