 I will go to explain what the theory predicts for these higher-order correlation functions and why they are interesting, what can we learn about the early universe from them, and finally I will talk about current and future constraints and observations. This talk will be sort of an overview talk, I didn't want to to to focus too much on my own work, I wanted to give a sort of overview but of course this is a biased overview because of course I will talk about my own work as I go on. So what is inflation? I won't bore you with telling with the usual story of the flat potential blah blah blah. I just want to say that what we care most about from inflation is the fact that it gives us a dynamical mechanism to generate primordial fluctuations that we observe in the CMB and that seed the formation of galaxies and the large scale structure of the universe. In particular, after much work one can write down the action, the second order action for metric perturbations and this looks like the action for a scalar field as you usually have in field theory with a few differences. First there is this coefficient in front which you know it's just a normal you can see it just as a normalization but more importantly you see that the space derivatives this this field is massless with no potential it looks like that because it's a description of the the the metric fluctuations and most importantly space and time derivatives are separated they have different coefficients and in particular this is due to the metric it's because it's not a mean cosky metric but an expanding metric and most importantly this looks like the usual scalar field that you quantize as harmonic oscillator like in standard quantum field theory but it has a time-dependent frequency since it has a time-dependent frequency this means that a quanta are constantly being created because if you start in in a vacuum state as time goes on this state will no longer be in the vacuum and you create a quanta and moreover so we can quantize this as scalar field and compute correlation functions as you always do in field theory so for example one can compute the two-point correlation function which is usually parameterized in this way so it's proportional to a direct delta of momentum conservation this this is three momentum sorry i forgot the arrows this is three three momentum we do it at a fixed time so it's proportional to a direct delta of momentum conservation it has some amplitude the one wants to measure and it goes like a power law when this number ns is equal to one this power law is scaling variable and we we think that these correlation functions can be observed when they are generated these correlation functions that are generated during inflation can be observed even if we don't know the physics between the end of inflation and let's say nuclear synthesis because uh outside of the horizon because of the way the scales evolve so basically if i take some scale in the problem say one over k the scale of some uh quantum of some uh fluctuation of some metric fluctuation and i compared with the communing horizon during inflation the communing horizon shrinks the scale exits the horizon and then it freezes so whatever information was there uh was encoded during inflation is frozen and kept for later on then inflation ends the communing horizon starts growing again and at some point in the in the future say after much much after nuclear synthesis but for example before the emission of the cmb or even after the emission of the cmb the scale reenters the horizon and we can observe it so we are directly observing observing what happened during inflation when this information was frozen outside of the horizon so this is the basics about inflation and we have learned a lot of course the name of the game is to compare observations with some uh that with theory so we have observations and you can try to model them using uh Boltzmann codes like camber class cmb fast starting from some initial conditions that are generated during inflation so you have some theory you compute these initial conditions and then you evolve to compare to observation and of course in this way you learn about the theory by using those observations now and we have learned a lot from the two-point function now these plots taken from from plank from the latest papers i think i don't remember uh have become famous so this this is the two-point correlation function of temperature so these are basically temperature fluctuations on two different points of the sky correlated and transformed to a sort of Fourier the composition of the on the sphere so you transform them using the spherical harmonics and the predictions from theory that comes both from a scaling variance spectrum and then from the physics of the early plasma that is computed by these Boltzmann codes the theory agrees very well with observations and this theory has been used to put tight constraints on cosmological parameters in particular this plot is also famous it has been used to put constraints on possible models of inflation so we have learned a lot from the two-point correlation function but there is more information so but this this is only probing the free field so it's only probing an action like this one this action was obtained by expanding the metric and keeping it up to second order of course there are higher order terms in the action that relate to the non-linear revolution of gravity but also to the interactions of of of the inflaton etc that we cannot see directly from this two-point function so we would like to go to higher order correlation functions this is similar to what you do in particle physics of course because in particle physics you do scattering to probe interactions and these scatterings are proportional to higher order correlation functions so this is not very different and I'm going to focus on the three-point function because in principle it's the easiest to observe each one of each one of these citas which are metric fluctuations is of the has been observed to be to the order of the order of 10 to the minus 5 so every time I include an additional cita is 10 to the minus 5 times smaller than than the previous one so I I don't want to pay too many citas so I stop at the three-point correlation function but in the literature also four-point correlation functions have been studied and constrained etc it's also very interesting but I limit myself to this and this is proportional to a direct delta of momentum conservation which basically means that the three momenta k1 k2 k3 form a closed triangle and whatever is left is what we usually call the bi-spectrum so if you ever have heard a cosmologist talk about the bi-spectrum he's talking about this three-point correlation function now if this bi-spectrum is scaling variant I can factorize one of the scales say k1 and everything can be described in terms of the ratios k3 with respect to k1 or k2 with respect to k1 and also this should be invariant under the exchange of any pairs of one two and three so all the information is contained in this triangle in the plane and people talk about I am going to talk about different limits in this plane that correspond to different configurations of this closed triangle that the momentum forms I'm going to focus a lot on the squeeze limit it's going to be almost my main point during the talk and the squeeze limit has nothing to do with quantum mechanics with squeeze states or so on it's only the limit in which one of the momenta is much smaller than the other two so the triangle looks kind of squeezed it looks like this and in this plane it belongs to this region another configuration that we're going to talk about that people talk out is the equilateral configuration where the three momenta are equal so the triangle is equilateral and also some some people talk out unfolded configurations which looks like a flattened triangle okay very good so let me start by talking about the squeeze limit the squeeze limit is very interesting so I'm going to tell you why from theory these things are interested and what we expect in the different configurations so the squeeze limit is very interesting because it encodes the relation between a very long wavelength meaning very small momentum meaning a very squeezed triangle with short wavelength physics and intuitively this this limit is kind of trivial should be kind of trivial in many theories and the reason is because the metric fluctuations are basically the gravitational potential and we know that the gravitational potential we have this Newtonian intuition that the gravitational the value of the gravitational potential has no physical meaning if I give you some value of the gravitational potential you can change this value however you want you can raise or lower the value and it should have no effect on your short-scale physics so if I approximate this long wavelength mode as a constant because it's very long wavelength then basically it should have no physical effect for example if I have a very nonlinear object like a galaxy which are super complicated and I rescale the Newtonian potential nothing should happen to the galaxy and the same happens to the gradient of the potential because a gradient of the gravitational potential is just a constant gravitational force so we should also be able to describe it actually we can do this so this this is Newtonian intuition we can do this even in gr to see it let me start from some unperturbed Friedmann-Robertsow-Walker metric which looks like this and now I do a coordinate change so I change time and space in this way and now the metric looks looks like this so it looks like a perturbed metric and indeed if I set this to zero and set this to zeta to be equal to zeta it looks like a perturbed metric of exactly the type that is generated during inflation however notice that this lambda is a constant this epsilon depends only on time such that this zeta is constant in space so this this only holds for a very long wavelength mode and you can do the same for a gradient and indeed for inflation out of the horizon epsilon should be zero lambda equal equal should be should equal zeta and what we learned is that a very long wavelength metric fluctuation is just a change of coordinates so as in the Newtonian intuition it has no physical meaning one can this was already noticed by many people Maldacena and also Weinberg one can generalize this also to the gradient following this Newtonian intuition and we learned that there is no correlation between a very long wavelength constant mode and short wavelength physics now what does this mean for the physics of inflation it means the following if I take the spectrum so this is this this is a symmetry of the theory if you want this is symmetry under the film morphisms and it's kind of it's spontaneously broken in the sense that the the metric does not transform linearly so one can see this the presence of this non-linear symmetry as inducing some word identities that tell you how the three-point function behaves in in in a soft limit this is a more particle physicsy way of putting it now the so we learn from the all all this that the squeeze limit contains a lot of information from the word identity or from these arguments that I gave you then we know that the three-point function in in a soft limit meaning when one momentum is going to zero should have a specific behavior with momentum so it should go like one over q it turns out that all these arguments that I gave you are only true if this zeta or this gravitational potential is constant in time and this is only true in strictly in single field inflation so if I have a single field inflation model I don't care about which Lagrangian which potential you gave this single field which crazy theory you are looking at as long as it's a single field inflation model excluding some pathological examples such as ultra slow roll inflation if I have a single inflaton field meaning a single light degree of freedom active doing inflation which with energy much smaller than than the energy scale of inflation which is given by h then the spectrum should go should go in this way from explicit calculations that people have done we know that if you have more than one field the divergence in the squeeze limit is much stronger so if we might if we manage to measure these divergence we will know what is the field spectrum of inflation we will know how many fields were active during inflation and if these fields have some intermediate mass close to the mass scale of inflation you can even get some intermediate behaviors I stole this figure from this paper here moreover people have also started looking at a bunch of people as you can see from this list and this list is already old and more people should be added have also started looking at what happens in the presence of fields with non-zero spin what what happens if fields with non-zero spin are active during inflation these fields can induce a three-point function in this way so this is this should be taken as a heuristic diagram it's only saying that the interaction between two scalar fluctuations in this higher spin field by higher spin I mean higher than zero can induce a correlation where I put one leg on the background can induce a three-point correlation function and it was shown first in this paper of 2015 and then later in others but generically in any in any of these theories when you have a when you exchange non-zero spin field you always get this kind of this characteristic angular dependence where the angle is the angle between the short mode the k and q is the angle between k and q so you get a characteristic angular dependence in this three-point function so you can learn a lot about the the whether inflation was single or multi-field and whether the there is there was a high a light higher spin field higher than zero spin field present during inflation by looking at the squeeze limit so it's very interesting but even if we restrict ourselves to single field inflation meaning that in the squeeze limit there is basically nothing there is still information in other configurations of the three-point function uh in particular one can there I forgot to put the citation here but uh Cheon, Kriminelli, Fitzpatrick, other people wrote a paper on sometime ago in 2008 on understanding single field inflation as an effective theory so as in any effective theory we first look at the symmetries the in this problem the symmetries uh are we don't have Lorentz invariance because we are on a curved background so space and time are separated so if I write the most general second order action I should write the the for a for a massless field which would be the a sort of Gauss-Golson boson that characterizes the difference between two a constant in that on hypersurface and a constant time hypersurface but that doesn't matter for now this this pi is connected to zeta there is a very simple relation they are basically proportional then if I write the most general second order action uh I can write special derivatives separate from space uh from time derivatives and I put some arbitrary coefficient so we learn that this field can propagate at a speed which is not that of light even if it's massless because it's coupling to the foliation of spacetime and up to here we we don't learn much uh but let's go to higher orders so if I go to higher orders I I would write down the most general cubic Lagrangian so then I write down the most general cubic Lagrangian with one derivative per field I stay to lowest order in derivatives because higher derivatives will be suppressed by some energy scale and this is one derivative per field and the two operators that I can write that uh and that separates space and time derivatives are these two and if the breaking of Lorentz is explicit the coefficients of these operators is general but the foliation at the curved spacetime uh preserves local Lorentz only that it's spontaneously broken uh I mean there is a in the universe there is a preferred time but this doesn't mean the Lorentz invariance is broken it's only a spontaneous breaking your your vacuum solution has a narrow of time and you can see this by the fact that if you impose this spontaneous uh you impose that Lorentz is still satisfied albeit spontaneously broken then these coefficients are not free in particular the coefficient of this term is fixed by the coefficient of the quadratic spatial derivative and kinetic term while this coefficient of pi dot cube is completely free so we learned that we have two operators containing information on the spontaneous breaking of Lorentz invariance two operators that are in principle are independent and they generate configurations which are not squeezed they tend to peak in other triangular configurations they generate three-point functions which are not squeezed uh and there are some newer developments uh that I don't have time to talk about uh for example it would it would be very uh if we are lucky and in the near future primordial gravitational waves are observed one can try to start to constrain the squeeze limit of a gravitational wave with two scalar fluctuations and it turns out that the squeeze limit uh is very much constrained even in multi-field inflation it cannot be large it can only be large if you break some very fundamental assumptions about inflation so this the squeeze limit of this three-point function basically tests some very fundamental assumptions about inflation things like whether isotropy whether it the universe their linear was isotropic or not or even the symmetry breaking pattern during the early years a more recent and more famous result is uh what they like what the the authors like to call the cosmological bootstrap it turns out that they showed that in single field inflation uh the the zeta the zeta isometries fix the shape of the three-point function and they managed to recover the simplest three-point functions it's still unclear whether one will be able to apply this to more complicated models but it's an interesting connection between this uh the field of computing amplitudes etc from symmetries and cosmology and also people are starting to look at going beyond correlation functions so looking at the higher order correlation functions not directly by themselves but looking at things like all possible cumulants in the probability distribution function etc and I put only one reference just to publicize work that people did in Chile by Gonzalo Palma, Bruno Shea, Ching-Chang and Speedo Sipsas so I think these are interesting newer developments now that's that's the size of the theory of course it's a biased view of the theory tell us tell us now how can it be observed the most direct way of observing it is by looking directly at the three-point correlation function of temperature fluctuations in the cmd and this has already been done by plant another way of doing it is by looking at the large-scale structure this is a picture of the galaxy distribution in the universe as measured by the slow on digit digital sky survey and so we can we can define a galaxy number over density meaning the number of galaxies at some in some region minus the average number of galaxies normalized and we expect that galaxies form close to where dark matter is more concentrated because dark matter dominates the gravitational potential and we expect matter to fall in this gravitational potential and the dark matter we expect to follow the metric fluctuations that were generated during inflation of course they evolve very very nonlinearly so we expect that matter to follow the the the gravitational potential that is the metric fluctuations generated during inflation and so we could look at for example the three-point function of this galaxy number over density but as i will tell you also in the two-point function of this galaxy number density there is information on long-dose unit so let's start by looking at the cmd first let's consider a phenomenological model as an illustration so imagine that i give you a field metric fluctuation theta which is some Gaussian metric fluctuation meaning that it has zero three-point functions and they add a quadratic term if i do this i generate a three-point function sorry this should be b that looks like this generate a three-point function looks like this and here i plotted in this triangle that i was showing you a while ago this thing peaks in the squeeze limit and this has a shape similar to that that would be generated by multi-field inflation now however this is a purely phenomenological model so what what do i mean when i say that it has a shape similar to the one generated by multi-field inflation uh people define an overlap between shapes as a sort of cosine in this way and two shapes are similar if they overlap and it turns out that until very recently data could only be analyzed for very simple shapes that are so-called factorizable shapes because a general by spectrum was prohibitively expensive for cmd analysis recently people have developed new techniques to look at oscillations and more general shapes but the these simple simple shapes the simple phenomenological templates are still being quoted so this this the one i'm showing here is the so-called local template and again it is similar to the one produced by multi-field models it has a very strong divergence in this in the squeeze limit and remember that single field should not have this divergence so if if we observe something like this if we analyze the data with this shape we observe a number which is high we know that the single field inflation is rolled out but people have created more general shapes so remember that in the eft of inflation there are two free operators and people so therefore one could in principle constrain this kind of non-gaussianities by constructing two independent shapes people indeed have constructed the so-called equilateral shape which is a bit of a misnomer it of course it's a non-zero three-point function all over the parameter space but it peaks in the equilateral configuration and then orthogonal shape which is orthogonal in the sense that it has nearly zero overlap with the equilateral such that you have two independent data points that you can compare with your single field model and Planck has put constraints on this encoding the recent 2019 constraints to sixty five sixty eight percent confidence level so the ones generated by single field inflation in equilateral or orthogonal configurations are compatible with zero but the constraints are not very good so if fnl equilateral of order 100 is still easily accepted while the one generated by multi-field the local shape is very is much better constrained due to these strong divergence it's much easier to see in the data it's also compatible with zero and the constraints are starting to become order one though i would say since this is just sixty eight percent confidence level i would say that they are more order 10 okay so what do we learn from from these constraints by Planck first so remember the local shape the one of multi-field is of order 10 first we learn that everything is consistent with single field inflation single field inflation predicts a very small value for this divergence it's it's zero but there are some projection effects that generate unknown zero value which however is very small so single field inflation predicts fnl local to be of order 0.1 and fixed by the two-point function so it's it's amplitude is not free it should be related to a two-point function that Planck already measures this power spectrum of Planck that it already measures so we are still a couple of orders of magnitude from achieving this precision but since it's compact but it's perfectly compatible with the data so it's consistent with single field inflation what does multi-field say so the natural values for the local fnl in multi-field are order one if the non-gaussianity is generated by some spectator field that is independent of the inflaton and the case into curvature fluctuates contributes to a curvature fluctuation of the case after inflation so then fnl is predicted to be of order one we are only one order of magnitude away from order one and if it is very if it is very coupled to to the inflaton if these are the additional fields are very coupled to the inflaton it's predicted to be of order 0.1 but free not fixed by the two-point function and we are still far from observing this what about the other shapes so the other shapes the equilateral the orthogonal etc from this we learned that the theory is consistent with a weakly coupled inflaton meaning such that these QE cooperators are not very large indeed from the t eft of inflation we learned that fnl equilateral but also orthogonal should go like h over lambda squared where lambda is the scale suppressing these higher order operators and current constraints imply that lambda should be bigger than order 10 times h so inflation is consistent with being weakly coupled so that's what we learned from the cmb and we one would hope that in the future we can improve on this in the future lies in the large scale structure in future near i'm showing pictures of near future surveys the euclid survey done by the europeans lsst which is which will take place in chile it's basically an american survey and this one i forgot i think this is this is desi or ds i think and fine the large scale structure is the future but it has a problem it's it's an uglier observable because the cmb is linear you can run a camber class or any boltzmann code to perturbative order and get get good results for the cmb but the the large scale structure is intrinsically non-linear so it's much uglier so it's like the difference between colliding leptons or colliding hadrons large scale structure will be like hadrons because it's it's it's very very non-linear and perturbation theory breaks down etc so to see it let me write down some simplistic model of large scale structure where i write the dark matter density as a fluid that satisfies the continuity and the Euler equations and we see that these equations contain non-linear terms as we all know from hydrodynamics hydrodynamics is very non-linear uh so we have to expand so while we can be perturbative one can expand this in a perturbative series but not only that this is just dark matter what we observe is galaxies and we expect we expect galaxies to trace the density of dark matter however uh and and and this connection between the number of density of galaxies and dark matter is called biasing and this but this biasing can be non-linear with some free coefficients it can depend on k and many other complications so all these non-linearities generate a non-gaussian signal which is difficult to quantify but doable we are people are working on it we are working uh so what are the observables of the large scale structure one can observe directly the three-point function that's kind of trivial but even the two-point function contains some information so as i said bias is the connection between galaxies and matter and let me consider the local model again so where i have a gravitational potential and i add a quadratic term this quadratic term correlates short wavelength fluctuations with long wavelength fluctuations so imagine a very simplistic model for galaxy formation imagine that i have some fluctuation that looks like this it's a long a short wavelength fluctuation superimposed on a long wavelength fluctuation and imagine that whenever density whenever the the dark matter density becomes higher than a certain value i form a galactic halo a very simplistic model for galaxy formation so in this in this picture i will have a halo here and a halo here this is for a final equal zero both the short wavelength scales and long wavelength scales are independent if it is positive the short wavelength scales will be enhanced whenever i'm on a hill and suppressed whenever i'm on a on a on a valley and therefore i would form more galaxies with the opposite sign the opposite happens so there is a correlate so when with f and l different from zero there is a correlation between the number of galaxies and the gravitational potential and this correlation goes like one over k squared because simply because simply due to a Poisson equation because density is the pleasure times gravitational potential this is the Poisson equation therefore the galaxy number over density is connected the galaxy number over density two point function is connected to the dark matter two point function and therefore to the primordial two point function without one over k squared dependence if we have a local non-gaussianity and moreover this is sensitive to the squeeze limit because it's precisely the coupling between a long wavelength mode and short wavelength mode so people are already using this to obtain constraints on local f and l which are starting to be competitive with the ones of blank and there are apart from non-linearities just to finish there are there is an additional complication which are which is the fact that one has to take into account general relativity when you compute this relativistic effects are very small in the large-scale structure because most of the large-scale structure most of the things that we're interested in are deep inside the horizon deep inside the howl radius therefore relativity is basically negligible but non-gaussianity is also a very small effect and they turn out to be of the same order of magnitude so if we care about non-gaussianity we have to care about relativistic effects and these relativistic effects just to give you an example of some relativistic effects we observe the number of density of galaxies at some redshift in some position of this in some direction of the sky this is what we actually actually observe and we separate this into an average plus this over density and this average is simply then the this average density of galaxies is the number of galaxies the average number of galaxies at some redshift divided by the volume of that redshift shell however for example the frequency of the photon is sensitive to the gravitational potential so the redshift will change with the gravitational potential so i will induce in this way a correlation between the gravitational potential and the number of galaxies which induces non-gaussianity uh people i wanted to give you an example but i don't want to bore you uh people have computed this for the two-point function trying to observe the scale dependent bias that i told you about and they see that indeed if you care about constraining fnl to order one which is what you would like to learn whether there were there were several fields during inflation or not uh this is degenerate with uh this degenerate with these relativistic effects we have also computed it for the squeeze limit of the three-point function and some preliminary results also show that the relativistic effects which are this red line and this orange line are degenerate with a primordial signal which is this purple line however we are still optimistic and uh so we we expect that near future observations like the ones i showed or the recently approved spherex will be able to constrain fnl at least the local one to order one and from that we will be able to learn where primordial fluctuations were generated by spectator field or not and we may even look for higher spin fields and if we are really optimistic uh as as observations improve one can hope to go further so to conclude to summarize non-gaussianity is sensitive to a field spectrum during inflation it can be measured in the cmb or lss measurements are underway current constraints are still far from the physical interest in reason but future surveys promise to start exploring that region and finally well just because it's the thing i'm working on recently gfx are important if we hope to achieve a precision of fnl of order one so that's the end thanks for using me thank you Jorge for the for the talk it was very interesting your seminar so uh before going to the question from the audience here in the in the zoom session let me remind the people that as you can see now we are not using hangout on earth now we are changing to the zoom since then thank you thanks to the university of higinois in this case and we want to also ask the people that are following us in youtube to subscribe to the channel also to our facebook page as well as to start to write your questions during the individual chat so maybe we can start with some question from the people here in the audience of the other presenters i mean other participants so so Jorge i have a question in the beginning when you you were talking about inflation so on is it possible to to include information or future information coming from the sector of gravitational waves because there are these stochastics that could lead some relation with inflation so i'll answer at two level first there is a there is ongoing effort to look for gravitational waves who is doing inflation in the polarization of the cmb so this would directly look at gravity waves produced during inflation i've seen some claims that they will be able to observe something like that during least but they are optimistic to say the least so i don't think that this future experience will be able to see gravity waves this gravity gravitational waves experiments will be able to see gravity waves produced during inflation unless you do something strange with your model well something let's not call it strange let's call it extreme unless you do something extreme with your model um so yeah so this has nothing to do with so i'm talking about the gravity waves produced during inflation this has nothing to do with the stochastic background of gravitational waves that may be generated during a phase transition in the early universe etc so i was mostly talking about fluctuations generated during inflation right so but in the i'm gonna what about in the do you do you expect to have some kind of super optimistic scenario in case of cosmologies or inflation in the case of modified gravities or some models of modified gravity can mimic some aspect of inflation yes but in especially during inflation the difference between modified gravity and not modified gravity is a bit blurry in the sense modified gravity will always add some additional degrees of freedom to your dynamics so many many of these models can be understood simply as adding additional degrees of freedom in that sense they are very similar to inflation now many of them that do inflation they are just doing inflation in the sense that the national degrees of freedom are inflating the universe so in that in that sense there is very little difference now there are alternatives to inflation they are in my opinion they are not very appealing yet maybe someone will come out with an appealing alternative i'm not saying that inflation is the truth but the ones that exist in the literature are not very appealing and they don't often involve modified gravity unless unless one is thinking about loop quantum gravity and those kind of things so so yes i would bundle most of the models of modified gravity for inflation inside the same group as inflation models because it's just some additional degrees of freedom you can see them as just some additional degrees of freedom are active doing inflation so many of the things that i that i talked about still hold in those models i don't know okay in youtube we have some questions but they were kind of not so relevant for the there was some discussion about the in the case of particle and what so i don't know if people in the audience has questions or the people in youtube that they they can still write questions but i wanted to ask you the what about the case of because you were talking about the future measurements with this the largest case survey to try to and all the only exactly the part that you're passing now so i'm wondering because most of the problems that there are when people study for instance structure formation the case of dark matter is if they include or not include variants because at the end galaxies forms in the sector where parents are i mean galaxies the observed galaxies are in the sector where there are over density of variants but they are basically some dark matter plans that are kind of invisible from the point of view of the of the emitting light or so on so in the sense because when we were talking about the multi-field inflation you were you have these waves that said that in the principle there is a connection between the gravitational potential plus the amount of galaxies observing that wave so there is a kind of is it possible to disentangle for example the gravitational potential itself or to include well no so in galaxy in galaxy surveys it's impossible to disentangle the gravitational potential from from galaxy number over densities i mean you cannot see the gravitational potential directly but the hope is that at least at large enough scales which is anyway where most of these effect we are looking for these effects the all these unknown physics of the involving variants making a mess when they form a galaxy etc can be encoded in bias coefficients like the ones that appear here they can be encoded in a bias expansion people have even written this in in an effective theory framework etc trying to argue that this is enough and so it seems to work well um you want to do something else yes however however these bias coefficients are unknown so you're adding new free parameters to your to the things you want to measure uh they are known and they can generate a non-gaussian signal so uh when you merge you have to marginalize over them because you have no independent way of measuring them and when you may marginalize over them unless there is a method that maybe i'm missing and when you marginalize over them of course you lose information on the non-gaussian signal however uh these bias coefficients cannot affect the squeeze limit this non-linearity is coming from baryon the evolution of baryons or the evolution of the last structure cannot affect a signal in the squeeze limit which is the most interesting one and the argument is basically this that no matter how complicated your galaxy formation this correlation with a gravitational potential can only be primordial it cannot be induced by non-linearity because the gravitational potential newtonianly uh you're basically blind to it yes so no newton no short-scale process can induce it because you have no way of generating some absolute value of the gravitational potential you can only generate secondary okay so so let me just check again in youtube so uh people from the audience i don't know maybe alejandro has a question no thank you Jorge for your talk it was very nice okay that was not a question a compliment okay so i don't know i i don't have more questions i mean i want to thank you Jorge because it's super interesting you your talk in fact i i mean i am not from the from exactly from the field i mean i'm not familiar so familiar with inflation but i really enjoy it because i learned a lot about the how to observe this how what is that the observable that you're looking at and what is the expected signature and let's hope that it's going to be a optimistic future with this okay so thank you Jorge for all the rest of the people that are looking the webinar series we are back we are going to continue with the same schedule that we were having in the past more or less each two weeks three weeks we're going to have a new webinar talking about different aspects of the physics astroparticle cosmology particle physics so on all the most of the fields of the science so and we are going to see again in the next webinar so bye thank you Jorge and thank you everybody for watching bye thank you for