 All right, so, today was a great, this morning's talks were a great introduction for mine, and also the talks of last week. So, yeah, I'll have something to add about, including baryons into the effective field theory of large-scale structures. This is work that I did with Ashley Perko, a grad student, and Leonardo Senatore. Stanford University, with some groups, Slack, KIPAC, SITP, some various names. Okay, so this is kind of my outline, and I'll just start. So, where's cosmology today? I guess we're all gonna see all these mini introductions of cosmology in all these talks, but it's kind of unavoidable. So, in the CMB, we learned a lot about, about sort of the background of the universe. We know that the fluctuations are primordial. Mattias talked about a lot of these things. They came from before this, from before the era of CMB. We learned that there's scale invariant, there's some tilt in the power spectrum, et cetera. One thing that we do learn, we put some upper limits on how much non-galcianity there could have been in the primordial fluctuations. Okay, so that was nice. Speaking to these limits on non-galcianity, one way to look at this is to look at the effective field theory of inflation, or to just sort of look at this pi field represents the inflaton. The first line is just the free or quadratic part. If that was all there was, then there would be no non-galcianity, meaning all the interactions are just quadratic. It's a free field. However, if there's some cubic interactions here on the second line, that means that you would see some kind of non-galcianity. So, when we put limits on how big non-galcianity possibly could be, really what we're doing are putting limits on coefficients of these operators down here. So, for instance, there's some energy scale that suppresses a higher-dimensional operator, call it some lambda u, and we sort of put limits then on a lower limit on what that energy scale could be that's suppressing these higher-dimensional operators. So, we had WMAP a while ago, and then we had Planck. And really Planck was great, he measured a lot of things, but it really only increased our knowledge in this suppression scale by a power of a square root of three. So, we didn't learn too much by the non-detection of the non-galcianities. This is to be contrasted with, say, the LHC, which billions of dollars, you better have something to say no matter what happens in the experiment. So, we found the Higgs, but if we didn't find the Higgs, it would have strong implications because we were going up to such high energies that if the Higgs wasn't there, it would have strong implications for the theory. It would have this perturbative unitarity, bound would be broken, and there would be constraints on theory, even if you didn't find the Higgs. So, that's kind of what we want to get at with large-scale structure and non-galcianities. This square root of three is not that kind of change in scales that is gonna tell us anything new about the theories. So, what do we do next? We hope it's large-scale structure. The main thing is that if we can have predictions at larger values of k, we get more modes, we get more statistics, and essentially we get more information out of large-scale structure, and that would be able to have constraints on F and L somewhere down to 10, one, something. The thing that we're looking for is if we can constrain F and L, either find non-galcianities, or constrain it to be less than one, that represents a really big step in the theory. So, this is kind of a plot, which these are the sort of current bounds on F and L that we have now, and what we're aiming for is some kind of like tiny dot here would be a really optimistic idea of what large-scale structure might be able to do for us. So, you could tell this is just a giant shrinking of this plot. If we can understand to percent level the observables that we're looking for. So, I'll just give a brief introduction about the effective field theory. We heard that basically what happens or in the standard perturbation theory we try to expand out in terms of small fluctuations, but fluctuations are only small on large scales. They get big on smaller scales. And so, when we try to do perturbation theory and expansion in terms of loops and all this stuff, these high scales enter and the perturbation theory breaks down. So, we have to do something about this ultraviolet part or this small-scale part. Another point which has kind of not been stressed so much is that dark matter really isn't a collisionless fluid. Like, it is, if you open Dodelson's book, I mean, the largest scales, it's a pressureless fluid, but if you go to smaller scales, it's just not. I mean, dark matter probably interacts and it does some stuff, but okay. So, if you just solve pressureless fluid equations all day long, you're never gonna match dark matter because it's probably not that. Okay, so how do we take care of that? We need to deal with this UV and this is called renormalization. These are the standard variables of Eulerian perturbation theory. There's some equations of motion which you've seen a few times now. There's Poisson equation, continuity equation, then Euler equation. This bottom equation is the Euler equation for a pressureless fluid. The fluid is really not pressureless. You can see that even if you take all your fields here and you smooth them with some scale, I mean kind of like group dark matter particles and some radii, what happens is that you generate, you just generate extra terms from integrating out those higher things. And so, on the right-hand side, there's really some kind of some kind of stress energy tensor which on the larger scales is zero but on smaller scales is just not zero. So, what happens is that how it looks when we actually use it is that it's proportional to some of the long wavelength fields here, delta. There's some scale here. This has two derivatives. So there's two values of k and k space. And there's some kind of coupling constant parameter here which depends on the scale at which where we set some cutoff because it's used to make sure that we cancel the cutoff dependence in loop integrals. And so that all of our quantities are independent of some cutoff or the smoothing scale or something like that. And this is called a counter term or coupling constant or something. So this is what we've tried to match or measure in simulations. So I'll just stress that when I say that we wanna correctly treat the ultraviolet, doesn't mean we know what's going on in the ultraviolet. We're not as good as a simulation. We don't know what's happening in the ultraviolet but we're just trying to describe what happens on the largest scales and sort of encapsulate or summarize what's going on in the small scales and just say how it affects large scales. We don't know what's going on in the small scales. Okay, so this is just a plot which kind of shows the current-ish state of the effective field theory and its comparison to non-linear simulations which you've heard about. This line on the top is the standard perturbation theory at one loop and at two loops it's kind of even worse. I don't have it on here but you can see that we're sort of fitting the simulations where we choose the counter terms in such a way that this is pretty good K, 0.5, 0.6, something like that. So if this continues, the amount of more information that we can get from large scale structure could really allow us to put constraints on FNL creeping down towards something like order one. Oh, the shaded area, so this is a two loop calculation. The shaded area would be our theoretical error coming from three loop, so we estimate the size of three loop terms and so basically we expect our curve to fail when our theoretical error becomes large. Okay, so, and there's been some other predictions which have been matching pretty well, bi-spectrum, velocity, correlation functions, et cetera. So, but let me get to the baryons. The idea is pretty simple. We wanna know how all these awesome processes like supernova and active galactic nuclei and heating gas and winds and cooling and all this cool stuff that happens with baryons. We wanna know how that affects the nice, placid distribution of the large scale structure. We don't necessarily wanna understand exactly what's going on there on the top, but we wanna know how it affects the large scale structure. Why? Well, like I said, we need to know these observables to present level accuracy in order to get enough information out of large scale structure to push down limits on F and L. So, if baryons have percent level effect on the dark matter power spectrum, we need to be able to take that into account. So, what are the challenges? Like, baryons certainly are not even close to a pressureless fluid on short scales. They have a pressure, they explode, they do lots of cool things. However, you might say that with dark matter at least, you could just rely on simulations because they are really simulating particles gravitating towards one another and that's what dark matter pretty much is. However, with baryon simulations, it's a little harder. There's a lot of sort of things you have to put in cooling or how much active galactic nuclei are there. You have to put in some winds to cool gas that gets too hot and it's sort of just still being developed and not really known a priori what kind of effects to put in and so that's one reason that we would want to understand this systematically. But maybe it's okay, maybe baryons, they explode but there's only a tiny, tiny portion of them that are being ejected away from black holes or something and it's just such a small portion that we'll take that as some systematic error in the calculation, okay, but maybe the bulk of baryons are still kind of just hovering around and we saw that kind of, yeah, in this intergalactic medium and on large scales they have some understandable effect. Okay. So I'll just get to the punchline. So what happens is that there's some counterterm expression in the power spectrum. So b here stands for baryons, c for cold dark matter. This is the sort of correction or error to a stands for adiabatic, which just means total matter. So the correction to the power spectrum, I should say these are just one loop results so we don't have any non locality in time issues. This is similar to what we found before what other people mentioned. There's some k squared p linear correction and now it shows up exactly the same for the baryons as it does for the CDM. Okay, so I'll just quickly show you. This is just, we do fluid equations except now we have two fluids. Yeah, there's coupled only through gravity. That's the only thing I'll say. So gravity just sources both the baryons and the CDM. Otherwise it's just two fluids. Forget about that. The end result is again sort of what I said. We have this typical standard perturbation theory expansion for the CDM and the baryons. You have your linear piece, which is P11. You have your one loop standard perturbation piece and then you have this counterterm piece. But now we have a second fluid. We have a second speed of sound or second counterterm and that's here encoded in these CAs and CIs. A stands for adiabatic, I for isocurvature, just a basis. Anyway, so we just add one counterterm. This CI squared, if it's zero, these two fluids are basically the same, which just means that there's no difference. They just act as one fluid. So having a CI squared different than zero is distinguishing the collection of two species as actually two unique species. So let's just go and look at some simulations. How much time? I guess I have more time than I thought. Five minutes, okay. So let's just look at some results. So this is the worst looking plot. This is, so let me just say what we compare to. So we got a set of simulations. We got a set of like 12 simulations. Each one including different kinds of baryonic effects. One has sort of, the best one has this active galactic nuclei included and then has some kind of cooling wind. And I have a table in here, but there's like all these different kinds of possible effects that you could run the simulation with. So we got a set of those. We get a simulation which has no baryonic effects, which is this one. With this one, we don't have very good data points. There's a lot of cosmic variants, but we try to get a rough idea of what the speed of sound is. We just basically try to make our prediction, EFT, divided by simulation close to one, get some value. I call this WB equals zero because that's the baryon fraction. So this would be our speed of sound with no baryons. So all the matter is just called, or is just like dark matter. So then they give us some simulations with baryons. And in those we could measure the total matter power spectrum and then we can see how the baryons affected the total matter power spectrum. So we get some pretty good fits. Like first of all, what we choose to plot here is in the simulation, we plot the adiabatic power spectrum for the simulation which included baryons and divide by the one which doesn't include baryons. These dots are from the simulation, the different colors are from the different simulations. These curves are pretty, the dots are pretty smooth because this ratio essentially cancels out a lot of the cosmic variants. And you could see that pretty much whatever simulation is on there, like our theory curves are pretty close to the dots. And in fact, it's like, it's pretty good. It's actually sort of too good. It's like less than 5% different. Now this K.6 is not what it seems like. This is in a two loop calculation. So our theory is really only good for the dark matter power spectrum to 0.3 which is the typical thing. But in this ratio, terms that we haven't computed are like canceling. So this failing at 0.6 is consistent with our one loop expectations. Anyway, so then we just look at the actual baryon power spectrum, PB, and we divide by the total power spectrum and this is fitting this isocurvature speed of sound or the baryon speed of sound. And again, the fits are kind of amazing and they fit for any kind of baryonic physics that you put into the simulations. Yeah, this one is about 1% fit. So okay, I guess what I wanna say is that baryons can have percent level effect on the dark matter power spectrum. It's complicated physics, but the functional form is known and all we need is one more coupling constant. So thanks.