 Hello, everyone. Welcome to this latest version of our Latin American webinar in physics. It is a pleasure to have today Professor Kim Badi from the University of Texas, Adostin, my former alma mater. And she's an assistant professor there and she will be speaking to us today about searching for dark matter interactions using cosmology. Dr. Badi is right now an assistant professor at UT Austin, but before this she was a postdoc at Johns Hopkins University and University of Hawaii. And she did her graduate education at Caltech. Her focus of research is on dark matter, cosmology, cosmic background radiation, structural formation. It is a great pleasure to have you today here, Kim, and take it away. Before you do that, let me remind everyone that please you should write your questions in the chat on YouTube. And please follow us in the social networks and subscribe to our mailing list and to our channel on YouTube so that you are up to date with our next webinars. All right. Thank you, Kim, and take it away. All right. Thank you very much. Thank you to the organizers for this invitation. I'm very happy to be speaking with you today. So let me get my slides up and started. All right, there we go. Yes, so today's topic is going to be about searching for dark matter interactions and cosmology specifically non-gravitational interactions. We want to understand what this dark matter could be. And so these are a few ways of how to go about that. So to begin with, let's look at the schematic diagram of what the cosmic history of the universe looks like. So here's the universe. And so time is running down. Another way that cosmologists usually refer to time is through the redshift. So photons will redshift as they travel farther and farther. And this is due to the expansion of the universe. So the universe starts out very small and dense and hot, and it expands and cools as it does so. So there are a few areas of interest to us in the sense that we have some sort of observational or inferred information from astrophysical observations. And so this, for instance, on that early times comes from big, big nucleosynthesis. So this is when the light elements were created in the early universe. And so here we have hydrogen, mostly we have helium, tiny bit of lithium. So this is what happens at some fairly early stages in the universe's life. As the universe expands, we have this process called recombination that occurs. And so recombination is when electrons and protons get together and they form neutral hydrogen. This allows the radiation in the universe to then free stream, no longer having to interact with charged particles in the plasma. And so this creates the cosmic microwave background radiation that we can observe today. And so this CMB data gives us a lot of information about what was happening at very early times in our universe's history. So after we have recombination, there's this era called the Dark Ages. And there's not a lot of observational probes that we have from this, the universe is mostly neutral hydrogen. And so there's not a lot of invisible probes from this era. And it's not until the era of Cosmic Dawn that we can actually see something. So this is the period of time when the first stars are born. And so there's radiation that's being emitted. And we have some hope for seeing what the earliest stars were doing at this time. So then the universe having created stars and having formed, you know, there is forming galaxies undergoes this period of reionization where the universe gets reionized all that neutral hydrogen gets reionized due to the radiation that is around. And then today we live in, you know, we live in the Milky Way Galaxy and we can go and observe different galaxies and the dark and in first things about the dark matter halo distribution in the universe. So these are a list of various cosmological probes that we can use to understand the nature of dark matter. And so this talk will focus on thinking about what happens when this matter component of the universe called dark matter has interactions. And so not just gravitational, we're wanting to let it interact specifically with particles in the standard model. And so these interactions, I'll focus on three different parts to this talk. The first part is going to probably take the most time it's dealing with this issue of small scale suppression. I'll talk a little bit about cooling of the intergalactic medium. And then, and then finally I'll discuss some newer work about thinking about the initial conditions for dark matter. And so these different points correspond to probing dark matter physics that happens at various eras and have an impact on various observables. So to begin with, the first point, the first part that we're going to look at can be summarized as dark matter scattering suppresses small scale structure formation. Okay, so what do I mean by that? So the structure formation of the universe happens because the universe is not perfectly smooth, right? We have little tiny density perturbations and matter wants to clump together. And so that gravitationally attracted matter will just clump and clump and clump. And that's the structure that we're talking about. So at the largest scales, we have the cosmic microwave background that I was talking to you about. So the cosmic microwave background looks very smooth in terms of the temperature of the photons across the sky that are measured. Temperature is about 2.7 Kelvin, but we're interested in the tiny fluctuations in the temperature of the photons across the sky. And so the Planck satellite has this image of the temperature fluctuations. You can also consider polarization fluctuations, but the, so here is what's called the power spectrum for the temperature anisotropies of the CMV. And so you're basically taking this map, breaking it down into spherical harmonics, and this is the multipole number here on the X axis. And so it's showing you at what multipole, how much, you know, correlation there is in terms of the temperature fluctuations on the sky. And so this is telling us information about the type of structures that we expect from these fluctuations. So the multipoles correspond to some angular scale in the sky. So, you know, at multiple of a thousand, it's about an angular scale of 0.2 degrees in the sky. And so you take all of the points, all of the temperature fluctuations that are separated by 0.2 degrees and you average them over the full sky. And this is the result that you get. So here are the data points, you know, shown in blue or red from the Planck satellite. And this is the best fit lambda CDM cosmology in this gray line here. And so you can see that the data get really, really precise as you go to these intermediate multiples. And so we have really good data, we have really good information about what's going on. And what we have to do is we have to, you know, have some baseline model to understand what these wiggles and bumps mean in terms of what the content of the universe is. So the standard cosmological model is lambda CDM. So lambda is just a cosmological constant. And you have CDM, which is called dark matter. So dark matter in this framework is assumed to be cold, not relativistic. It's assumed to be effectively collisionless. And so its primary purpose is actually to be a gravitational source, right? It's a matter component of the universe and it just will allow gravitational collapse to happen. So it's six times more abundant than baryons. And by baryons, what I mean are, you know, the protons, the helium in the universe that we also have electrons. The baryons are not baryons, but we just lump them into what we call the overall baryons fluid. So this dark matter is really important in terms of forming the gravitational structures that allow baryons and photons to move. So what are all these bumps and wiggles that we see in the CMB power spectrum? These are just acoustic oscillations. So you can imagine that you have some slight overdensity of dark matter. There's a little bit more dark matter located here and here, for instance, and our purple baryons want to fall into these dark matter potential wells. But there's also radiation around. And before recombination, this radiation is very strongly coupled to all the ions, you know, all the electrons and protons that are in the universe. And so what's happening is that you have this competing effect of baryons wanting to clump with the rest of matter and the radiation trying to push things out. So you can imagine that this picture can be repeated at different at different scales. And the idea is that this falling in and pushing out motion. This is just simple harmonic oscillation. And this is just the Fourier space description of the acoustic oscillations that are happening in the early inverse. So this was the standard picture of standard lambda CDM where this these dark matter potential wells just exist for gravitational purposes only. So how do we change this picture when we introduce non gravitational interactions from dark matter. And so what I want to focus on is just dark matter scattering. And so here I have this Feynman diagram, where I'm imagining a dark matter particle chi is going to come and interact with some baryonic particle. You know, electrons are included in this electrons protons helium that exist in the early universe and there's just some elastic elastic scattering process. And so the quantity that cosmology actually cares about is called the momentum transfer cross section so it's this weighted cross section. And you can imagine having different different shell cross sections from different types of scenarios so for instance if you had a Lagrangian that just looks like Kyber chi f r f this corresponds to some velocity independence been independent interaction. And all of these sorts of scenarios can be reduced down into some, you know, overall factor some scale for the cross section times the relative velocity between your between your standard model particle and your dark matter, right, to some power You can actually get negative values. So you can have inverse dependence on the velocity. If you assume, say for instance that dark matter has an electric dipole moment or that dark matter has some, maybe small amount of electric charge. And so this would give, for instance a cool and like scattering. And the behavior of the of the cross section looks like V to the minus four. So to be as model independent as possible. When thinking about this process in cosmology. I want to completely neglect the effects of annihilation. So of course there's going to be a diagram that you can flip on its side, you can flip this diagram on the side to give you annihilation. But, you know, these Lagrangians do not uniquely map to a value of n right for a single value of n there are multiple Lagrangians you can write these are very simple interaction structures and so you could imagine something much more complicated. So the, the annihilation and the scattering, you know, relationship are going to be dependent on whatever model you choose. So for the purposes of what I'm going to show you, I'm going to completely ignore any model dependent annihilation relationship to scattering. And I'm not going to address any sort of issue for how you create this dark matter. Right. You could have some, for instance, asymmetric scenario where you produce, you know, dark matter and you you live in a dark matter only universe for instance and no anti dark matter. And so the these are my assumptions and it's just because I want my constraints to be widely applicable. And so I can say, Alright, I have a scattering. What happens when I actually introduce this scattering into my cosmological model. And so the answer is, in summary, small scale suppression. So if you go back and remember the little schematic that we had where you had this dark matter potential well but you're going to have this potential well because there's some of dark matter particles. And when you have these interactions, you know, your very own could come in and knock away one of the dark matter particles outside of its potential well. And so the, the hand wavy sort of way of viewing this is that your interactions are washing out these small over densities of dark matter. And you can test this with the the CMB. So much more much more math here, you don't have to look at all these equations I don't want you to I just want to show you that there is some Boltzmann equations that are associated with this so it's a it's a it's a well defined question and we can think about the density perturbations of dark matter dark matter, baryons, and also what the evolution of their motion is so this is in Fourier spaces is the divergence of the of the velocity of dark matter. And so all these terms in red or something new that has been introduced into what would otherwise be standard Boltzmann equations you have a temperature of baryons and it now a temperature of dark matter caused by this interaction. And so the most important aspect of this story is the momentum transfer rate. So when you have scattering, you're going to transfer momentum between the dark matter and the baryons. And so remember that our cross section scales is some sigma not pre factor times v to the end. And so this is the individual particle velocity. But when we want to think about the entire fluid we're going to have to average over velocities right and so in the momentum transfer rate you can see this velocity effect coming in here so this temperature over mass is essentially the thermal square of the thermal velocity. And so here you're seeing the thermal velocities come into play with some power of with some power of n. And so this is this is the momentum transfer rates that you that you're working with. We have our sigma not coming in here. We have dependence on our masses. And also the momentum transfer rate depends on how many target particles you have. And so it depends on the number density of standard model particles in the universe. There's also heat transfer which you know gives the temperature some non trivial evolution. And so he is being transferred between the baryons and the photo or sorry the baryons and the dark matter. There's one slight technical complication that I'm actually not going to get into though I'm happy to answer questions about it. This this thermal velocity here that we've kind of substituted in for this particle relative particle velocity. So this is OK to do unless your thermal velocities drop too low right and then you have to consider the overall motion of the fluids so you have to consider that the dark matter fluid may have some relative motion with respect to the baryon fluid. And so if that is no longer a negligible part of the velocity between an individual dark matter and an individual baryon particle, then you have to you have to make some approximations and treat this differently. And this is relevant for these negative powers of N. But like I said I'm not going to get into it. It's just it's just a technical detail that one has to just be aware of. Okay, so these are the Boltzmann equations. We can go and you know modify a Boltzmann solver say for instance class and say OK what does this do to my CMB power spectrum. So here is the this dashed line is is what the best what best fit to point data give you and if you turn on a lot of dark matter scattering. This is what happens. So you have some various effects like enhancement of this first peak you have you know the phases of your peaks are a little bit off. You can really only see these because I've turned up the cross section to be incredibly large. But the main effect that will be constrainable is going to be this small scale suppression so as you get to higher multiple, which correspond to smaller angular scales in the sky. The the power spectrum is noticeably less than what you would have for your Lambda CDM case. Right, so this scenario that I'm showing you right now is well ruled out remember blank data are very close to the theoretical line. And so we're looking for fairly small changes to the CMB power spectrum. All right, so before I show you essentially the results that we get from trying to fit CMB data. Let me just say that so recall recall that I said that the momentum transfer rate was a crucial component of this whole story. So the momentum transfer rate. Have to go through all this. Okay, momentum transfer rate tells us actually a lot of information about what's going on and how we should think about these different types of models. So I'm going to plot for you the momentum transfer rate over the expansion rate universe as a function of redshift and this is the redshift region that's approximately relevant for plank. And I'm going to cheat a little bit and go ahead and set this overall pre factor here to what I will show you on the next slide, which is the 95% confidence level upper limit. So if you look at this line that's drawn at one. If you are above this line, it means that there's a lot of momentum transfer compared to compared to the expansion rate of the universe so you have a lot of efficient scattering. If you're below this line, the Hubble expansion of the universe wins out and you start not being able to have a sufficient, you know, density or sufficient interaction rate to actually scatter in any sort of efficient manner. So if you go ahead and look at all the different possibilities for the velocity dependencies and how the momentum transfer rate evolves, you get these various lines. So, for instance, if you have your velocity scaling of v to the four for your cross section, that means at early times, so you have higher temperatures higher thermal velocities. You're going to have a lot of momentum transfer because your cross section is going to be large. And so that's why at high red shifts, this line is well above this, this grade baseline here at one. So you have a lot of scattering at early times and then it falls as the universe expands and cools. This is the general trend for most of the cases except for v to the minus four. So this fact will become interesting a little bit later in the second part, but this v to the minus four actually gives you less efficient scattering at early times and it becomes more efficient later. So all of these lines seem to be clumping around, you know, this level of the momentum transfer rate at this particular redshift. This is just indicative that that plank data have very good error bars at a certain a certain range of multiples. And so this is where plank data is deciding that it has the most constraining power and so this is what our fits force us to force these lines to exist at. If you wanted to adjust this sigma not to not be at the 95% confidence level upper limit. These lines would shift up and down. So I can show you what the results look like we don't see any evidence for dark matter scattering with the very unfluid. We can imagine scattering with just the protons in the universe. So just hydrogen. And you can imagine scattering with just electrons. And this makes it easier because they have different features in the constraints that I want to point out. So you see that there's some overall slope to the line and then there's a break. And then there's another rather straight slope that occurs with all of these constraints and this break is coming at a mass of that where dark matter the dark matter mass is approximately the mass of its target so for protons this dark matter masses about a GB and for electrons. This mass for dark matter this King happens at around and maybe so these are the constraints on Sigma not everything for a given model a given line and above it's excluded by CMB data. I also mentioned that helium also is is around in the early universe and if you're scattering with protons you might you know wonder about scattering with helium because helium also has protons in it. And so this is this is something that I looked at with with my students Stacy Möller and I'm showing you the result for just a spin independent type scattering. And the complication with helium is that if you want to scatter on the protons that are in helium as well as in hydrogen then that cross section becomes model dependent. It's determined by whatever model you have but so this is this is a non trivial thing to look at what the scattering amplitude should be for hydrogen and helium they are related to one another. The only ways that you can get out of this is by saying maybe I only scatter on helium in that case I would only scatter on neutrons in helium and I wouldn't scatter on protons. So this could come from some like ISO spin violation or you you've constructed a model where you want to preferentially scatter with neutrons. And and you can get rid of scattering with helium by just thinking about let's just make it a spin dependent interaction. Right and so the spin of helium is zero so if you have a spin dependent interaction your your dark matter is only going to scatter with hydrogen. For any other case you're going to have some relationship between hydrogen and helium and so the the main takeaway from from this work was that the helium scattering is actually rather important. It's model dependent but for large arc matter masses and for non negative values of your of your velocity dependence. The the fraction of helium which is only about 25% of the of the massive variants. The scattering with helium is actually dominant which is sort of counterintuitive given how a few helium particles that there are. But but yeah helium scattering actually drives the constraints for dark matter masses well above the GV and and and these scenarios. Okay, so these were the CMB constraints for these different scattering targets I took each of them individually so you can see the different effects that they have and this plot you know shows incorporating both scattering on two different targets. And I haven't given you much context for what the size of these cross sections should be. These are very large cross sections and if you hold on for just another couple minutes I'll give you a little bit more context of how these cross sections and these cross sections over here compare to other types of constraints. Okay, the only other thing that I want to say is that you know the the dark matter mass here. We cut it off that at a TV, our analysis usually cut off there, because this becomes a this becomes a straight line essentially. So this is you can just extrapolate to hire, hire masses, and if you go to too low of dark matter mass then you start running into trouble of some of the assumptions that we made we assume dark matter was cold. And scattering non relativistically, you have to worry about dark matter potentially becoming warm. So there are warm dark matter constraints at lower masses. Okay. So, with the CMB taken care of let's go back to this picture of small scale suppression. We can wash out these over densities of dark matter in the early universe but that has consequences for later on when structure is wanting to collapse and form and supposed to form actual dark matter halos that can host galaxies. So if you wash out these density fluctuations at early times they don't exist anymore. And so there's no structure that exists on some scale and smaller so here's a simulation that's done with just lambda CDM this is all dark matter and so you can see where dark matter is clumping. And here's some, you know, larger host galaxy and a whole bunch of tiny satellite galaxies within it for instance. And if you just have this very generic small scale suppression. What you'll see is a washing out of structure, so that you don't have all these little individual points here that could potentially host galaxies. But we can take our own Milky Way for instance and say, we know that there is substructure, we know that the Milky Way has satellite galaxies that are make a good candidate for testing to see what dark matter interactions have to say about the existence the sheer existence of these galaxies. And so this boils down to what's called the suppression of the linear matter power spectrum. So we want to show on the y axis here what the matter power spectrum looks like in some collisional universe with with dark matter interacting with variants versus what happens in just lambda CDM. And this is being plotted as a function of the scale k. So higher k means this is this is one of our lambda right this is higher came means smaller scales. And at the top axis I'm plotting the corresponding halo mass of a mode, a certain size entering the horizon, and having some average mass of the corresponds to the massive in the universe at that time. So, for this n equals zero case, a spin independent velocity independent interaction is going to look very, very similar to what warm dark matter does. So these dotted lines are warm dark matter. And you can see as you increase the cross section, you're suppressing more and more structure. So you're suppressing structure that goes to larger and larger scales or smaller k. And this is a very similar thing to what warm dark matter does warm dark matter, you keep decreasing its mass and it's going to wash out more and more structure. So the n equals zero case is pretty easy. The higher velocity cases are the higher power velocity cases are a little bit more difficult. Right, we have simulations we have a understanding of warm dark matter. And so we can kind of borrow what has been done for warm dark matter and apply it to this n equals zero case. For higher powers of velocity, you start getting very noticeable acoustic oscillations. So these are dark acoustic oscillations that are occurring and so you have this large loss of power and then it recovers a little bit and then another large loss of power and it recovers. So, so we have some conservative estimation that we've done by just insisting that the power spectrum for these oscillatory features all lie under what we know is the warm dark matters limit line drawn in black here. So we're being overly harsh, but we're not wanting to essentially simulate these universes with these oscillations because that takes a lot of time and computational power. So this is just a very quick way that we can get some rather conservative limits. So by doing this procedure, we can develop constraints for Milky Way satellites. So as a function of dark matter mass. I'm showing here for instance the dark matter electron cross section we also have it constraints for proton scattering. And you can see how there's various dependencies on the velocity constrain the cross section coefficient here at different levels. Okay, so I promised at some point to to actually put these numbers and the magnitude of these cross sections into context. So let me do that with the simplest case which is no velocity dependence. And so this is the CMB bound that I showed before. And this is a Milky Way satellite analysis and so this plot comes from a DES collaboration paper that was done to analyze this scenario along with some others. And you can see here this direct detection bound. So we're looking for a scattering simple scattering process and this is exactly what direct detection experiments look for in the lab. Direct detection for dark matter proton scattering is very sensitive. So you're looking at masses or sorry you're looking at cross sections that are extending down to like 10 to the minus 46 centimeters squared. So really really low. On the other hand, if you increase this cross section to be rather large. These direct detection experiments are placed underground, they're on earth and so dark matter would have to traverse the atmosphere, traverse layers of earth to actually get to your detector. So if the dark matter is very large or sorry the dark matter proton cross section is very large. It's not, it's going to scatter a lot. Before it ever reaches the detector. So there is some detection ceiling that has been approximated. And this direct detection bound is not a true limit that extends all the way up to arbitrarily large cross sections there is some constraint here. Or sorry a loss of sensitivity here for direction detection experiments. There's another thing that direct detection also suffers from. This is for nuclear recoil direct detection right that's that's most on par with scattering with protons in the universe. And that is you can't get much below a GV in terms of constraining power. And that's because direct detection is just looking for dark matter particles that are moving at speeds that are relevant for particles bound to our halo. And so, you know, at lower masses you're not going to get enough recoil from a dark matter particle hitting one of the target nuclei in your detector. Without having velocities that are larger than the escape velocity so there's a really large loss of sensitivity as you go to lower dark matter masses. And so the CMB doesn't have this problem. Cosmology doesn't have this problem and so you know the Milky Way satellite CMB do very well at at these lower masses. So, this shows that the CMB bound is is much less constraining than Milky Way satellites. This makes sense you know CMB is not probing as small of scales as Milky Way satellites. And remember the effect of scattering gets more and more pronounced as you go to smaller and smaller scales. But this is for a very particular model it's not going to be the case for all powers of N. And so, at the very least I just want to show you what the constraints look like when you consider scattering with electrons. And so here you're wanting to compare to direct detection bounds for electronic recoil to make an apples to apples comparison. And so this is the dark matter electron cross section in phrased in a way that is typical for for the direct detection bounds. And so they use this different definition for for the cross section than what I've been using, but we translate our bounds and show what our bounds look like in terms of of the dark matter direct detection parameter space. So you see here for n equals minus four, right, there's a very strong constraining power that Plank has. And we actually haven't done a Milky Way satellite analysis for these inverse powers of velocity, because they don't behave. And the matter power spectrum doesn't behave in a similar way as what I've showed you. And so this is a much more complicated problem to handle. But so we haven't published anything about this yet. And so this is also going to be a case that the Milky Way satellites I don't expect to have an incredible amount of improvement over the CMB as as it does here. And so these inverse powers of velocity interactions really do the CMB really does well in constraining them. Okay, so that is, that was the large part of the talk. And so I want to move on to a slightly different topic that is very much related to what we've discussed. These next two parts will be much shorter. And this next part is basically saying that this dark matter scattering that we've been talking about can actually cool the intergalactic medium during cosmic dawn and even in the dark ages. And so you saw that there was a coupling of the temperatures between dark matter and baryons. And so this coupling is going to be relevant for affecting observations of cosmic dawn. And in particular, I'm going to focus on the 21 centimeter global signal. So the idea here is that you have this background bath of CMB photons. And before Reionization occurs, you have these hydrogen clouds, right? And hydrogen has a ground state and it has an excited state due to, say, a hyperfine interaction. And so this corresponds to a wavelength of 21 centimeters. And so it's possible for a CMB photon to absorb, be absorbed by one of these neutral hydrogen atoms, exciting the 21 centimeter hyperfine transition. And so the CMB photons eventually get detected. This is a radio telescope out in the middle of the desert. And you can detect these photons and you're looking for a deficit of CMB photons because they've been absorbed. And so CMB serves as some backlight and you're looking for some temperature contrast between the CMB. Yes. All right. So this table here, this satellite, or this receiver is the edges experiment is one of the receivers for edges. So this is the experiment to detect the global epic of Reionization signature. So this is what the absorption that edges has seen. This frequency is, of course, redshifted because you're looking at this effect happening at cosmic dawn. And so it's not exactly at the frequency corresponding to 21 centimeters. It's redshifted. And there are various strange things about this signal. One of the strange things is how deep it is. And so in the extreme case in just ordinary standard cosmology, you would not have an absorption signal that large. And so this paper came out in nature in 2018. And accompanying this results paper was a paper that was published at the same time. A theory paper by Barcona that said, ah, there's this work that's been done on dark matter very on scattering and in particular looking at its effects during the dark ages and cosmic dawn. So maybe this can explain why we're seeing such a large absorption this v to the minus four scattering it's going to cool the gas and allow it to absorb more more photons. Okay, so that's the idea. But as I showed you before we have constraints from the CMB on this scenario so how does that compare with what you need to explain this absorption bit. And so everything looks fine naively right so here are you know plank 2015 is when this paper but this paper used and so here are the CMB constraints so everything above this line. And here are some rough projections for an upcoming CMB experiment, and these other lines here are the cross sections that you would need in order to get an absorption depth of a certain size, right. And so it looks like there's no problem that this this scenario could explain the edges signal and not be inconsistent with the CMB. However, as collaborators and I pointed out these these lines that were drawn here in this paper. And the lines that Barkana assumed, assume that first all dark matter interacts in this way. But it neglects the suppression of the matter power spectrum. So the thought was is that the interaction is very weak at early times because it scales like v to the minus four right so high velocities at high temperatures. Surely it doesn't it doesn't matter much, but there is a little bit of suppression of the matter power spectrum and this has a big impact on what you can do in terms of trying to fit this, this edges signal. And so there's a very, very limited amount of parameter space that can even do this. So that's one thing. The second thing is that in for the CMB constraints, we didn't care whether or not the dark matter was scattering with protons or with hydrogen with ionized hydrogen it was all the same right. This was before hydrogen recombined and became neutral. And so the at later times though it does matter. So at later times after recombination, there are very few ions that are in the universe. And so if you want to have dark matter ion scattering, you have to account for the fact that you have a very, very low ionization fraction after recombination. So you have to basically take these lines and boost them up a few orders magnitude and then that becomes disallowed by the CMB. You can think about dark matter hydrogen scattering so it doesn't matter that, you know, this hydrogen is neutral. But that tends to be highly constrained as some authors shown by fifth force constraints, for instance. And so the solution was to allow only a fraction, a very small fraction of dark matter interact. And so you can get away with a very, very large cross section, but a very small fraction of dark matter that actually has this interaction. So in this same millicharged case, Plank actually loses sensitivity. If you have dark matter that is only, you know, 0.4% or less of all dark matter, and you can go to very high cross sections. And the reason for this is that it's basically hiding in the uncertainty of the baryon density. And so there are error bars on Plank and so you're just hiding in those error bars. And so we looked at the viable parameter space of millicharged dark matter. And this was back in 2018, as I mentioned before, this paper looked at also the suppression of the matter power spectrum that accompanies this process to further constrain things. But that was for 100% dark matter, sorry about that. This small fraction of dark matter is not going to impact very much the matter power spectrum. Okay, so that was a scenario surrounding this very talked about topic edges in 2018. But it's a nice way to sort of realize that dark matter interactions have this other new channel, this new era of cosmology that's upcoming and hopefully will have some more data about Cosmic Dawn. And, you know, tests of what edges has seen to verify to validate the results or not. And this just opens up a new window and in different time in different era of cosmology to study dark matter. So from that aspect, it's very exciting. The last thing that I will talk about is something slightly different. It's based on work with my postdoc Nicola Belomo, who's shown here, and postdoc at Sony Brook Kimberg House, who's shown here. And so we're going to submit it to the archive tomorrow, which should be on people's lists and posted on Sunday evening, if all goes well. So this is talking about a very different type of dark matter scenario but still looking at interactions. And the summary point of this section is that dark matter freeze in impacts your initial conditions for dark matter. So for dark matter freeze and what are we doing here we are considering a dark matter particle, and it's going to be very weakly coupled to the standard model. And everything that I was talking about before that had really strong couplings to the standard model this is very, very weakly coupled. And so it's very reasonable to assume that there's no dark matter that's created during the reheating of the universe and so its entire abundance has to be generated. And so we look at a particular example of freezing dark matter in which dark matter has a millicharge. And so you can generate its abundance through positron electron annihilations into dark matter into dark matter. And that's how it gains its abundance. And the dark matter is so dilute, especially at early times it's being created that that Hubble expansion will just never let these dark matter particles that are created. And so, unlike a standard freeze out scenario that you may be familiar with, dark matter here is not in equilibrium with the thermal bath, it does not have a thermal distribution. Right. And so the question is how does this impact how dark matter behaves at later times and impact our observables. And so we don't have a thermal distribution and so we need to know what the thermal distribution for dark matter actually looks like. So we have to solve some collisional Boltzmann equations to numerically compute what the phase based distribution function looks like. And so, this top panel is showing you the background phase based distribution function so the leading order effect and this is as a as a function of, you know, some co moving momentum over this T not it's just the temperature of the CNB today. And I'm showing you different curves here for different masses of dark matter, and comparing it to what a Fermi direct curve would look like all these curves are normalized such that their area is one. And so don't pay too much attention to, to the, to the amplitude it's just saying that this particular peak is just more narrow and so it has to have a higher amplitude for normalization purposes. And compared to a Fermi direct distribution all these PSDs are shifted to lower momenta and, and so they don't really in any way represent what is normally assumed for a thermal particle. So, this has been studied the effects of this background phase based distribution function have been looked at before. And so like I give a few references here, but no one has looked at what the perturbed phase based distribution function looks like so you go essentially to higher order. In your, in your expansion of the phase based distribution function, and you need this to investigate the initial conditions for your dark matter perturbations and their and the evolution of those perturbations. And so what we actually find is that there is an isocurvature mode that is induced because of the freezing process. So freezing is is non thermal and isocurvature is is just saying that you have some relative density perturbation in this case with perspective photons. That does not come about from ordinary, you know perturbations that you get from single field inflation. Right. So that is just a curvature mode is what we call it. And the isocurvature mode is deviations away from that. So this is a curvature is usually thought to be developed from inflationary models, but this sort of is a curvature that is being induced is happening post inflation has nothing to do with inflationary physics, but it's caused by dark matter physics. The thing is is that the once the isocurvature is set in though it's not like any, you know, cosmological experiment or anything can really distinguish that, you know, whether the isocurvature is primordial in nature, or occurs later at say, you know, dark matter freezing. And so their current constraints that we have on isocurvature. So we find that the this induced isocurvature between dark matter photons is totally correlated with the curvature perturbation, which is what we get from single field inflation which is, you know, the normal everyday cosmology that people think about. Isocurvature is is constrained to be fairly low. And so here I'm showing as a function of dark matter mass what our freezing scenario gives us in terms of the amplitude of isocurvature compared to the curvature perturbation, and it is this blue line here. So, Plank 2018 data exclude this scenario completely in the mass range that we're looking at. So Plank 2018 is saying that you can't have this because it induces too much isocurvature. Simon's observatory and CNBS4 will be able to do a little bit better, but it's all still excluded. And the thing that we can do now is say, okay, we have this this exclusion range, maybe we can make a fraction of dark matter be frozen in. And this isocurvature perturbation is just going to scale linearly with the with the fraction of dark matter. So remember that we're looking at a, you know, these numbers, this line is from a very specific scenario. We are thinking about freezing dark matter, and we're working in a mass range where most of the dark matter abundance can, we can confidently say comes from positron annihilation or positron electron annihilation. And so we can put this exclusion in terms of constraints on on the millicharge dark matter parameters space. And so here's this dark matter electron cross section that was shown before. This is the CMB bound you saw. This is a direct detection bound. These are some other bounds on millicharge dark matter that come from stellar, stellar cooling and supernova 1987 a collapse core collapse bounds. And this is the freeze in line. This is the amount of, you know, scattering that you the corresponding amount of scattering that you would need in order to have an annihilation cross section that corresponded to freezing in all of dark matter. And so plank 2018 data exclude this. And so this is why our exclusion region covers this covers this curve this freezing curve. And also if you go below this curve, it means underproducing dark matter. So, in other words that freeze in dark matter can't explain all of the density of dark matter. And so in those cases you're looking at fractional freeze in dark matter cases and as I mentioned on the previous slide that gets constrained and so you can ask, Well, how low can I make this fraction at a given mass, such that plank still excludes the amount of isocurvature that's developed. And so you get this region of parameter space that's ruled out by plank 2018 data. And these are, sorry, this, this red curve, this red region is showing how CNBS4 and SO will further push this bound down. And so some final thoughts on this, this isocurvature, this generation of isocurvature is really driven by the fact that you have a strong biased energy and momentum transfer. So you're basically taking, you know, your baryon and photon fluid and dumping a whole bunch of energy transferring a whole bunch of energy into a dark matter fluid that doesn't return it. Right. So it's not in thermal equilibrium right. And so you have this energy that's just transferred out. And that is essentially the main driver, the energy transfer is the main driver of this isocurvature. And so that's a pretty generic statement. So this is what we find numerically for our specific case, but this case is expected to hold in a whole broad class of freezing scenarios. And so we expect freezing scenarios in general to feature isocurvature. And the amount of isocurvature generates will surely be dependent on which particular model of freezing that you're looking at. And, you know, this could be constrained by current and future CNB data. And so this is, we're looking into more scenarios of freezing, we're looking into expanding the mass range where, you know, our simple assumptions don't really hold anymore in terms of what generates the freezing dark matter. So, you know, stay tuned for that. So to recap, I should do three different ways of sort of probing dark matter interactions with the standard model. The first two were at least very related to one another. They looked at pure dark matter scattering, no regard to any other process that could happen. And in one case, we're looking at small scale structure formation. In the other case, we're actually looking at the energy exchange between dark matter and the baryon gas in the era of Cosmic Dawn. And then the third topic was this new work that I wanted to talk about that looks at how dark matter freezing does impact initial conditions and all that has to be carefully calculated. So these are really exciting times to think about different cosmological and astrophysical probes of dark matter, right? This is something that we didn't a priori expect freezing to have this big of an impact and generate this much isocurvature. But, you know, so there are plenty of probes that could be, you know, hiding in plain sight and we just have to go and look for them. So this also leads me into putting in a plug for a KITP program that I'm a co-organizer for. And so we have dark matter theory simulation and analysis in the era of large surveys. So we're going to have a whole bunch of new data. We're going to have new CNB data. We're going to have new large-shell structure galaxy surveys. We're going to have a lot of data and it's going to be important for us to kind of get together and talk in a way that is, that makes the most use of this information. And so this involves theorists, simulators and people who actually go and observe. So application deadline is February for a, you know, for a 2024 program and then there's an associated, there's an associated conference with it. And with that, I will end. Thank you very much, Kimberly, for this great talk. Let me now open the floor to see if there is any question among the people in Zoom. While we ask these initial questions, let me remind everyone watching on YouTube that you may ask your questions on the chat and I will then read them to Kimberly. Thank you. I'll go, Walter. Just a very nice question. This is not my field. Do we have any other ways to test these dark matter electrons scattering from astrophysical sources or something like that? Yeah, I think that there are certainly things that you can think about that are astrophysical probes that are much more local. So the answer is yes. I haven't worked on any of them myself directly, but there are certainly, there are certainly people who do think about that. And this one's very stronger, right? I'm sorry. These ones are like the bounds that you can put are stronger than the ones we can potentially do with astrophysical sources. Are they comparable or is that totally different regime? I think, I would say that there are probably different regimes. You have to have, at least for the effect that I was looking at in terms of the dark matter electrons scattering for some particular model. You have to really put a lot of energy transfer, a lot of momentum transfer to be visible in the CMB. And you might just be sensitive to a completely different mass range or a completely different cross-section range for different astrophysical probes. I can't quote numbers to you at the moment, but I would expect them to be complementary and not completely overlapping. Thank you. I have a question that is going to send this in a different direction. So all these constraints that you've obtained, they deal with the interactions between dark matter and the standard model. So with the changes that you saw in the matter power spectrum or in the acoustic oscillations, how much would you expect that this would change or make the constraints stronger or less stringent if you added self-interactions among the dark matter particles? So that's a great question. Let me see if I can reasonably go backwards. It's fast to go backwards. It's slow to go forwards because of the different builds. So the effects that we see, these dark acoustic oscillations are very similar to the dark acoustic oscillations that you get from dark matter, dark radiation scattering. So in that scenario, you have dark matter that's coupled to a radiation bath, a separate radiation bath. And so those produce acoustic oscillations like just for the baryons have because they're coupled to photons. You get the same effects if you have dark radiation. And so for that scenario, for instance, of those types of self-interactions, you're going to have limits that you can place on how much interaction there can be. So in that sense, there's a very analogous thing in talking about the suppression of structure due to completely dark sector physics. So just because it doesn't interact with the standard panel doesn't mean that we can't see its effects gravitationally. And so that's a nice way of probing dark sectors. That's just an example. There are a whole other sorts of, it depends on what self-interaction model you're talking about. Thank you. Any other questions from the audience here? So in this part, do you need the dark matter to be in thermal equilibrium? So could you have a freezing dark matter that has got very strong self-interactions? So the question is, does it work in freezing? Ah, yes. So for 10, let's see. There we go. Okay. So this plot is important. So this plot is just telling us that for at least this 0, 2, 4, 6, whatever power you want to go up to, those are all situations in which you can't help but be thermalized. Because the interactions, at least at the level of constraints of cosmology constraints, you are going to be thermalized at early times. So for this case though, which is the millicharge case, which is the case I also thought about in freezing, that's a different story. So in this case, the temperature is very cold and it only kind of catches up at much later times. Certainly if you had some self-interactions due to a thermal radiation bath, this would change because you would have different perturbations. Right? So you would need to include that in your Boltzmann solver, basically. And so the answer would be different. In terms of connections to the freezing case, and now I'm going to have to actually just jump to the slide because it will take forever to scroll through. There we go. Right. So for the freezing case, I restricted myself to look at a very specific mass range. The authors that I know, DeVork and William and Shutz, looked at a much lower mass range for dark matter and incorporated the effect of not only the modified background phase-based distribution function, but the interactions as well. And so they put in both. And so that works particularly for lower masses. And so there are, you know, there's structure, small-scale suppression. That happens in these cases, not to mention you have some modified phase-based distribution functions. So those two things can coexist. Okay, okay, great. And I'm still on the free scene, but now on this iso-curvature constraints. Do you have any constraints, because I think that you stopped at like 10GV or so for masses of 10GV? Yeah. Yeah, so the, right, at higher masses, we have to start making a choice about our millicharge scenario. Because if you want to do, if you want to generate a millicharge due to kinetic mixing between a dark U1 and the photon, then you also have the Z that can contribute to the rate. So we stopped it here, because at least in that scenario, we could say, you know, confidently that we don't want to, we don't want to start getting the Z bows on, contributing any significant portion of this under that given model. And so we were just trying to get away from having to specify that, basically. But we're expanding this in work that's currently ongoing to actually just go ahead and say, fine, let's have a dark photon. It'll have some Z contribution, some Z exchange that can happen for higher masses and on to real rates. So that's the reason for cutting it off there. I see. I see. What's your expectation then? So my expectation is that it will certainly change the numbers, right? It will certainly change the form of this curve. And so the form of this curve, I'm not expecting it to suddenly not generate iso curvature anymore. But the shape of this and how far it is above this exclusion limit tells us essentially what fraction of millicharge dark matter could be responsible or could exist in this freezing scenario. And so, and so that number I don't, I don't really have a good estimate for it without doing the calculations. Okay. Thank you very much. All right, the Brian Stevens had a question on YouTube, but I think he just made a comment saying that everything was covered so no questions anymore. So I think that there are no questions from the YouTube channel. So if there is no other question here, let me thank again a professor buddy for this awesome talk. Thank you for sharing your soon to appear work with us. So everyone stay tuned to see it tonight or tomorrow on the archive to everyone to everyone watching through YouTube. Let me remind you that the next webinar is going to be in two weeks. Subscribe to the channel or through the social network so that you are always up to date. I hope to see you all and to have you all connected in a couple of weeks. Thanks again, Kimberly, and I hope that you have a great rest of the semester. Yeah, thank you everyone. Right. So goodbye everyone. Bye bye. Okay, we are not live. Okay.