 Great. Thanks very much for the invitation to come here to Trieste, my first time in Trieste. So I've been charged with the topic on particle dark matter, which I think will be nicely complementary with what Sergeid is doing on axions and some of the things that you're hearing on BSM cosmology. But we're going to dive into this, I think, fairly slowly and just as a reminder at where we're at in particle physics in the last decade. So this part of the pie right here, the cold dark matter pie, which is ratio five to one in our universe over ordinary matter, is the reason I work on particle physics. So we know that there's a vast amount of the matter and energy in the universe that isn't described by the standard model. Now this part of the pie, the dark energy part of the pie, we don't know that that's physics beyond the standard model. It may just be a constant, a fundamental constant of nature. And the dynamics might be in some selection mechanism. So you could argue that this might just be a sign of a multiverse and somehow we need to understand more about the vacuum structure in the universe or the multiverse in order to be able to piece this part of the puzzle together. On the other hand, we know that what is sitting in this cold dark matter part of the puzzle has to be some physics beyond the standard model. And that's what we're trying to do is to piece together what that theory is. Now I believe that probably most of you are believers in dark matter, its existence, and the fact that it must be physics beyond the standard model. But I thought that it was worthwhile, partly because later on in the third lecture on Friday we're going to come back to understanding what it is that the universe tells us about what the dark matter can and cannot be. And so because we're going to use these same tools to understand what the dark matter can and cannot be, I'd like to start by talking about what we've learned at each step in the universe about why it is that dark matter has to be physics beyond the standard model. So it all starts when the universe is about a second old. This is really our first direct measurement of the universe at Big Bang Nuclear Synthesis. And what we really get here is a good measurement of the ratio of the baryon to the photon number. At the CMB at Bach, the cosmic microwave background, that's between 300 and 400,000 years. People say that we actually get a good measurement of the dark matter. It's actually an indirect measure of the dark matter and I'll tell you why. But the CMB actually measures as well as that the universe is flat. It also gives us an independent measure of the baryon density that turns out to agree well with BBN. So we'll talk about that and why that by itself is evidence for dark matter. Then later on, only once structure starts to form in the universe, from about a billion years onwards in large scale structure, there we get a direct measurement of the matter density. Through supernovae, they tell us about the universe's expansion rate and therefore the presence of dark energy. And then lastly, the classic thing, the thing that it all started with was galactic rotation curves. So let's break this down and look at each one of these. Okay, starting with BBN. BBN plus CMB. Okay, so first of all, you can ask, well, why is the dark matter have to be some form? Why is it not just dark baryons? And in fact, that's what they first thought. That the dark matter was just some form of dark baryons. That's what an astronomer, of course, would natural think. And the reason for that is because the measurement that we make of the baryon density from the CMB epoch and from BBN agree with each other very well. And that would only be the case if dark matter was non-interacting, or pretty highly non-interacting. So if you take the CMB multiple spectrum, these beautiful curves that by now have actually been measured much better than what's shown on this picture, what do these ringing curves tell us? Well, the location of this first peak here actually tells us about the epoch of matter radiation equality. So that's a good measurement of the fact it turns out that the universe is flat. And then you see as you go from one peak to the next that this thing dams. And the rate at which it dams from one peak to another tells you what the baryon density is in the universe. So the ratio of that first peak to the second peak actually fixes the baryon density. So now you can put what you measure for the baryon-de-photon ratio from CMB. That's what's this blue hatched. And then you can measure the amount of helium and deuterium and lithium in the universe. So that's what's plotted on these three. This is the helium abundance and the deuterium abundance. Let's just focus on these two. These are the measured abundances of helium and of deuterium. And if you just see where do they agree with each other, so this is a prediction of BBN, which is dependent on this baryon-de-photon ratio. You just see where it lines up with each other. You can see that BBN and CMB lined right in this range they agree with each other. And that what you would only be able to get those two measurements. So BBN is not sensitive at all or almost at all to the dark matter density. But it is highly sensitive to this baryon density. And so you would only be able to get these two measurements right if in our universe we had baryons plus some form of non-interacting matter known as dark matter. So that's the first hint. Secondly, we have another measurement, independent measurement of dark matter from the rate of formation of structure in the universe. So I said before that what CMB does well is to measure that the universe is quite flat. What the expansion of the universe does is to measure omega lambda quite well. And the formation of structure in the universe measures omega matter quite well. You can see that that's pretty insensitive to the dark energy density and to the curvature but it's pretty up and down in terms of the matter density. And you can see that if you take any one of those measurements away it wouldn't actually impact the result. So you have these three independent measurements, CMB which is happening between three and 400,000 years old and these late universe measurements which are happening when the universe is billions of years old you take any one of them away completely different systematics and they all agree with each other. And this is what makes the case so strong that you have these measurements from very different epochs that give the same thing. Okay, so let's make another measurement. Now let's look nearby. Let's just pick up a galaxy. Let's take the Large Magellanic Cloud which is close by here to the Milky Way and let's see if we can measure dark matter in clumps. So people said, well, BBN and CMB tell us that dark matter can't be free baryons. Let's just try to bind those baryons up into some type of compact object. That makes them non-interacting. Okay, and yet I would still be able to see them as clumps if I look in some nearby objects. So that's what they did. I take a nearby object like the Large Magellanic Cloud. It has, you know, you can monitor. This is a remarkable thing. You can monitor millions of stars. And if dark matter is in the form of a massive compact halo object which were short for machos what I can do is to use a gravitational lensing effect. So the idea is that if one of these objects comes transiting through what happens is that this object, as it passes between me and the star through this Pachinsky effect will actually change the intensity of that star. So if I just sit there and monitor that star I can actually put a constraint on the number density of these objects. And so they went and they did that. And through these surveys what they found is I can put a constraint on the fraction of the LMC density that's in machos. As a function of the macho mass this plot here goes down to 10 to the minus 7 solar mass. On the high end it goes up to about 100 solar mass. So you can eliminate machos as being all of the dark matter in this mass range above 100 solar mass. So in this range up here that's what this plot is meant to show. You can actually directly see the clumpiness of the dark matter. And the way that you see the clumpiness of the dark matter is by measurement of the power spectrum. So what's known as the power spectrum. I'm not going to define this very rigorously. This is the power spectrum. All I want you to know is that the power spectrum is a measurement of the clumpiness of the dark matter. So the measurements here are in black as a function of wave numbers. So this is scale. So as you go to higher wave numbers that's going to smaller scales. And what you can see is that as I add in clumpy objects of say a thousand solar mass which is what this blue curve is you can see that I get an amplification in the power spectrum. That means I can actually see the clumpiness that's due to this massive compact halo object of an order of a thousand solar masses. And that actually allows me to rule out the rest of this window at higher masses. Now it could be that dark matter is actually a macho. Some type of baryons which have been bound into say ten to the minus eight solar mass or smaller objects. But in that case I need physics beyond the standard model to actually make these objects. And so what we've learned is it seems from all the evidence that dark matter has to be some type of you need some type of new physics beyond the standard model. So then the next thing people tried to do was to say well okay if I can only get all of these measurements here from adding in some form of non-interacting matter which is not free baryons then why don't I just try to modify gravity. Well there are two problems with that. The first one is that modified gravity theories just in general tend to be sick. You really have to find some way to try to theoretically try to cure them. Now it's possible that at the end of the day it could be some modified gravity theory that's up to this point just been hiding. On the other hand you still have to just get the entire range of these observations right. The modified gravity theories tend to just go after the galactic curves. They don't tend to get all of these other things as well. And so we really need to be able to explain everything from the formation of structure from BBN observations from this bullet cluster which shows this is the gravitational center of mass of two clusters of galaxies. This is a gas which has been stripped off and so this seems to indicate that there were two clusters that passed between each other and stripped off the gas. The gas was stripped off because it's interacting and the dark matter just passes through each other as if nothing happened because of the very weak interactions. And so could it be that it's not particle dark matter? Well we're never going to be able to I think conclusively say on the other hand dark matter is such a simple theory that explains this whole range of observations from the time the universe is a second old up until today it doesn't require us to theoretically stand on our heads we should still keep in our minds always other explanations besides dark matter but I like this sort of proverb which says that if it sounds like a duck and it walks like a duck and it looks like a duck it's probably a duck. So by the duck theorem dark matter everything that we've seen in our universe is consistent with needing some type of new particle beyond the standard model that just expands, that's cold, that expands with volume as the universe expands is weakly self-interacting and does not have many interactions with us and that's going to be the starting point for this talk. So before I jump into the next part you have questions. So people have tried to use modified gravity to explain this what they end up doing is to modify gravity plus add in some form of massive neutrino. So they typically have a neutrino which is maybe a couple EV in mass and it's that neutrino with a couple EV in mass that is making up these parts of the bullet cluster. So even in the MOND theory if you want to explain this particular observation they usually end up invoking some type still some type of physics beyond the standard model. So usually what people use these types of observations of pairs of clusters that are recently collided with each other is a constraint on the self-interacting cross-section because if one were to observe a substantial change in the shape of these objects due to the dark matter self-interactions then you might be able to see that in the form of these. Now on the other hand some people have claimed that for example the cores of dwarf galaxies all the way to clusters of galaxies are actually a little bit more flat than you might expect from non-interacting cold dark matter and so they've posited that you may need self-interactions. So it's a little bit of a it is an open question to the extent that we have some constraints but maybe if we understand a little bit about how the baryons actually interact during the process of structure formation and how that affects the dark matter density then we may be able to get more rigorous constraints. Right now I would say that there's definitely a part of that which is an art. That's often the case with this question of baryons and dark matter in clusters of galaxies. Taking it alone I wouldn't take clusters of galaxies as proof of dark matter. I think when you put it in concert with everything else it adds to the case. And hopefully as we understand more of the way baryons and dark matter interact with each other as structure forms we can actually get more rigorous constraints from these objects. Any other questions? So oftentimes so it's going to depend on the particular analysis. Oftentimes the curvature of the universe will be a parameter that you'll marginalize over. That tends to be pinpointed very very well and not be degenerate with other parameters by the CMB. So somehow you have to get that if you want to make the universe radically not flat somehow you still have to get that observation right. Do we see what? So the closest thing that we have are dwarf galaxies which they're such low mass halos that they have a hard time holding on to their baryons. And the ratio of the dark matter to the baryon density in those is very high. And people have tried using those as basically laboratories for dark matter because the baryons even in the center of these objects are not a big fraction of the gravitational potential. The problem with those is they're very faint so it's hard to get information about them. Because they are faint you're looking at them in our own generally in our own Milky Way galaxy where they're going to have interaction with for example the disk of our galaxy. So even in that case they're not as pure of dark matter laboratories as you might like them to be. And so people are finding that before they thought oh these are you know if you have some deviation from what you expect from cold dark matter that must be an indication of new physics and they're actually finding in closer examination that's not the case. Okay so we don't actually have yet what we would call a really pure dark matter laboratory. Alright so we're going to work now with particle dark matter for the rest of these lectures. And really once you're comfortable with the idea that dark matter is physics beyond the standard model it's really not hard to write down theories. And in fact it's so easy that there have been a huge plethora of theories of dark matter. You can have supersymmetry, extra dimensions, you can have a massive neutrino. MEV dark matter is one that was motivated by an axis in the galactic center. You can have some form of scalar dark matter and axion. However this list actually I don't think is as diverse as it could be. In particular if you look at what's been going on in the literature at least up until about five years ago they were really kind of focused on two things. So you can see that this plot has an interaction cross-section in picobarn. A picobarn is 10 to the minus 36 centimeters squared. So we're talking about 12, so it's a little bit actually larger than wheat cross-sections as a function of the dark matter mass. And you can see how many ranges this covers in log parameter space. And it looks like there are a lot of different objects here that have been proposed as dark matter candidates. On the other hand if you look at it just a little bit more closely what you'll notice is that they can kind of be organized into two areas. One is the axion which you're hearing about and the other is kind of variations of things that come out of weak scale physics. Mostly super symmetry. And so this is really I would say where up until a few years ago 90-95% of the effort within dark matter has been. And there's a reason for this. One is that these are very well motivated theories theoretically. And they fit the bill. And thirdly they're pretty strongly constrained by the theory. Once you take a theory and you grind through it you have a few free parameters but nevertheless the theory actually predicts some things for you. And so you usually end up with this paradigm of dark matter which is that the dark matter is in most cases one particle. It's stable. It's some type of sub-weekly interacting dark matter. And of course it's neutral. And one of the things that we're going to come back to in the third lecture is that this notion that our thinking about the dark matter sector has really shifted. It shifted away from this idea that the dark matter is necessarily some monolith of a single stable weekly interacting particle to the idea that in a dark matter sector even if we were to discover a supersymmetric particle or an axion that in fact the dark matter sector might become very complex or that the visible sector has a lot of dynamics in it. You know, there are all the quarks, all the leptons, the forces. There are multiple stable particles that are both gauged in global symmetries. And so our thinking about the dark matter sector has shifted in this direction to try to think about what kinds of experiments should I try to design to try to get as many different regions of this dark matter parameter space as the dark matter theory space as I can. Now you're sacrificing something when you do that. Just a minute. You're sacrificing something when you do that. The thing that you're sacrificing is a theory which is motivated by solving another problem. So in supersymmetry you solve a naturalness problem. With the axion you solve the strong sea-proof problem. You have definite predictions and you can go after them. You're sacrificing that. And if the dark matter turns out not to be one of those things, you're probing a much broader region of the theory space. And so one of the things that we've been thinking more about is what are those kinds of experiments and how do I look for these types of theories? So you had a question over here. Gravitationally you can't. Well, okay. So gravitationally it's very difficult. So what's going to have to happen, so actually determine what the theory of the dark matter is. Let's say you discovered supersymmetry at the LHC or you saw an axion and experiment. It would be very hard to say off the top from the starting gate that that is the dark matter. It would be very tempting to do so. And in fact one could say that would be the leading order place to start. But once we've discovered dark matter, that's the beginning. You're opening a new field, not closing one. Okay. And that's kind of the... And that's the direction that I think we're moving. Now I think all of us would be overjoyed just to have one signal in some experiment. But it's going to be a long road and it's obviously difficult because we don't know to what degree the dark matter sector is sequestered from us. Okay. So let me now with that introduction tell you what the program is going to be for the next couple of days. So the first thing I want to do is to start by outlining the ways that the dark matter density gets set. Okay. And the reason why that's so crucial is because this is a direct connecting point between the macroscopic world and the microscopic world. We have one thing, measurement of the dark matter density. And if we can connect that to microscopic properties of the dark matter, we've already made some progress. So I'm going to talk about the various ways that this can happen. So we're going to talk about freeze out, which is the most common one, freeze in, asymmetric dark matter, freeze out and decay. This misalignment, which Surjit will talk about in the context of axions. So I'll touch on that only briefly just to emphasize that it's quite general beyond axions. Then, so hopefully we'll be able to get through a substantial part of this today. Tomorrow, because it's so prevalent in the literature and also because we're looking for it at LHC and direct and indirect detection experiments, I want to spend some time on supersymmetry and tell you exactly what it predicts in direct and indirect detection from a microscopic point of view. And then on Friday, we're going to spend time looking beyond the vanilla wimp. We'll talk about motivations for that and experimental search techniques. And then we'll talk about in general how you use cosmology to constrain dark matter. So we'll talk about a more detailed BVN, CMB formation of structure, stellar capture and dark matter self-interactions. Obviously, we're not going to be able to get into any one of those things in detail, but at least be able to tell you the kinds of things that these different markers and cosmology tell us about dark matter. And then lastly, we'll talk about LHC searches for particle dark matter. Okay, so let's go on and talk about paradigms for dark matter density. Thermal freeze out even though this is by far the most popular is only one mechanism for setting the dark matter density. So, as I said before, why is dark matter density so important? Well, the reason is that you're relating this macroscopic observable, the total energy density in dark matter to the microscopic properties of dark matter. Okay, so we're going to talk about thermal dark matter freeze out, freeze in, I already said all this asymmetric abundance production through decay. And when I say microscopic properties, what I really mean is Lagrangian. So thermal dark matter, what do I mean by thermal dark matter? Well, in the standard paradigm, thermal dark matter means that the dark matter has strong enough interactions with the standard model, usually through some two-to-two process, whether that be scattering or annihilation, annihilation and inverse annihilation, that causes it to thermalize with the standard model, by which I mean that it takes on the same temperature. So, in the standard FRW cosmology, you essentially imagine the universe is like a balloon contained with dark matter and ordinary matter, baryons, neutrinos, photons that have an energy distribution which is set by either Fermi Dirac, if it's a fermion, or Bose-Einstein distributions, if it's a boson. And then I compute its energy density by taking this Fermi Dirac or Bose-Einstein distribution, folding it with the energy and then integrating over a phase space. And one of the key things about this is that if the particles remain in thermal equilibrium throughout the universe's history, as the particles become non-relativistic, their number densities become exponentially suppressed. So, if I just take this expression for the energy density, and now I take the limit that the particles are relativistic, the energy density of relativistic particles, this is for a fermion, goes like t to the fourth, pi squared over 30, and then there's the 7A factor for a fermion, or the number densities now go like t cubed. So, I'm just going to drop all these factors. And the other important thing is that in the non-relativistic limit, this goes over to something that looks like an e to the minus m on t. So, these are the only things that you need to remember. Energy density t to the fourth, number density t cubed in the relativistic limit. And when they become non-relativistic limit, as long as they remain in thermal equilibrium, I'm just going to get an exponential suppression e to the minus m on t. If I want to compute the energy density from the number density, I just multiply by this mass as I would normally for a non-relativistic particle. Now, that's the standard thermal dark matter paradigm. I'm going to take a thermal dark matter prime paradigm, which is a slight variation of the thermal paradigm. The only difference that I'm going to make is now the dark matter has strong enough interactions at early time that it thermalizes, but it doesn't thermalize with the standard model. So, I have my standard model sector here. It's happily going along. It has strong self-interactions that causes it to have a Fermi Dirac or Bose-Einstein distribution. The same thing happens in the dark matter sector. Strong self-interactions that causes it to come into thermal equilibrium, but there's some barrier between these two. They don't strongly self-interact with each other, and so there's two different temperatures in these sectors. And this is perfectly allowed with all the constraints, and the ratio of these temperatures will typically be set by the epoch at which they decouple from each other. Okay, and so you can just imagine. Now, I just follow the thermal evolution of these two sectors, but now I do it separately, and the only way that they talk to each other is how? Yes. Yes. So, I would have my standard model sector. It would go through the usual things of, you know, say weak interactions freezing out. So, I would go through E plus E minus, and I would have the usual kind of cosmology in each of the sectors, but it would happen separately, but what would be the coupling between the two sectors? There's one thing that Bose sectors see that actually causes them to not be 100% decoupled. Gravity. Someone said gravity. So, they both see the same Hubble parameter. Okay, and so there's still gravitational interaction, even if there's not thermal interaction between these two sectors. So, that's just another thing to keep in your mind, that if for some reason you want to not have the dark matter have an overly large impact on the visible sector, one way that you can do it is just to keep the two sectors decoupled from each other and keep the dark matter sector a little colder than the visible sector. No, they don't. Yes. Yep. I should have changed that to you, too. You're right. The chemical potentials absolutely do not need to be the same. The separate dynamics in those two sectors that can set separate chemical potentials in the two. In some cases, actually for some models, that's critical. If they're in chemical equilibrium, so if you have a process that causes them to share, say I have a dark matter number and I have baryonyleptide number and I have some interaction that causes them to exchange those numbers, then I would tend to equilibrate those chemical potentials as well. But if they're completely thermally decoupled and completely chemically decoupled, then I can have different chemical potentials in the two sectors. Yes. And that's an important distinction that there's thermal equilibrium and there's chemical equilibrium and the temperatures at which those two things decouple can be different. So in the standard paradigm of thermal dark matter, what happens is that dark matter follows this Fermi-Dirac or Bose-Einstein distribution until the point at which it becomes so rare that it drops out. So here is what by now has become a really classic plot. It computes the co-moving number density. And what we mean by the co-moving number density is the ratio of the number density in the dark matter to the total entropy density in the universe. So the entropy density, I haven't written down the formula here, but entropy density, I guess I have, entropy density goes like T cubed. And the number density early on also goes like T cubed, just for relativistic particles, so it starts out constant. And then what happens as this ratio of the mass to temperature, so the temperature drops, so time is going this way, temperature is dropping in the universe, then as this drops below the dark matter mass, that this is starting at one, then what happens is that dark matter starts to annihilate and you get this exponential suppression factor. And that's causing this ratio to drop like e to the minus mT on some ratio of the temperature to the mass. I think it's m on T to the three halves. So it's dropping exponentially and that happens until the dark matter drops out of thermal equilibrium with the standard model. And so it becomes so little of it that now it just starts to freeze out. And then once it freezes out, then the number density becomes constant and so we'll go over what the dependence is on the cross-section. So I just want to spend two slides, which are kind of a qualitative explanation of what you need to know to understand the behavior of those curves. So in cosmology, the time back of the envelope estimates work just fine until you want to get all the factors right. So you basically need to know two things. You need to know the Friedman equation and you need to know the Boltzmann equation. That's all you're going to need to know for the purposes of this lecture. So Friedman equation is just an energy conservation equation. h squared is 8 pi g on 3 rho. And Newton's constant scales like one of the Planck density squared. This energy density, when you have relativistic particles, go like t to the fourth. And so you just plug that in there and you find that the Hubble parameter goes like t squared on m Planck. And the reason why you can always use this as being dominated by, as happening during radiation-dominated epoch. So that means the energy density is always going to go to t to the fourth because the dark matter energy density is always a sub-dominant component. And so we have this result, h is t squared on m Planck. The other thing you need to know is the Boltzmann equation. Boltzmann equation just tells you about the evolution of number densities. So in the standard Friedman cosmology, you imagine that the universe is like a hot-air balloon, I think is a good analog. So it has some typical size, which you denote by the scale radius a. And then some energy density inside that scale radius. And then if I want to compute the way the number density saved dark matter, which I'm going to call dark matter x throughout these lectures, the rate at which this evolves. It turns out, in the absence of annihilations, the Boltzmann equation just tells you it's plus three h and x. And the reason why it's three h and x, can anyone guess? What? Three dimensions, three spatial dimensions. So if you just plug that in, the Hubble parameter tells you about the rate of change of the scale factor. And then you know that the scale factor goes inversely like a temperature. So as the universe gets larger, radiation cools like the temperature. So if you just plug these things in here, the fact that the number density, you just imagine that as the universe expands, the number density just dilutes with the volume. And so that's the reason why when you plug these things into this equation, you need this factor of three. It just tells you that the number density of a particle scales like the volume in the absence of interactions. Now you add in interactions, left-hand side of the equation stays the same. And the thing that gets added is a cross-section times velocity. Cross-section times velocity times number density gives you a flux. Cross-section times velocity times number density gives you a flux. So if I want to compute the rate at which one dark matter particle sitting here annihilates against another one, I need to compute the flux and then multiply it by the number density. So that gives me n squared times sigma v. And the actual equation is n squared, actual number of density of dark matter minus the equilibrium number density of dark matter squared. So the point is that when dark matter is in equilibrium, so when the right-hand side is zero, then dark matter density just scales with the volume. And that's why on s equals constant, which is what we saw going back to this plot, that right-hand side being zero is just the epoch when y equals constant here. That's before annihilations in one direction have become important. So now I just do a substitution of variables. It turns out it's helpful to use the ratio of the number density to the entropy density. And then again I use this x's m on t variable. I plug it in. And now I have just the slightly modified version of this. I've gotten rid of this form because this 3hn, because that gets absorbed into my definition of y when I take the derivative with respect to x. And then it turns out when you do the scalings, I pick up an additional factor of the entropy, and then it just scales like y squared minus y equilibrium squared. And so just to describe the behavior of this equation, y is constant when y is equal to y equilibrium. Then once the dark matter becomes non-relativistic, that y equilibrium drops like e to the minus m on t. Once this starts to drop precipitously, then the right-hand side becomes non-zero. My number density starts to drop precipitously until this right-hand side becomes small enough and then I'm back into the y equals constant regime. That's how that works. Questions about this? I think this is the most tedious or should I say detailed part of this lecture. Completely straightforward physics. And when does it drop out of equilibrium? Written up there. It drops out of equilibrium when this, the typical time rate of change of this is always going to be limited by the Hubble parameter. If you're looking for something that has dimensions in the first time, you always want to use the Hubble parameter because that's telling me about how fast my universe is expanding, which is to say how fast my number density is changing versus how fast my annihilation is happening. So this happens efficiently as long as the annihilation rate, which just goes like this number density times the cross-section times the velocity, as long as that is larger than the expansion of the universe, then I can maintain equilibrium. But once this annihilation, once this number density drops so small that it's no longer larger than the Hubble parameter, then that's when I start to leave this equilibrium curve. I can't keep up anymore. And so that's at this point that you leave this equilibrium curve. And that's the reason why this says increasing sigma v as you go down. So the larger your annihilation cross-section, the longer you can maintain this equilibrium number density before the particles become so rare that the annihilations just don't happen. Now the other thing that I'd like you to observe is that the point at which you leave this curve is really sensitive, the number density is really sensitive to sigma v, but it is not sensitive at all to the m on t. It's only logarithmically sensitive. And the reason for that is this thing is just dropping exponentially. So if you just want to back of the envelope it, what you should do is to compare n sigma v at whatever temperature it is where you leave this curve that's called the freeze-out temperature to whatever the Hubble parameter is at that temperature. And then that allows you to actually solve for the number density by just plugging in the freeze-out temperature. So I want to do this calculation, or at least sketch it for you because it appears everywhere. This is the reason why people are focused on weak-scale dark matter is because I can just take, follow up what I said before, take rho on m, this is my number, one on my number density, so I'm going to take n sigma v and equate it to the Hubble parameter, okay, because that's when freeze-out occurs. I'm going to do this to get a calculation of what the number density of dark matter in our universe is today. So the reason why I'm pausing on this is I want to emphasize the importance of the fact that you're getting a microscopic parameter, the annihilation cross-section from the fact that I can measure the number density in dark matter in the universe. Okay, so just take this n sigma v is equal to h. Now, rho on mass, okay, I'm just going to take, that's related to the number density in dark matter. Now I'm going to rescale it from the temperature at which it froze out to the temperature today because this is something we measure today and this is just a rescaling with the volume from the fact that it becomes constant out here at late times. That's what freeze-out means. And now I just go one step further and I have something that's related to an energy density in dark matter which I can go and measure, a ratio of mass to temperature at freeze-out, a temperature today, also measurable, and then m-plank which we know. So now I can plug everything in and as I said before, this number here is not very sensitive to the annihilation cross-section. It's only logarithmically sensitive and the reason for that is that this is an exponential curve. It drops really steeply. So I just know what that number is. It's something about 20, 20 or 30. So I just take that now, plug it in here. Tf on mx is 20. Temperature today in photons is about 10 to the minus 4 EV. I know what the energy density is in dark matter. That's what all my cosmology has told me. And the number that pops out when I do that exercise, which I would encourage you to do as a bedtime exercise tonight, is 3 times 10 to the minus 26 centimeter cube per second. And this has probably been the most important number in dark matter physics for the last 30 years. Because when I take this 3 times 10 to the minus 26 centimeter cube per second and I convert it into natural units, which is to say particle physics units, the number that comes out of that is 1 on 20 TeV squared. And you say, okay, well, that's above the weak scale. But then I say annihilation cross sections should actually have some type of coupling constant in them. Probably a pi or a 1 on 4 pi. And so that comes out to be something like approximately G week to the fourth on 2 TeV squared. Yeah, so the velocity factor turns out to be about a third. So that's sitting in there as well. It's not an important factor because that frees out dark matter is not that far from relativistic. So you can put that in there as well. So this has really been the thing that has motivated in large part the search for dark matter at the weak scale. And I think it's a great motivation. I think it's a compelling reason that we should look for dark matter at the weak scale. It may not be the way that our universe actually works, but I think it's a great clue for where to start looking. So questions about this, because I'm going to move on to the next mechanism for setting dark matter density. Yeah, so for example, so one very common thing that people do and each one of these scales like G week. So if I calculate a diagram like this, for example, it's going to go like G week to the fourth. So for example, we'll see this tomorrow. But if this happens to be a Wieno or a Higgsino, the superpartner of the W or the Higgs, then you do end up with factors that go like G week. So it does end up scaling like G week to the fourth. So oftentimes this is very parametric. So when you say this points to the weak scale, you have several orders of magnitude slop. Because for example, I can have a Higgsino dark matter and then I have some mixing angle that suppresses the rate. And so this is true within four or five, six orders of magnitude in the cross section. Which is why I don't think that this is a home run. Because the reality is that you do have a lot of freedom for setting the dark matter, but this is what has motivated people to look at weak scale dark matter. There are free parameters and those free parameters enter like the fourth power or squared. And they can have an order of magnitude either way and so when they enter you can get several powers in the annihilation rate. We'll talk about that a little bit tomorrow when we talk about supersymmetry. So let me move on to the next mechanism for setting dark matter. So one thing I want to emphasize about this thermal dark matter is that the energy density in dark matter is set in a way that is completely different from the standard model. So how do I set the standard model energy density in our universe? Anyone? Well, I give you the answer on the slide. It's set by the particle-antiparticle asymmetry. So I have more matter than antimatter in the universe. The ratio of that asymmetry to the thermal number density is about one part in 10 to the 10. So it's a really tiny asymmetry. But the fact that I have electrons and opositrons left in the universe is just because I have this little matter-antimatter asymmetry. And it's completely different than what's usually imagined for the dark matter. What's usually imagined for the dark matter is I don't have any particle-antiparticle asymmetry. It was just the thermal-freeze-out effect. So people have started to say, well, what about using the chemical potential? Why not doing a similar kind of thing with the dark matter sector? Have it have a dark matter, anti-dark matter asymmetry and have that set the dark matter density? And so one of the key things here is that even though I can't draw one part in 10 to the 10 asymmetry, I have this thermal abundance, which is T cubed. And now I have to get that down to a one part in 10 to the 10 part that's left. Now, how does that work in the standard model? Well, in the standard model, I do leftogenesis or barogenesis. And that generates a small particle-antiparticle asymmetry. And the way that I get myself down to having only electrons, so I have only matter left, is that, for example, I have E plus E minus annihilating to photons. And that process is really efficient until I run out of positrons. And once I run out of positrons, then I'm just left with my primordial electrons. Now, the reason why that works in the standard model is that I have a force, namely the photon, that makes it work. But the idea of chemical potential dark matter is just that, well, it works for the standard model. Why don't I just do it for the dark matter sector as well? There's some particle-antiparticle asymmetry. There's some darkogenesis process that generates an asymmetry for the dark matter sector in a way that's similar for the visible sector. And so, therefore, I have some matter-antimatter asymmetry in both the dark and the visible sectors. Now, is there any advantage to doing this? Well, I can tell you the obvious disadvantage. So, we really like the fact that this thermal-freeze-out mechanism gave me a number that was weak-scale. Okay? I like that fact. On the other hand, I sacrifice something in the sense that it's really an accident that this ratio of dark matter to bearing on density is a factor of five. Our priority, there's no reason why those should be so close to each other. People might say, well, anthropics did it for you. Anthropics are telling you that the ratio of these energy densities should be so close to each other. But maybe not. Maybe what I should look for is some mechanism that relates those two to each other. And so, the idea then would be that if dark matter has a chemical potential, just like the baryons do, and furthermore, if those chemical potentials are related to each other, then I might actually be able to relate the energy densities. But it's not exactly the energy densities that I'm relating to each other, because relating the chemical potentials actually relates the number densities to each other. And so, if I relate the number densities to each other, and then I use the fact that observationally, this ratio is five to six in that range, then I get a dark matter mass, which is observationally, you know, if I just, this is all back in the envelope, it depends in detail on your model, sort of naturally five GEV. So, how do these models work? So, these models are called asymmetric dark matter. And I'm going to go through this really quickly, so I just want to point out that there's a review now on this. So, the idea of asymmetric dark matter is that you have, you relate these two densities to each other by sharing this asymmetry. So, you say, okay, I'm going to take this observation seriously, and I'm going to have a mechanism that relates the chemical potential in this sector to the chemical potential in that sector, okay? And so, I'm going to share the asymmetry, the particle-antiparticle asymmetry between the two sectors. Now, that's great in the early universe when I can have chemical and thermal equilibrium. What happens if I just allow that to continue as the universe cools? Well, if they're in thermal and chemical equilibrium, it's going to be exactly the same thing that happens with thermal freeze-out. Namely, I get an annihilation. I wash out that asymmetry. Exactly the same thing happens with the chemical potential. So, what I actually need to do is to somehow decouple whatever mechanism is sharing these two asymmetries with each other. And then, at the end of it, once I've decoupled them, so now I have a dark matter asymmetry, I have a baryony asymmetry. These two asymmetries are happily floating along, completely independent of each other because they've decoupled. Then the last thing that you need to do is to get rid of the thermal abundance of dark matter. So, in the standard model, the way this happens is E plus E minus annihilates the photons. You need to have some analogous way that happens for the dark matter that annihilate away the symmetric abundance. Now, there are three ways of doing this, three ways that exist in the literature of doing this. How do I share this particle-antiparticle asymmetry? So, one is that you can use electroweaks phalerons. And I'm not going to go into any detail on electroweaks phalerons, except to say that they're related to some of the field configurations that Sergeet was talking about earlier. What these things do in the standard models, they violate baryon and lepton number. And if you say, well, dark matter is also going to carry, say, lepton number. Well, if dark matter also carries lepton number, then these electroweaks phalerons will also mix and give a particle-antiparticle asymmetry to the dark matter as well. That's the basic idea. And it's actually a great idea, which would work in principle, except for the fact that lep, in particular, puts enormously strong constraints on putting in additional particles that are charged under electroweak quantum numbers. It's actually quite hard to do this theoretically. LHC is making it worse. So just from a purely practical matter, this number one mechanism doesn't work so well. It's hard to do. However, there are other ways that you can do this. One is to use higher-dimension operators. So I'm going to just... And the other is to use a decay. This has different dimension dynamics than the higher-dimension operators, but it actually has the same Lagrangian. So I'm just going to explain to you this number two and then refer you to here for more references on the decay model. So let me just tell you the idea. So the idea of the higher-dimension operators is just to say, I'm going to have dark matter interact with something in the standard model that's neutral. Any combination of standard model and neutral states that also carries baryon and lepton number will do. Any combination. So here, for example, is a neutron. I have an up quark and two down quarks. Carries baryon number one. This combination does not carry... So these are SU2 singlets, all of these. And an up quark and two down quarks is also an SU3 color neutral, or a combination of it is an SU3 color neutral. Okay? So I have this neutral thing now talking to the dark matter. I'm glad that I have neutral dark matter now, but this thing carries the chemical potential of the baryons. And this is an interaction between the neutrons and the dark matter. And early in the universe, there is this at high energy, you don't see this barrier. So let's say these are all fermions. This is going to be suppressed by one on some mass scale. So as I cool down the universe, I start to notice this barrier, but at really high temperatures I don't see it at all. These two just talk to each other freely back and forth, back and forth until the universe cools down. Now I notice this barrier and what happens when I notice the barrier? When I notice the barrier, this thing just decouples. And so now, in the early universe, I shared the chemical potential, universe cools, and now these two sectors separately freeze out from each other. And they just carry on happily. I have a dark matter asymmetry, I have a visible asymmetry, and everything can go on. And you can generalize this. To any combination of standard model particles, LH, LLE, QLD, UDD, all these things don't carry any standard model quantum numbers. They're neutral. And so now I can have this talk to any combination of dark matter fields, and it does exactly the same thing. So questions about this mechanism? Yes? Well, so one can look at it two ways. So there are two things one could say. One could just say, this is another mechanism for setting the dark matter density. It's different from thermal freeze out. You need to have some mechanism for setting a particle, antiparticle asymmetry. If I set a particle, antiparticle asymmetry, then it's going to give me a different relation between the dark matter density and the visible energy density. And so because this mechanism tends to set the dark matter and energy and carry on number densities to be the same, if I have this chemical equilibrium between the two sectors, it gives me a different mass scale for the dark matter. So that's one thing you can say as well. I'm just going to look at this ratio of dark matter and density, take the observation, and then ask, what might that tell me about the nature of the dark matter? That's one way of saying it. Another way one could say it is, well, maybe that ratio gives me some clue for what the nature of the dark matter is. Maybe it's pointing to some mechanism which relates the energy density of dark matter to the visible sector. Either way, one is sort of a bottom-up approach and the other is more of a top-down approach. Either way, what I'm really after is different kinds of signatures of dark matter. I don't want to put myself into a box. I want different theoretical ways of setting the dark matter density. Well, so this is sort of, all of these are tildes. All of these are tildes. So for example, there are some models of dark matter where I can have this ratio to be large between the dark matter and the baryon density. If that ratio is large, then I get a different mass scale for the dark matter. So the meaning of this barrier, so the meaning of the barrier is it signifies a higher-dimension operator. So let me make an analog with the weak interactions. So you know that at low energies, weak interactions, the cross-sections scale like one on the z mass to the fourth power. And the reason why that is is because the z and the w bosons, if they're much heavier than the energy of my interaction, then we know that the cross-section scales like e squared on mz to the fourth. But as I go to higher energies, now I can't integrate out the w and z boson anymore. And so now at high energies, the cross-section doesn't scale like e squared. It scales like one on e squared. Because now I have to keep the w and z boson in my interaction, in my theory. This is exactly the analog of the Fermi operator. So you should just think of this. For example, you can think of this as the analog of the four Fermi operator. At low energies, at low energies, the weak interactions are decoupling because they go like e squared. But at high energies, they actually become very important. And that's the analog of this. At high energies, these interactions are important as I go to lower energies. So this barrier would be like the particle that's being integrated out. So you can think of it as being like the z boson. The z boson is like a barrier. I could have my neutrinos. I have my visible particles. And those interactions are mediated by the z boson. And the heavier that z boson is, the weaker those interactions. Make sense? Not necessarily. It turns out it could be weak scale. This could be mediated by weak scale particles and it would be just fine. It turns out that just like for the weak interactions, they start to decouple once you drop below the mediating particle mass. A similar type of thing is happening here. As you drop below the mediating particle mass, the interactions become less important. So it depends a little bit on the details of the model, which I can't go into here, but it turns out it doesn't have to be very heavy. No, it doesn't have to be. In fact, if I were going to pinpoint a weakness in these models, that would be it. It does not name a scale for an interaction with the standard model. So supersymmetry is nice from the point of view that you look for things that are near the weak scale. So in this case, because you just need them to be in equilibrium at some point in the early universe, they don't necessarily need to have a low scale for the interaction. It's going to make it harder to see in the universe today the higher that scale is, but you're not guaranteed from that point of view to have a detection. Basically, you have a very big range for these interactions to happen. That's correct. Okay, so let me move on to the next kind of detection just in the interest of time. So what we talked about here with thermal freeze-out and with asymmetric dark matter were two kinds of mechanisms where you tend to set the density early in the universe and then as the universe cools, those interactions decouple. I can actually do the opposite, which is to say dark matter is not going to be in equilibrium with the standard model at all in the early universe, but I'm actually going to populate it late in the universe. So it's actually inverted from that point of view. I don't populate it in the early universe, but I populate it in the late universe. Those mechanisms are known as... We're going to talk about freezing and then freeze-out and decay. So let's talk first about freezing. So in freezing, dark matter is not in thermal equilibrium to start. The production of dark matter is actually dominated in the infrared, which is to say it happens at low temperatures, which also means that you don't have sensitivity to initial conditions in the universe, except to say that the dark matter doesn't have a high density to start. The standard models in thermal equilibrium, like it is usually, but there's no dark matter production. So this idea is that you have this visible sector at some temperature T. You have some coupling, this coupling, this is the key thing to the dark matter sector has to be tiny. And the other thing that is really important is that the dark matter never comes into thermal equilibrium itself. So there's no T-cube number density in the dark matter. Dark matter number density in the very early universe is zero, or very, very small. And then what happens is that as the universe cools, these interactions with the standard model sort of gradually leak in to the dark matter sector. So you imagine these interactions are very, very rare, but every once in a while you produce a dark matter particle. And that can happen either through, say, two-to-two processes. So V, say, stands for some standard model particle, which goes to another standard model particle in the dark matter. Or I can have some decay process that goes to standard model particle plus the dark matter. And naive dimensional analysis, which we're going to go through on the next slide, tells you that this process is dominated in the infrared. In particular, it goes like whatever the coupling constant in this interaction is squared times ratio of M-plank over temperature. So let me go through this naive dimensional analysis. Going back to the Boltzmann equation, some standard model particle. Okay, so it's some particle that's in... So let me be more general. It's some particle that's in... So for example, one thing that you could do would be with a sterile neutrino going to a neutrino plus dark matter. That would be an example of a Friesen type of process. So let's see how this works. Going back to the Boltzmann equation that we had before. This is just the same equation as before. Now we rewrite this back now in terms of the number density. So the evolution of the number density of dark matter goes like this number density squared times this cross-section. The number density in the standard model just is going to go like T cubed. And so this cross-section, now just by naive dimensional analysis with no mass scales in the problem except the temperature, it's just going to go like whatever the coupling constant is squared over the temperature squared. So now if you plug this back in, what you get for the equilibrium, the late-time number density goes like one in the temperature. So if you put this into platform, the way that this looks, this was freeze out. I started with y constant and then I get rid of it. Friesen acts in the opposite direction. So I start with very little dark matter and then the point is that occasionally I produce a dark matter particle and as I produce those dark matter particles, they grow and they grow actually up until the point that it saturates, which is to say when the temperature becomes on some typical mass scale, say the mass of the mediator or the mass of the particle that's producing it, until it saturates to this number. And so it has a very different scaling than the freeze out kind of process. Questions about this. You're wondering whether you can... So you do need some type of... So you would have to work awfully hard to get the CMB observations right without having dark matter. I'm not saying it can't be done because strictly speaking, you don't actually fit the dark matter density with the CMB, but getting the ringing of those curves right while getting the baryon energy density right and fitting the matter density today would be really challenging. So generally speaking, yes, this would have to happen before CMB epoch. Certainly fine if it happened after BBN epoch, but certainly by CMB epoch. No, you don't end up with much... So note that it goes like lambda squared. So the final amount of dark matter that you get is going to be set by both the size of this coupling, which is to say how often you produce a dark matter particle and then also the time at which it stops, which is set by whatever this mass scale is here. So you're free to dial whatever the dark matter density is to fix it to be today. This certainly can happen... No, you're imagining this happening well before CMB epoch. So this is happening... You can see on this plot, you imagine that this is happening at temperatures on order of the mass of whatever particles say sterile neutrino, which is decaying and producing a dark matter particle, for example. So this is still happening in the very early universe. It's just that you're not starting from the dark matter and thermal equilibrium. You're doing it through another particle basically slowly populating the dark matter sector. Really small. Oh, so you wouldn't... Generally speaking, you would not detect this through the same coupling that would be setting the abundance. The coupling is just too small. In that way, it's similar to asymmetric dark matter that in many cases you're not detecting the dark matter through the interaction which is setting the abundance. It's some other type of interaction. I'm going to come back to this point later. There are well-motivated reasons why you might expect to be able to see it through some detection mechanism, but it's typically not the mechanism that's setting the abundance. It depends on lambda. Yeah, it can be very massive. Yep, it can be very massive. So I just want to spend a little bit of time the next few minutes on these last two mechanisms which I'm going to go through fairly quickly because they're related... Well, first of all, to what Sergeid is talking about, but then also to actually the things we've already talked about. So another one is you can just combine mechanisms. So you can have freeze-out and decay. So the idea is that I have some particle that freezes out in the early universe, but that particle that freezes out is not the dark matter. What happens is eventually that particle that freezes out decays to the dark matter. So a classic case where this is often used is for Gravitino dark matter. So the idea is that I would have a superpartner of one of the standard model particles would freeze out and then those particles would float along and then eventually decay to the Gravitino. So for example, I could have one of the scaler superpartners of the standard model freeze out and it would be quasi-stable if the coupling to the Gravitino is small enough. So the idea then is that I set the density of this guy, but that is not actually the final energy density, the dark matter, because this thing eventually decays to the Gravitino. But you can relate the energy density, here it's called the super weekly interacting massive particle, a Swimp, that in this case would be a Gravitino, which would be related to whatever the energy density is in the parent particle that froze out just by a ratio of the masses of these two particles. So you can also have freeze-in for Gravitinos, very similar type of calculation except your naive dimensional analysis changes. You can have a dependence now that it's going to go one on M plank squared and then what happens is the abundance actually goes linearly like the temperature, so T max ends up being the reheat temperature. So I think I'm going to stop there because Sergeid is going to talk about the misalignment mechanism, probably in quite a lot of detail, and then just summarize so that we can have a few questions before we finish. So thermal freeze-out has been the dominant paradigm unquestionably, and I think there is a good reason for that in the sense that it relates this macroscopic parameter, the observed number density or energy density in dark matter to the microscopic parameter, which is the cross-section. And it really gives us a good reason to go look for dark matter at the weak scale. That said, as I'm going to go through in more detail tomorrow, unfortunately we have not seen supersymmetry so far, and there's going to come a point the experiments are becoming good enough, in particular direct detection experiments are becoming good enough that if we don't see dark matter in one of these direct detection experiments, we're going to start wondering about focusing so much of our energies on wimps. And so fortunately, the quest for understanding what the dark matter is does not stop there. It's forcing us to reevaluate different types of paradigms to look for dark matter in different places, and so I gave you a few examples, really simple examples of other ways that you could set the dark matter density, and as we'll see in the next couple of days, it actually tells you about different ways to go and look for the dark matter, and I think that's the crucial part. So dark matter can have a chemical potential analogous to the visible sector. It can freeze out first and then decay. It can have this freeze-in mechanism. It can have some misalignment, which is to say an oscillating scalar field. And what we're going to talk about next time is the way that this freeze-out and also freeze-in is realized within the supersymmetric extension of the standard model. And what we're going to do is go through direct and indirect detection basics and see if these experiments were really designed in the context of looking from the wimp for supersymmetry. So I'll stop there and then take a few more questions. Sorry, in this freeze-out that you were explaining, I don't know, perhaps I'm just asking something you will explain tomorrow. But when you're saying that, okay, so you have a parent which is freezing, and then decay... I have a, sorry, what did you say? A particle and then it's freezing out and then it's decaying into dark matter in another particle. What's happening with the other particle? So oftentimes it's a standard model particle that it will decay to. So for example, I could have a snutrino, for example, be that scalar particle which then would subsequently decay to a neutrino and then the dark matter particle. And then once I decay to the neutrino or to the standard model particle, it just thermalizes with the standard model. And then the standard model proceeds in the way that it normally would. But still... So there's going to be some BBN constraints in particular if that parent particle carries any type of standard model charges. There's going to be constraints from BBN, for example, that I can't decay too late. So... And in fact, there have been very nice papers written on what exactly those constraints are. So you... There are constraints which you do need to pay attention to. But oftentimes the thing that you're decaying to is in the standard model. There are other models I can write down where that's not the case. So I can construct an entire hidden sector where that particle belongs in the hidden sector and then it decays to another hidden sector particle. Say that fermion is really light and the temperature in the dark matter sector is colder than in the visible one. Then I could have some mechanism where I have some dark radiation which is psi and then the dark matter particle which is non-relativistic would be another example. So I was wondering because like that doesn't explain why is there this symmetry in the dark matter and those baryonic matter? So this is a separate thing. This is a freeze out. So in general I wouldn't have a particle anti-particle asymmetry in this context. Thank you. So my question is actually related to the machos. You said that above 100 solar masses they're actually constrained because they would have an impact on the matter power spectrum? Yeah, it's actually more like above 1,000 solar masses than 1,000 solar masses. There are some other things that would happen like the disruption of the disk. And so it's at that point that you start to get a little bit into hand-waving sort of structure formation arguments for why machos cannot be in that small window. My question is also, I mean in the cold dark matter paradigm you have this hierarchical structure formation so you would also expect small scale dark matter structures which have a similar mass. Why is it that they are not constrained that much by the dark matter power spectrum simply because they're less? That's precisely what this is. It's a constraint from the dark matter power spectrum. So what you would see it is exactly a constraint from the power spectrum. So it's the fact that on small scales we have such good measurements of the power spectrum that you would actually see the graininess. You would actually be able to see the fluctuations from the presence of these guys. And it's the fact that on large scales normally you expect the power spectrum to scale like one on K cubed and an impact from a macho-like object actually doesn't have a one on K cubed it inserts a white noise that just is flat in K and you can see that amplification in the power spectrum. I think subhalos of these masses are not constrained. I mean they're not ruled out, right? Subhalos of these masses. Yeah, just cold dark matter subhalos. That's because they form in a different way. Exactly. So when you talk about so if you seed something from inflation so you start with a power spectrum that's just the ordinary inflationary power spectrum that has a power spectrum that goes like one on K cubed. When you seed fluctuations you're talking about in order to make these objects they're going to have order one fluctuations on much larger scales and so what that does is to actually insert much larger fluctuations on small scales than what you get from the ordinary inflationary picture. Thank you. In the asymmetric dark matter paradigm can you comment on mechanisms to explain why the mass of the dark matter is related to lambda QCD? So many of these models it's not. So a particularly strong model might relate the dark matter mass itself to lambda QCD. In other of these models you observe that the dark matter mass is not too far from the weak scale. So it might relate the dark matter mass to the weak scale times you'll call a coupling that's not much smaller than one. So in asymmetric dark matter models you're not fixed by one or two. You might say that the real mystery in these models is why is the weak scale so close to the QCD scale confinement scale. But people usually say that's a logarithmic tuning. These the coupling mechanisms are sensible for more than one dark matter candidate. The coupling mechanisms production dark matter. No. The like Frisout and Decay these mechanisms, these kind of mechanisms are sensible for more than one dark matter candidate. But there are general aspects of distinguished between one kind of one dark matter candidate or two model independently. So I think in general more one decides to not restrain oneself to only the QCD axion or to weak scale supersymmetry. The more one's options open which is positive in the sense that it motivates you to build more types of experiments. And negative in the sense that you don't paint yourself into a corner. In the sense that if you did have a signal you're going to have to do a lot of work to actually reconstruct whether that is a dark matter or one part of the dark matter or what exactly it is that you're looking at. So it comes back to what I was saying earlier. Once you have a signal that you've confirmed in some experiment that's not the end, that's the beginning of dark matter physics. But a semenylation of dark matter, for example. Yeah, so that's another mechanism where you're not having dark matter annihilating against itself, you're having a dark matter annihilate against some other particle. So it's related to freeze out in the sense that I'm having a dark matter annihilation process but you don't get exactly the same relation between the number density and the annihilation cross-section that you do for the standard freeze out mechanism. And also in that case you can end up with a particle, anti-particle asymmetry. So it's sort of a hybrid of some of these models. The CMB measurements for example are insensible for this. So that would also be happening in the early universe well before CMB epoch well before BBN epoch. So in most of these cases what I'm really talking about is definitely before CMB epoch in most cases before BBN epoch that you're setting these densities. So these are things that are still happening in the early universe. This freeze out and decay and the other mechanism, the freezing they are always constrained by Big Bang nuclear diseases and the CMB or there is a way out. I always have to take those constraints into account. For example, if freeze out and decay is happening solely in a hidden sector that had a temperature lower than the typical standard model sector temperature then you wouldn't get much constraint from BBN for example. So it's exactly what the constraint is and whether you're allowed to do something after the BBN epoch or not is a model dependent question. CMB like I said before you'd have to work hard not to have dark matter of that epoch. Everything should be present, right? Not if it's weakly enough coupled to the standard model and if the read temperature is low enough. So for example the gravitino the gravitino is a good example. So the gravitino can be so weakly coupled to the standard model that it never thermalizes. And so the only way that you populate it is either through this freeze mechanism or through the freeze out and decay of another particle. So it's certainly possible to have some particle that just never thermalizes and that's when this freeze mechanism is important. But at super high temperatures wouldn't the gravitational coupling itself be strong and you would do this. Sure, so that's why it depends on the reheat temperature. So it depends on how high you heat the universe after inflation has happened. Just one more question. Do we have any example in the standard model something like this freeze out or freezing and decay and freezing. Is there any particle in the standard model which goes through this kind of process or it's just a new idea that In the MSSM it can happen. Not standard model, it's beyond the standard model. In the standard model everything is coupled strongly enough that you're going to populate it. So if the weak interactions happen to be weaker than they were so it doesn't happen in the standard model. So it happens in the MSSM. One more question. Okay, let's think.