 Yeah, thanks. First of all, I would like to thank the organizers for giving me the opportunity to give us all And we've had some PhD students in the Netherlands working at the Leiden University and Yeah, I'm happy to present you our current project, namely incorporating Primordial non-casual entities in the framework of effective theory of logical structure This project is done in collaboration with Valentina Sassi, Daniel Baalman, Enrico Payer and Drian van der Waude who's sitting over there Yeah, they have been working actually quite hard to get the paper published this week and tomorrow it will appear on archive So stay tuned Yeah The bottom line of the project is that we develop a consistent perturbation theory for dark matter with non-caution initial conditions That's better The motivation is that we would like to improve our the sensitivity on measuring Primordial non-calcianities Suppose we were able to detect Primordial non-calcianities then we directly probe into the early universe and we will Yeah, we will Find the world of information Turns out that most extended models of inflation that they predict a certain amplitude of above a certain threshold of non-calcianity given by FNL of order one So if we would be able to turn to reach the sensitivity of FNL equal to one then even absence of a detection we Would learn quite a lot So are we going to look at logical structures or the CMB? The CMB of course is very nice because you can describe it by linear physics However, the amount of information you can get from there is quite limited because It's only a two-dimensional survey. So the info information skills with the area And more over we only have access to a limited range of skills because on large skills It's limited by cosmic variants whereas on the small skills. We have silk damping so We should probably turn our attention to logical structures Which is a three-dimensional survey so the information skills with volume However, there's many sources of late-time non-linearities which makes this problem very complicated and the range of skills we can describe is actually Yeah, a question mark. So the effective theory of logical structure is an approach to Going to the monthly non-linear regime Well to give you an idea of what all the challenges are if we want to start with Yeah, with primordial non-calcianities We first of all have to understand the non-linearities induced by a gravitational interactions Then secondly, we don't measure actually the dark matter distribution, but we measure galaxies or halos And we have to understand the bias between them Then also the galaxies they have peculiar velocity So that there are redshift space distortions and there are many other effects we have to understand So it's very challenging in this project. We only focus on the description of the dark matter perturbations and We focus on the biospectrum as an observable So dark matter biospectrum there So how are we going to extract this primordial non-calcian signal? The first first thing you have to do is understand fully understand the background so we fully have to understand the non-linearities induced by gravity and this has been done in This paper for example, and also a paper by Leonardo Senator, by the way and the second thing is that We have to understand how gravitational non-linearities affect the signal we want to measure namely primordial non-calcianity And from there we can if we understand this then We know we can try to answer the question how distinct primordial non-calcianity is from the background and How well we can distinguish between different types of primordial non-calcianity So let me illustrate this last point by this picture So here It's plotted the relative ratio of the contribution to the biospectrum coming from non-calcian primordial Initial conditions as function of scale and So that you can see for three types of primordial non-calcianity what the relative scaling is you can see on large scales They scale quite differently but on the due to the Corrections due to gravitational non-linearities on the smaller scales you can see they start scaling in the same way So actually that this is a bad thing Okay, let me just go back to the Problem so how how are we going to solve the fluid equations for dark matter? So dark matter is Collisionless particles, so it's described by the flash of equation taking the first two moments You'll end up with the fluid equations, which you already have seen before Which looks schematically like this so there's an Linear time evolution operator and on the right-hand side you get for the density contrast of dark matter And on the right-hand side There's the non-linear corrections and actually there's also some velocity dispersion term for the short scales and the the old way let's say to solve it was just by neglecting this velocity dispersion and then solve Protervatively for the density contrast so first solve the linear equation then use the green's function to solve order by order However as Matias Salariaka already pointed out there are some problems with this approach namely small skills are Don't have a small density contrast. So actually there's no well-defined perturbation parameter and Since we don't solve the short-scale physics by this approach We don't know What they are and we also don't know how they back react on the long skills more over the the loops in This approach which coupled the long skills to the short skills They give the wrong result because we don't solve in the right way for the for the short-scale perturbations all right, so I put all those problems in the left-hand side of this table So the effective theory of laska structure is a way to solve solve all these problems and the idea is that You're going to smooth over the short skills so integrating out the short skills This means that you end up with a set of equation which are which only describe long wavelength perturbations So it means that then then you will have a well-defined perturbation parameter. So that already solves the first problem Also because we integrate out the short skills this will give this should can rise to correct corrections to the equation of motion because Which yeah parameterize the back reaction of the short skills on the long skills. So this will give rise to an effective stress tensor But it doesn't mean that we know the the physics of the short skills So the only thing we can do is parameterize our ignorance So we assume that the short skills depend locally on the the long wavelength perturbations and then we expand and Also consistent with the symmetries of the problem and then we expand the stress tensor In the long wavelength fluctuations and this will describe the back reaction of the short skills then Turns out that these new terms in here in the equation of motion will exactly provide the right right counter terms to renormalize the loops and then We end up with the right results. So the effective theory of laska structure solves all the problems at the same time now in this paper we Want to include primordial non-gaussianities So we in the in this framework so we smooth over the short skills and expand the stress tensor. It was done in the In these papers before and especially this one for the for the biospectrum and Because we start with non-gaussian initial conditions the long and short skills are initially correlated So this will give rise to new terms in the effect of stress tensor proportional to the primordial potential So this is a very sketchy way to To show it but in the paper we define large classes of non-gaussianity by by the scaling and angular dependence and We classify all the contributions to the stress tensor in a systematic way Anyway, so this will give us a consistent perturbation theory and We solve the perturbation theory to first order in non-gaussianity and loops and We check explicitly that all the counter terms gift provide the right counter terms to renormalize the loops then in second part of the paper we do in numerical evaluation of all the con non-gaussian contributions to the biospectrum so we I'll compute the linear contributions the loop contribution the counter terms and a question you can ask is how how well can we distinguish primordial non-gaussianity from the gravitational non-linearities for example and this The answer will depend on for example the amplitude of the signal the scale dependence relative skill dependence and the range of skills We can reliably describe We didn't do a full analysis, but I will just show you a couple of plots to give you an idea so This is an example where we started with local primordial non-gaussianity with FNL equal to 10 and Here are plotted all the contributions to the biospectrum in the equilateral configuration Again as function of scale And so the here the blue lines. That's really the part which comes from gravitational linearities. So this is the background The red part is also The background, but it's just an estimate of the background so Actually, the red line will denote How bad we actually know our background and Then the the black lines denotes the non-gaussian signal So here you can see in the equilateral configuration. We don't really trust a large a large range of skills because here the The higher order corrections to the background become quite seem to become important. So 10 yeah So here we can only describe the non-gaussianity up to this this skill and but if you go to the squeeze configuration the situation looks much better and We see that the estimate of the higher order contributions are lower than all the non-gaussian contributions to the Biospectrum so this gives us hope that we might be able to detect non-gaussianity in the primordial non-gaussianity in the in the biospectrum and More of also the counter terms I Mean, okay, we plot is actually the counter terms with a coefficient But actually we don't know the coefficient so it could be also a little bit lower or higher But they seem to be an important seem to be important and we have to include them in the analysis For the full analysis we would like to do a Fisher analysis So that's what we are working on right now to make more precise how well we can constrain primordial non-gaussianity from The biospectrum Then another thing Which would be nice to do is fitting to embody simulations to fix the parameters and the effect of stress tensor So it's that if we if you in the end want to compare to observations, then you only need to measure FNL But before you can actually compare to two observations You first have to understand the halo bias or galaxy bias and redshift space distortions So including primordial non-gaussianities also have to be has to be extended to these Things So the summary of the project is that We have extended the effective theory of a logical structure with non-gaussian initial conditions we found new terms in effective stress tensor which Provide exactly the right counter terms to renormalize all the loops and We did a numerical evaluation of the contributions to the biospectrum and tomorrow you should check the archive Yeah, and I would be very happy if you want to have more details to discuss it Maybe later on or you can of course ask me any question right now