 Good morning or good afternoon, everyone. Welcome to our Latin American webinar for physics number 124. It is a pleasure for us to have today Professor Jesse Shelton. Professor Shelton got her PhD at the Massachusetts Institute of Technology, and after that, she was a postdoc at Rutgers, Yale, and Harvard Universities. And today, currently, she is an associate professor at the University of Illinois at the Vanishing Pane. We are very happy to have her here today to talk to us about non-standard theme histories and the small-scale matter power spectrum. Thank you very much for joining us, Jesse. Before you start, I want to remind everyone that you are very welcome to post your questions on the chat of YouTube. Please, if you write your questions there, we will be happy to read these questions to Jesse after she has done her presentation. Please participate and let us know your comments and questions. Thank you, Jesse, again, and you can take it away. All right. Thank you very much, Walter. It's my pleasure to be here. Slide sharing is again doing something unexpected. Give me a second to find... We tested this. Interesting. Keynote is crashing. No worries. In the meantime, we can say, like, stay tuned for the next season, which is going to start in January. We have a lineup, again, quite interesting speakers. You can follow us on YouTube and social media. Oh, I made it. I make this commercial. Okay. Okay. Take it away. Today, yes, I'm going to talk about non-standard thermal histories and the small-scale matter power spectrum. Usually, when people start a particle cosmology talk, they will show some version of this slide. I'll say we have lots of independent lines of evidence to understand the existence of dark matter, starting from a cosmic microwave background through the evolution of structure on large scales, meaning galaxy clusters, galaxies, and so on, growth through time. At late time, of course, we have evidence for the existence of something that sources the gravitational interactions without tracking the baryons that we can see. Of course, historically, one of the first lines of evidence was galaxy rotation curves, which show a bigger gravitational potential and be explained from visible matter. Of course, recently, and rather dramatically, lensing evidence from the bullet cluster that shows there's more mass than baryons and physically displaced. I am going to be very interested in the matter power spectrum and what it can say about the history of our universe on the moments of time that are buried in this mysterious white glow here. Back at this very early time, we don't have pretty pictures. We have mental cartoons. What do we know about the very early universe? We know some things. We know that there was the standard model in the early universe, and we know that it was there and in thermal equilibrium, definitely at the formation time of the CNB, and then our earliest evidence about the ingredients in our universe comes from Big Bang Nucleosynthesis at temperatures of order and MEV. We also know from the CNB that there had to be some form of dark matter, and it was new, cold, limited interactions, both with us and with itself. Then we also know that there has to be some period of inflation or something that does its job, that gives rise to the fundamental perturbations, the primordial perturbations that grow into the large-scale structure. This is earlier than an MEV. This is very poorly constrained and very poorly understood. We know that Big Bang Nucleosynthesis tells us what the universe looks like up to order of 10 MEV. This is our cartoon for the expansion history of our universe. We parametrize the expansion history of the universe with a scale factor little a. This is the energy density. At late times, roughly the formation of the CNB on to us. I'm not going to talk about cosmological constant. I'm interested in very early times. The universe was dominated by matter, dark matter as well as us. Then at times prior to recombination, the universe was in radiation domination. We know that happened all the way up to BBN. Then we don't really know what happened before BBN, but we figured that there was some period of post-inflationary reheating that let the universe transition from the inflationary phase into radiation domination. We don't know the scale, so standard cosmology just says, okay, radiation domination all the way back to some reheating scale which has to be early enough that BBN is fine, late enough that it's subplonkian because otherwise, you know, it doesn't make sense. But of course, this is assuming that this goes all the way back for orders and orders of magnitude in temperature, therefore scale factor is a big assumption. We don't actually know that our universe did. That is the minimal assumption. It's the assumption that follows from the ingredients that we know about. But there's a lot of other things that could have happened and it's interesting to ask what could have happened and how would we know? That's mostly what I'm going to talk about today. So early departures from radiation domination, so everything I'm talking about now is before BBN, early departures from radiation domination can naturally arise in a variety of interesting, well-motivated theories of physics beyond the standard model. Historically, one of the first places people noticed this happening was modulus domination. We have a massive scalar field when the universe cools down to the point where the field notices that it's displaced from its potential. It will oscillate back and forth that behaves like matter, that coherently oscillating scalar field behaves like matter and it can easily dominate the expansion of the universe until it's until it decays. Similarly, if you have a coherent scalar field, but instead of oscillating it is rotating rapidly in its potential that is known as canation and that can dominate. And then something else that I'm going to talk about today which has been noticed somewhat more recently than this variant, modulus domination, is suppose you have a hidden sector of fields by which I mean a bunch of fields that are standard model singlets interact with themselves enough to keep themselves in thermal equilibrium for some interesting part of time. But then in this talk, they're always going to be out of thermal equilibrium with the standard model. So, hidden sector will have its own temperature that is separate from the standard model temperature. So, one idea you can have in mind is this is a sort of minimal, non-minimal cosmology. You have some period of inflation and it ends with some reheating and the inflecton can decay not just into standard model stuff but also into hidden sector stuff. Hidden sector stuff will go on, you know, self-thermalize. It's very easy to make sure that hidden sector stays out of equilibrium with the standard model in this scenario. And I'm going to be mentally imagining that dark matter is born out of the hidden sector radiation bath without direct involvement from the standard model. That's not, you know, something that has to be true about the universe but A, it's very natural. B, it easily explains a lot of, you know, null results from standard model experiments like, you know, direct detection, collider production and so on. And so, this is the scenario that I'm mostly going to have in mind. You can think about this idea in part as a way to look for very secluded dark matter and try to track the effects of these kinds of hidden sector dark matter models. So, the maximally pessimistic scenarios where they're never in sort of interesting non-gravitational contact with the standard model. So, if you have one of these hidden sectors, internally thermoids hidden sectors, this is a macroscopic amount of stuff in the early universe. Only part of this is going to go on in the dark matter in the same way that if you wanted to make a WIMP dark matter theory, right, and WIMP dark matter is born out of the standard model radiation bath, but most of the energy during the radiation dominated period in the standard model radiation bath is carried by standard model radiation. In the same way, only a small fraction of the hidden sector's energy density in this cosmology is going to ultimately end up being dark matter. The rest of it is stored in hidden sector radiation. Now, there's basically two possibilities. Either the lightest state in the hidden sector is light enough that it can go on and be dark radiation, in which case we can try to look for it gravitationally, or it's massive. If the lightest state in the hidden sector is massive, then once the universe expands enough that the temperature of the hidden sector is comparable to the mass of that state, then it registers like matter, but you have a thermal number abundance of it. This is enormous, and it can easily come to dominate the expansion of the universe. And in this case, you get matter domination, but because the micro-physics of this early matter dominated era are different from the micro-physics of this early matter dominated era, you can get some interesting things in this setup that you can't get in this setup. So if you do have a early matter dominated era, it means you have a pre-big bang nuclear synthesis slow down in the expansion rate of the universe. And that in turn is interesting because it gives matter a head start on clustering on very small scales. So first I'm going to talk about head start on clustering, then I'm going to talk about on very small scales. So here is a plot of the growth of a perturbation in dark matter. This is delta, which is the delta rho over rho, where rho is the energy density in dark matter at a given wave number k, cool moving wave number. And then this is the scale factor again. So this shaded region is when this particular co-moving Fourier mode is outside the horizon. So nothing happens when it's outside the horizon. Once it enters the horizon, so once the Hubble horizon has grown to the point that this mode fits inside the horizon, then it gets a bump, roughly an order of magnitude bump, just standard thing that happens when modes enter the horizon. And then during radiation domination, the standard solution for a mode undergoing linear evolution is logarithmic. So it grows, but very slowly, just logarithmically. So not much happens until at late times in the standard cosmology, the universe becomes matter dominated. And then you get linear growth during matter domination. Again, a standard result for perturbation in linear evolution. So of course, linear growth gets you much stronger, much faster enhancement in the density contrast than logarithmic domination, logarithmic growth during radiation domination. So if you have an epoch of early matter domination before the standard matter domination starts, then you have even a relatively brief interval of matter domination, you have an epoch of linear growth for the perturbation. And that can give you a big enhancement over the standard cosmology because linear growth is a lot faster than log growth. So this description is, of course, using linear theory. So you might be suspicious when I start talking about perturbations that are ordered unity. And indeed, if you have a perturbation that crosses the so-called critical density collapse threshold, then that's when linear perturbation theory stops being a good guide to describe the physics of this mode. At this point, we say that this cutoff, which is in matter domination, the standard cosmology, about 1.686, at that point, this mode becomes self-gravitating. It detaches from the Hubble flow. We say it forms a micro halo, and at that point, this is now the regime of nonlinear structure formation. We're talking about halo's locally bound gravitational structure. You can see that in fact this mode is so strongly enhanced. It crosses the collapse threshold, not during matter domination, but even earlier during radiation domination. In this case, the critical density is higher. It's partly because the universe is expanding faster. They have to get more stuff in one place to get enough local gravitational potential to really ensure that collapse happens. So we're mostly going to be talking about things. We're going to start talking concretely about micro halos. We're going to be focusing on the more understood story of matter domination. Bottom line, what I want to make sure everyone takes away from this plot. If you have a period of early matter domination, you collapse much earlier than in the standard cosmology. So what this looks like now is this plot was for one specific co-moving Fourier wave number. Now I'm showing what happens to a range of scales. What I'm plotting here is a function of the scale of the perturbation is the transfer function that happens in this altered cosmology. So understand this as the relative change in the growth of a perturbation in reference to the standard cosmology. So how much more growth do you get in these scenarios? Or sometimes less than if you just had standard lambda CDM from the beginning. So as I go up in K, I go to smaller and smaller scales and that means I go back in time in terms of modes to enter the horizon earlier and earlier and therefore saw more of the altered cosmology. So I start out with no change because these modes didn't enter early enough to see any altered cosmology. Then there's a time when whatever was dominating the early universe decayed and so we could match back on to the standard radiation domination that we know we have to and we're going to get that CDM. This I'm going to call reheating. This is separate from post-inflationary reheating. This is the reheating that gets us from our early matter dominated era into standard radiation dominated physics. So most that entered before reheating saw some of the radiation, saw some of the departure from radiation domination means they saw more growth. The earlier they entered the more growth they got and so this you get a characteristic rise in how much growth you got that scales like K to the fourth which you can get by understanding how the horizon is growing as well as the duration of time that mode spent inside the horizon. But this doesn't go on indefinitely. Ultimately something cuts this off and this cutoff is sensitive to dark micro physics with a specific physics of whatever you know thing is dominating the universe at this time will tell you the shape of this cutoff and what wave number cuts it off. In other words location of this cutoff and this cutoff is particularly interesting in these models with you know modified expansion history and small scales because as you can see this ends up telling you which scales are going to see the most growth and therefore will dominate the you know ultimate clumpiness of matter on on on very small scales following the collapse of these perturbations into gravitationally bound structures. So understanding what this cutoff is is super important in these models with enhanced growth on small scales and I'm going to talk about some fun stuff about developing more ideas for what kinds of cutoffs we can see and then talk about how we can test them. So there are a couple cutoffs that show up from you know standard early matter dominated histories that are new for early matter domination with relic dark radiation deaths and you can't get in models with moduli domination. So the tight coupling to a relativistic species cuts you off at the gene scale of the relativistic species that is actually what's cutting you off here. The is also the possibility that some of this nice early growth is cut off at late times because dark matter has too much kinetic energy and wanders out of the over densities and washes them out. And what I'm going to talk about today is cut off that you get when you have interesting self interactions among the particles themselves making up the thermal bath even after they become non relativistic. So the other thing I want to say before we get started on that is to give ourselves a reality check about exactly what kinds of scales we're talking about. This is going to let us make a map between the wave numbers that we're talking about and the resulting physical size of the potentially enhanced dark matter density fluctuations in the late universe. So if a mode enters the horizon right at the transition out of this early matter dominated era and into radiation dominated era well by definition that means the co-moving wave number is equal to product of a times h or h is of course Hubble by reheating and trading a's for temperatures that tells us that the mode that we're scale of where we start to expect modified structure modified number counts scales linearly with the reheating temperature. So bigger reheating temperatures mean bigger k's and therefore smaller scales. I can convert a temperature or a wave number to a mass you know how much mass is contained in the resulting halo that forms from perturbations on that scale uh by saying okay you know here's k. I construct a sphere corresponding to the physical size of a mode with that wave number take all the mass inside that and that gives you something related to the density of dark matter like so. Plug in numbers and you find given what we know from Big Bang Nuclear Synthesis about the smallest acceptable reheat temperature again we have to map back on to the physical cosmology that BBM tells us we have to have it late times. We're talking about enhancements to halo populations on scales that are smaller than the earth mass so very small this is a very different regime from the kinds of small scale structure that people talk about in our galaxy which is something like 10 to the 6th into the 7th solar masses. So we're talking uh micro halos. So now let's talk about uh this micro physics and the small scale cutout uh something that is very amusing to consider is the case where your relic dark radiation bath doesn't behave like you know the standard model radiation bath. It behaves in a way that is only possible for a hidden sector that is thermally decoupled from the standard model. This is the case where the lightest state in the hidden sector becomes non-relativistic but it still has interaction self interactions that can keep it in full thermal equilibrium meaning chemical equilibrium as well as kinetic equilibrium. This means it has to have number changing self interactions that let its uh you know face to face distribution function track the you know thermal equilibrium distribution as the temperature decreases when the universe expands. So this sounds exotic but that's just because particles in the standard model this doesn't need to happen everything in the standard model is an equilibrium with you know the relativistic photons and so there's no time for any epochs of this form to happen. Very simple field theories give you this kind of behavior in particular the simple you know phi to the fourth theory exhibits cannibalism is everyone's favorite and basic example model. Here are in the so this is a case where I have not assumed a z2 symmetry we have therefore three to two interactions these are just a couple of the Feynman diagrams you have three particles in the initial state they go to two particles in the final state. Phi to the fourth theory is also of interest because it is a good toy model for hidden glue balls so if you imagine that you have a hidden sector where the you know where you have a non-abillion gauge group that you know confines at the bottom of your chain this is a reasonably good toy model to describe this you're perhaps more theoretically appealing hidden sector. So if you look at what's going on in these interactions they let you trade rest mass for kinetic energy and this is what lets the cannibal you know keep its number abundance tracking the equilibrium value. I'm going to parameterize the cross section for this to happen in terms of an effective coupling constant alpha c notice this goes like well on m to the fifth. All right so the thing about cannibals is they cool down slowly right they're continuously converting they're continuously converting the rest mass and kinetic energy and heating themselves up so if you track what happens to a this is a simplified the fourth toy model. Radiation back that is cooling down it's made out of these things it starts out relativistic you know we start our initial our simulations when the temperature is 10 times the cannibal mass starts out behaving like radiation you can see the energy density times a cubed is falling off like you'd expect for radiation but then as the temperature gets to be of order the cannibal mass the mass starts to become more and more important then here is a regime where we are using mackleboltsman statistics to model a cannibal and here it cools down very very slowly we have like three decades of evolution here but the temperature drops by only a factor of a few in fact the energy density is falling off logarithmically therefore the temperature also evolves logarithmically with the expansion but of course this can't keep going indefinitely these reactions require three particles in the initial state and so eventually they'll you know you'll run out of cannibals to have this reaction happen efficiently while the universe is expanding and so they will freeze out and after that they evolve just like matter so it's hard to get more than a few decades of cannibalism it's relatively insensitive to both the mass and it depends on alpha c to the the two-thirds power so you can't get you know too much of this epic of cannibalism but this has an interesting effect on the cosmology of what happens so the Hubble rate is different from either radiation or matter and this you know in principle is important for understanding perturbation growth even more important though is the fact that the difficulty of the cannibal fluid and cooling gives you pressure support in the fluid so here we're showing the evolution of the sound speed and the equation of state with scale factor um this is the equilibrium values and then you can see uh so this is cooling down from the relativistic value to the cannibal value and you can see this drops slowly um and then uh after sudden freeze out you see the equation of state starts deviating from the equilibrium prediction almost immediately but the sound speed hangs on uh relatively large for the factor of two-ish before it starts to drop but here you know what we're showing is the difference between uh the sound speed that you have in this cannibal model versus if you have the same sound speed at you know wait times what you'd expect if it were radiation all the way down and so you see you know it takes pardon I misspoke if you just take the non-relativistic matter and extrapolate how it uh how its velocity uh scales with scale factor you get these lines so you see uh took a cannibal many decades to get the same kind of cooling that you would expect from just dust so following freeze out um you can have a potentially substantial epoch of matter domination this is controlled by a different combination of particle parameters and then eventually the cannibal realizes this unstable indicates and then this is reheating and then uh uh cosmology marches on so what happens to dark matter perturbations in this kind of cosmology well here what I'm showing in the top panel this blue line indicates the horizon so it starts out growing uh like radiation uh you see Hubble slows down uh once the cannibalism uh becomes important then it goes like matter uh all the way up through reheating at which point it goes back to uh radiation uh type growth the other thing I'm plotting is the gene's length if you have a component of your universe that has you know important uh pressure you can compute in terms of the sound speed and equation of state a gene's length that separates growing modes from oscillating modes so modes that are uh smaller than the gene's length oscillate modes that are outside the gene's length can grow so basically the gene's length is telling you where pressure support is important so we've plotted here this uh uh the growth perturbation with this particular co-moving wave number so let's focus on the red first because that's the cannibal that's the thing that's dominating uh the universe and therefore the thing that sources the gravitational potentials um so you see it's flat outside the horizon it enters it gets that kick and then it grows but only up until it crosses the gene's horizon at which point it turns around and it starts to oscillate when it keeps oscillating um even after it frees out it stops oscillating because the sound speed is still high note that the gene's horizon is growing a little bit even after it frees out that's it because again the speed of sound stays high for a bit after it frees out before it drops so it keeps oscillating and it doesn't stop oscillating until you know decades of expansion after it frees out because that's the time at which the gene's horizon has finally decayed enough that this mode escapes the gene's horizon and starts to grow and then once it escapes the gene's horizon we're now deep in matter domination and it grows linearly with scale factor like you expect for matter domination so dark matter in blue uh is very subdominant so it is seeing the gravitational potential generated by the cannibal and so it's flat outside the horizon gets its kick and then ah the cannibal's oscillating so that means there's no net source for the potentials and dark matter doesn't do anything it just sits there it's flat all the way up until the cannibal's gravitational fields finally start being important at which point dark matter falls into those fields and gets the linear growth that you expect from matter domination radiation meanwhile it oscillates a lot it's basically just around for the ride so made a couple assumptions um first that the dark matter and the cannibal are coupled only gravitationally second that the cannibal species is always dominant i'll come back and if time permits talk about relaxing those but uh before we do that uh let's take a look at what happens to other modes so here um this blue line shows a mode that does very similar things to what we talked about uh in the last slide uh it enters the horizon and gets stuck oscillating the gene's horizon and then escapes and grows this mode in red uh enters late enough that it never really sees the you know sound speed part it just it enters the horizon and it grows and that uh is something you can see over here it enters the horizon gets a kick and it starts growing uh linearly because as far as this mode is concerned this isn't really matter dominated with no funny business so the mode that gets the most growth in this theory is therefore the mode that enters the horizon early enough to get the longest period of growth you know it sees the most amount of deviation from the radiation dominated cosmology but doesn't enter the sound horizon at any point because oscillation suppress growth so that's this uh black mode here you can see here the cannibal uh enters the horizon starts to grow it sees a little bit of impact from the uh pressure but never enough to actually make it oscillate and then it grows this mode experiences the maximum amount of growth modes that enter later don't get as much enhancement because they didn't have enough time modes that enter earlier uh get trapped in the oscillatory phase before they have time to grow and so that ends up giving us a transfer function something again that encodes the different growth in this model uh compared to lambda cdm that has a characteristic early matter dominated era type rise and then a peak where both the location and the slope of this peak are set by the micro physics of the scalar field so the location of the peak again this corresponds to the physical mass of the micro halos that we expect in the late universe is directly related to the freeze out scale when the interactions froze out the amount of enhancement is related to uh how long the early matter dominated era following freeze out lasted so how long in between freeze out and the heating and you can make very nice simple estimates for those things in terms of the underlying Lagrangian parameters so uh in the interest of time I will skip I will only flash this and say I spent this much time talking about it because it's fairly robust it doesn't matter uh whether the dark matter has big interactions with the cannibal species or not you get essentially the same prediction for the things you can observe namely the location of the peak and the height of the peak um and I will skip this in the interest of time um of course you can't directly see transfer functions right what we see are you know micro halos and so in order to say anything about whether or not we can observe enhanced structure formation on small scales we have to have some way to go from the transfer function which is linear easily computable to micro halos which are non-linear not easily computable so the two most important things in this transfer function are the location of the peak because that will set for us a characteristic scale and the amplitude of the peak because that sets the characteristic formation time the more growth you have the faster you will reach the collapse threshold and the earlier you will form gravitationally bound structures that matters because the earlier you form the denser you are and the denser you are the easier it is to A survive and B give potentially measurable impact on observables today but to connect so it's not too hard to model these are primordial population of micro halos that form out of a given transfer function uh but connecting the first forming micro halos to the micro halos that survive in our low red shift universe where we can make observations requires detailed modeling um and uh to go further I'm going to have to make a bunch of sort of spherical cow assumptions to make some estimates uh and you should understand that I have to say uh with that caveat so these statements I'm making are based on sort of a stick stick figure uh idea of what the low redshift universe uh micro halo population looks like to make these estimates uh I am using a standard uh semi-analytic model for how to get uh micro halos out of a linear uh matter power spectrum known as the extended press-sector formalism uh it works uh very well uh on large scales where it's been tested it has not really been validated on small scales uh the the sort of micro halo scales that I'm talking about but uh this is what we can do so we're going to do it the first question you might ask is okay fine you're talking about all these um modifications to the matter power spectrum on extremely small scales and that's all fine and good but did they survive in galaxies there's a lot going on on galaxies a lot of stuff around that you know is important on scales remember that we're talking about things that are smaller than an earth mass scale stellar encounters can rip these things apart so we think that probably these micro halos survive in galaxies in the sense that uh an order one fraction of these things are likely to survive uh even after all of the effects of you know stellar stripping um merger uh into big halos and so on however the surviving fragments are likely to be tidally stripped so the dense inner core survives but the uh less tightly bound outer skirt so the halo will be stripped away and probably in the dense galactic bulge environments at the center of big galaxies like the milky way probably there are too many stellar encounters and most of these things are likely to be destroyed so the early formation redshift is really critical in making these statements we find uh we need the redshift of collapse to be bigger than about 250 to survive in the milky way it's an estimate from from this work um this is backed up by studies uh numerically in this uh sort of particle dark matter early matter dominated context by delos and people have done similar estimates for axion mini clusters which are uh very similar objects these are objects that are born around uh born at early redshift with order one density contrast and so they have very similar uh properties in terms of these gravitational questions this plot is from work by uh these people on axion mini clusters um and the scenario of interest for us is this um uh dashed line that is green that's the way to map their model into these uh mini clusters and they're showing the survival probabilities a function of uh distance from the center of the milky way so we are here and so you know their estimates uh give uh you know order one uh surviving fraction but you see it drops off as you go into this galaxy the other question is sure but how are you ever going to see these and here my answer is we can probably expect to see some of these things but it's futuristic there are a couple different uh things that people have used to get a handle on uh this sort of you know extremely small scale structure there's a uh a lot of work by uh captain zurek and collaborators on signals these things can make in pulsar timing arrays uh there's a lot of work by adria and air check and collaborators on uh the gamma ray signal that you expect when dark matter has an interesting uh annihilation cross-section to annihilate into stuff that ultimately makes standard model photons um and then something that uh i've worked on with uh my colleagues uh has been signals of uh lensing uh of an of one star by an entire galaxy cluster this is based on the work uh by other people in the context of um axion mini clusters which again have a lot of similar properties to these early form micro halos so this idea is that if you have a single star that is being lensed by an entire galaxy cluster in the absence of you know lumpy micro structure you expect a uh signal like a light curve this is in the time domain um the star will brighten uh as it crosses uh plastics and then drop off the signal of lumpy micro structure is jitter uh because uh you're sensitive to variations in the local surface density on you know scales that are the right length scales to probe these kinds of micro structures so we make an estimate in terms of the size of these halos relative to the sun mass so again we're talking about for early matter domination uh you know sub earth mass that's roughly here uh and then you're also sensitive to how dense these things are earlier forming things are denser um so the uh so my collaborators uh based this uh sensitivity on uh couple observations of a couple stars that have undergone such lensing events and used for those characteristic uh scales in making this estimate the width of these bands corresponds to what fraction of dark matter is bound up in uh these micro halos varying from 0.3 to 2.1 um so the the in order to say what kinds of halos we expect to see um we have to know you know where the peak is you know how much enhancement you have and then also you might wonder well how much does it matter you know the shape of the peak so we uh looked at that you can see that varying the the rise gives you the shallower the rise the longer a tail at larger masses the varying of the peak fall slope um tells you you know how much stuff you get on very small scales so very sharp cutoffs like exponential genes like cutoffs give you this but cannibal like cutoffs here give you a bigger plateau and so on and so if you take one of these things and you run it through a you know semi-atlantic machine to get the uh distribution of micro halos um your one sigma density fluctuations give you a curve like this for this particular parameter point this is a relatively low reheating temperature parameter point and two sigma fluctuations give you something bigger so the important thing basically these are rarer density fluctuations therefore you get more um the a form earlier these dash lines are telling you about the redshift of collapse again the earlier you collapse the denser you are so the more interesting your signals you have in any given random density field uh some fluctuations that are rare and will collapse earlier on bigger scales which is why the rarer fluctuations give you a bigger uh signal one sigma the sort of the the things you normally expect and they land here so this kind of scenario is potentially very interesting for uh getting some handle on whether or not we have a fine grained structure in the in the uh dark matter distribution um here's a situation that gives you even more structure on small scales which is related to uh things that I sketch for time it can go back and fill in uh if there are questions so the pulsar time of erase story is somewhat more mature than this caustic microlensing uh study and so whether or not these preliminary estimates end up being representative of the ultimate realistic capability is still an open question but uh we think this is a very promising potential method to discuss to discover uh microstructure in uh dark matter distributions which would then say something interesting about the uh you know potential evolution history of our universe before bbm although the ultimate sensitivity of this uh at very small scales is limited by the requirement that uh the jitters in a smaller scale uh you go the smaller and more compact structures are so the you know faster a star will go through them and therefore they get uh you know unresolvable and there's a finite resolution in these time domain signals here all right so let me flash the summary. Relic dark thermal bats can easily come to dominate the expansion of the universe before big bang of the asynthesis you get uh early uh departures from radiation domination that can potentially give you an handle on ways to look for dark matter that is born out of uh stuff that never talked to the standard model in an interesting way otherwise almost inaccessible to experiment. I've had fun playing around with uh really cannibal dominated eras where uh you can really map very precisely the properties of the linear matter power spectrum to the parameters of the scalar field that is dominating the early universe so uh you can identify the mass the self-interaction strength and the reheating temperature and map those to the key scales that control the astrophysics and then using these uh input you know small scale structure models you can talk about uh you're trying to detect the resulting enhanced structure on small scales in the late redshift universe today a variety of observational prospects pulsar timing cluster caustic microlensing and annihilation into gamma rays um this is the easiest but it requires uh non-trivial uh assumptions about what the particle physics can be these are gravitational and therefore don't rely on uh particular you know particle properties of what the dark matter is you know doing whether or not it was a you know thermal wimp in the hidden sector or not um but observational prospects for gravitational observables are still somewhat futuristic but they're interesting enough to merit further work and there is a lot of further work that needs to be done in really solidifying the uh description of the late universe signals that follows from given early universe physics but this is a very interesting uh and promising avenue for uh pursuing the interface between particle physics and early universe cosmology and the ultimate hope is that we will get a new way to understand the evolution history of our universe uh in the mysterious uh effect in between inflation and big bang physics thank you very much for your attention i will stop here thank you very much hey jessie for this very nice talk a round of virtual applause for jessie and and now we are open for questions nicolas hello can you hear me yes thank you jessie very very nice talk um i have a question i think it was one of your first plot you showed a ratio of the temperatures and you have the this uh increase and then a big cutoff i think was the ratio of standard mode temperature in the case we have this non-standard cosmology compared to the case with uh exactly that one good yeah or no i think was next plot or previous yeah that one yeah good not temperature not temperature transfer function so relative change okay okay i was looking we don't have enough letters okay thanks all right any further question from here i i have a oh okay go ahead gillian hello can you hear me yes it's nice talk by the way um i have a couple of questions one is what is the initial conditions you assume is this good good adiabatic initial conditions um that is an excellent question that is important um so the secretly what i have in mind is this scenario where i've got single field inflation that gives rise to both the radiation as well as all the hidden sector stuff that guarantees everything has you know boring adiabatic initial conditions because there's just one field that sources all the uh energy density but you could easily imagine that there could be you know relative iso curvature um between you know the radiation and the hidden sector um that's also interesting and this is not something that we've studied uh completely but you can show that iso curvature modes don't grow as much sub-horizon as adiabatic modes and therefore typically um the most interesting scenarios from the point of view of observability uh in gravitational observables from this clumpy distributions are from uh the adiabatic the simple adiabatic scenario but it's a very interesting question um and it is worth um exploring further you know what happens when there's relative iso curvature yeah that was my interest too but so with with the iso curvature you could have larger um initial power spectra right so you could have a larger amplitude and you so you could produce more later yeah you can um and in some cases that can offset the um that can compensate for the fact that sub-horizon they don't tend to get as much gross um right so that is something that we looked at in uh this paper although we considered only you know pure iso curvature pure adiabatic we didn't consider cases where uh where there's a mix and also for the adiabatic case i guess you extrapolate the blank results that's right yeah that's right we assumed a um we assumed that there was a underlying uh you know scale you know nearly scale invariant spectrum all the way up to these unproved scales and then um so in the case of um you know early matter dominated cosmologies you know all the interesting stuff happens sort of as a consequence of sub-horizontal growth um and so yes you know assuming that you start out you know perturbations of order one part into the five is you know that's not a tested assumption that's absolutely true bigger uh initial density contrast of course give you interesting stuff sooner um but then the story gets complicated yeah um we also considered in this paper which i didn't really have time to get into um other scenarios where dark matter is sort of born within with a peak in the power spectrum uh as a function of how it's produced usually by inflationary uh you know um origin um those are then iso curvature scenarios um but that's probably something we should discuss last night yeah no it's a very interesting question um i have another one if i can ask i'm curious about this uh how you use the pulsar timing arrays uh oh good yeah so so i should say this is this is not my work these are the experts um uh the idea here is that um you have your pulsar timing array and you're looking for again time domain signals so you're sensitive to um you're a couple different regimes there's a stochastic regime and then there's a single halo regime so let's start with a single halo so the idea is you have your pulsar and you have the earth and you have a micro halo that goes in between and that will give you a blip um and then depending on how concentrated and how massive your halo is you may or may not be able to see the blip um usually uh for you know relatively small things the stochastic signal you get from a bunch of these blips is more interesting than the signal from any individual blip um like so this is different from these pulsar timing arrays to they take gravitational waves for example right that's right that's right this is a different use so um this is a very nice set of papers that is more um experimentally mature than this uh proposal here these are um looking for um micro halos in our Milky Way because that's where the pulsar timing array is located which means we're talking about necessarily things that are um survived the dense busy Milky Way environment um cluster caustic microlensing is sensitive to the dark matter distribution in a galaxy clusters these are usually like in the cluster itself as opposed to any individual galaxy and therefore you get potentially things that are less highly stripped um but there has been nowhere near as much you know detailed study of systematics in uh this observable compared to these observables however you see very nice projections for these um one of the questions uh for how well these projections will actually be realized ultimately comes down to how many pulsars will we see for how long and with what control um and you can make both optimistic and pessimistic assumptions about that and get a range of possibilities but the most optimistic possibilities which look you know very attractive and the point of view of what you can see are futuristic in the sense they require a lot of pulsars for a long time thank you any questions from you know I have a very naive question uh I mean whenever I see peaks that uh that that you generate in in perturbations early in the universe I always remember the formation of primordial black holes yeah so I guess I will hear like a very different scale for k modes or this is restricted by this bound that you that we mentioned from bbn that uh that uh on the rehealing temperature so that you have a very low very low mass so basically is there a region in the parameter space for this for example cannibal model where you can actually grow so fast or doing that so that you yeah for for the same reason that um you know standard dark matter uh planet clusters doesn't you know easily form black holes um so in the case of uh cannibal models right we start out with a fairly featureless spectrum so everything has to form through sub-horizon evolution um which means um you know usually when you collapse and form a gravitationally bound structure um you know same reason that dark matter halos are elliptical uh rather than discs right you have too much angular momentum it's hard to shed um same thing here uh just on smaller scales um so uh since we're starting from you know very small density contrast in in the cannibal models and getting all this enhancement from sub-horizon growth you don't really expect a change in your black hole formation compared to standard cosmology right and then a simple a simple question in these cannibal models so the assumption is that these number changing uh interactions they are or these processes that like five to two or or sometimes four to two they are the dominant processes in the so there is no there is no like a significant coupling for example between the cannibals and dark matter so that they do two processes or yeah yeah good good so yeah so we've assumed for simplicity that dark matter is already frozen out um so that was mostly an assumption that we did for you know to keep things simple because we didn't want to you know do all this conflict all this expensive numerical integration and then let you know the um number of relative degrees of freedom change throughout this process um so just for simplicity we said local have dark matter freeze out you know early enough that we don't need to deal with the very ng star but that's really the only effect that's important here um if you're talking about dark matter you know annihilating with the uh of the cannibal species um if I wanted to use this so so there are two to two interactions between the cannibal particles that help you make sure that the cannibals stay in kinetic equilibrium even when they're not in thermal equilibrium and we we checked to make sure that the loss of internal kinetic equilibrium isn't important for setting the you know the the cut off so it really is the the cannibal self interactions that set the cut off um so if you want to take this you know simplify to the fourth model and really promote it to a uh cosmological history of what happens with say glueballs then in addition to the you know one cannibal species uh which is like the the lightest glueball you also have like a bunch of other glueball species uh with similar masses and so they will often have these kind of cannibal interactions too but they have you know you have a bunch of them they'll have masses that are like multiples of the climate scale and they have different cp properties and some of them will freeze out and some of them will and so that cosmology starts getting a bit more complicated but sort of fundamentally the things that are really important are um for understanding the growth of structure this the gene's length and uh how that and then the the ultimate amount of uh energy density because that controls how long this goes on and then when they decay thank you very much any questions before we say bye to the audience yes Roberto yes I have a question for for Jesse first of all very nice the the webinar is very very interesting so I was wondering uh the the basic question for me I mean is is it compatible the cannibal mechanism with because as I far understood in many work when your dark matter is already frozen out kind of just the product you show but is it possible to embed it or have you explored this scenario in which you have for instance a warm dark matter or a free scene dark matter kind of because the the the coupling are so different in those scenarios that I don't know if the yeah it could be embedded also the the same mechanism yeah for sure um so um this might help answer this question so this is again from from from the same paper we were mostly interesting in understanding what happens to dark matter density perturbations and not thinking so much about the model building but if you can see this line here these lines are telling you what part of this parameter space this is the cannibal mass and the reheating temperature what part of this is actually even compatible with having uh wind dark matter at all so there are parts of this parameter space where basically uh you get so much um energy injection or sorry entropy uh injection when the cannibal decays you dilute the dark matter abundance so much that you would have to have you couplings you can't deal with in order to get like wind dark matter and so yeah they're definitely parts of this parameter space you can for cannibals where they're not consistent with any sort of you know hidden sector wind at all and so you'd have to have some other kind of model to get dark matter out there um so our analysis applies without modifications as long as that relic abundance is in place sort of at the beginning of the evolution my guess is a lot of other scenarios will give you a fairly qualitatively similar uh evolution um but with some you know more complicated like the varying g-star you know and so on um if you have some other mechanism but yeah i haven't thought too much about the details so there could be fun stuff hiding in there yeah sorry color code correspond to what oh good um uh how much enhancement you get the the amplitude of the peak something i didn't have time to get into is this region here we stopped color coding this for more than a factor of 10 to the 4 because at that point um you collapse during the early matter dominated era itself but then those pillows are mostly destroyed after reheating and so you get signals in this band but not in not in here and here you have to look for other ways to get at these signals excellent thank you very much uh for for your presence today to all of you who watched on youtube and uh thank you very much jessie for for this amazing talk it was great to have you to all of you to all of you who who watched the video uh remember that uh we have an upcoming webinar uh two weeks from today on december 8 camilo posada will be giving the webinar number 125 please join us and follow us through the social networks and be and stay tuned for a upcoming announcement and have a great day or night for everyone okay and roberto yeah i forgot the day