 Okay, we are live now. So hello everyone and welcome to our Latin American webinars on physics. So today we are super happy to have Tommy Tenkanen. Tommy is a postdoc at John Hopkins University and today he will talk about Spectator Dark Matter. So are you there, Tommy? I am, yes. And thanks a lot for the invitation, it's really a pleasure. Tell me when you want me to start. So yes, if you want you can share your slides and get started. All right, can you see my screen? Yes. All right. And the slides, everyone can see them? Yep. All right. So yeah, indeed the title of my talk today is Spectator Dark Matter. The talk is going to be based on a recent article that we put out together with Arthur Rajantia and Tommy Markonen who work in Imperial College London. And it's going to be about an entirely different way to produce the dark matter abundance we observe in the universe. As an appetizer, let me make four claims about what dark matter can be. First of all, I claim that dark matter can be entirely decoupled from the rest of matter. It can be produced during inflation. It can be entirely of isocurvature nature and still very natural. Don't worry if you don't know what isocurvature perturbations mean. It will become clear in due course. Already at this point, I can say that there are very stringent constraints on so-called dark matter isocurvature perturbations that have been obtained from precise measurements of the cosmic microwave background radiation. And despite them being very stringent, they can be avoided in a very natural way in a model that I'm going to present in this talk. However, having made these four claims, the question then obviously is how? How is that possible that dark matter could be of these four things simultaneously? So that's about the appetizer. Let's talk about dark matter genesis. How the dark matter number density that we observe in the universe, how was produced in the first place? What is required to fulfill these four criteria that I presented? The model that I'm going to discuss in this talk is a very, very simple one. Let's assume the following Lagrangian for dark matter so that dark matter field here denoted by Kei has a canonical kinetic term, quadratic mass term, and a quadratic self-interaction term. No couplings with the rest of matter whatsoever. So that's one of the assumptions. And furthermore, when it comes to cosmology, when it comes to cosmological history, let's assume it to be entirely standard. So that first, there was cosmic inflation. At some point it ended. There was reheating. The universe became radiation dominated right away. And from that point onwards, it continued to be so until the time where the universe was roughly 50,000 years old and the universe became matter dominated. So entirely standard cosmology, when it comes to dark matter production and everything else. When it comes to cosmic inflation, let us assume that this field Kei, which is to play the role of dark matter, was energetically sub-dominant during inflation so that it is not the field that drives inflation, not the inflectant field, but a so-called spectator field that sort of just hanged around during inflation that was energetically sub-dominant, but yet, if it was light, it acquired fluctuations. That is, by lightness, I mean that its effective mass was small compared to the Hubble scale during inflation. The effective mass is just the second derivative of the potential and assuming that the quartic term in the potential dominates inflation, that the fluctuations were so large, then the condition for lightness is that lambda Kei squared during inflation was smaller than Hubble squared. If that was satisfied, then even this field that didn't take part in driving inflation acquired fluctuations. And those fluctuations are the very source of dark matter density that we observe in the universe. So how that works in more detail is that all light fields of this sort can be this field Kei or other light fields that do not take part in driving inflation, for instance the standard model Higgs field could have been a so-called spectator field, which instead of lying at the minimum of its potential acquired fluctuations. And these fluctuations were typically very large. You can think of these fields as marbles in a bowl, but instead of just lying there at the minimum, they acquire fluctuations because they are, if you will, quantum marbles. They all the time acquire small fluctuations. And as a result, we end up having patches in the universe where the field has a value that varies from patch to patch. And the question is that how large were these fluctuations? What is the distribution of field values that we have at the end of inflation due to these fluctuations that all light fields gained during inflation? And that fluctuation spectrum, the distribution of field values, can be computed by using the so-called stochastic approach or the so-called Starobinsky-Jokojama approach named obviously according to its inventors, Starobinsky and Jokojama, who put a paper out on this in mid-90s. What they did in that paper is that they split a light scalar field into sub- and super-horizon parts. So that, for instance, this field chi, which in general is both position and time dependent, is split into a coarse-grained super-horizon part here denoted by chi-bar and a sub-horizon part, which is essentially a usual quantum field in Minkowski space so that it can be written in terms of mode functions and usual annihilation and creation operators. And by doing that, one can track the motion of the super-horizon part, chi-bar, and in particular the distribution function that describes the super-horizon values. It can be shown, as Starobinsky and Jokojama did in that paper, that the distribution of super-horizon field values follows the Fokker-Planck equation, which takes the following form. P here is the distribution, which shows how the field chi evolves in time at super-horizon scales. What kind of distribution of field values we have at the end of inflation? That can be solved from this Fokker-Planck equation where essentially the time derivative of the distribution function is proportional to some chi-dependent operator, which is a little unspecified here, but which can be found in the literature. And if inflation lasted long enough, this equation has an equilibrium solution for the distribution function at some point, regardless of where, at which value the field started at the beginning of inflation or long, long time ago towards the beginning of inflation. Regardless of that original field value, the distribution function that describes field values in different patches takes an equilibrium form. And that means that from that equilibrium form for the distribution function, we can compute, for instance, the typical size of fluctuations of light scalar fields due to their random motion, random walk during inflation. And that equilibrium solution for the distribution of super horizon field values takes the following form. And here is just a normalization factor which guarantees total probability of unity when integrated over all field values. And seen in this equation, the distribution depends on two different things. On the potential of the field chi in which it was gaining fluctuations and on capital H here, which is the Hubble scale during inflation. Its step, its fluctuation typically is of the order H, so it has to enter to the solution for the distribution function and V of chi, the potential of the field, characterizes that in what kind of potential the field was acquiring fluctuations. What kind of restrictions there were for it, for these fluctuations, I mean. And from this distribution function, one can compute, for instance, the typical displacement of a field, which in the case of quadratic potential takes the following form, the typical displacement being the variance of that distribution of field values is proportional to the Hubble scale and to the parameter that characterizes the steepness of the potential in which the field was gaining fluctuations, that is, in this case, the self-interaction couple. And that means that at the end of inflation, there indeed were very large, not only there were very large fluctuations, but in each given patch in the universe. And that, for instance, today constitutes our observable universe. The field was displaced from its vacuum. And that means that there was, at the end of inflation, a non-zero condensate of this chi-field, which is to become what we observe as dark matter. And the field had energy density, which initially took this form where the energy density rho of chi at the end of inflation was proportional to the potential of the field, where the potential is obviously, the energy density characterized by that potential is proportional to the displacement of the field. And note that this is a position dependent quantity, meaning that we have these different patches in the universe where the field takes a different value and hence it has a different energy density in different patches. However, typically that energy density indeed is very large and indeed it turns out that it can constitute all dark matter we see today. What happened after inflation, the field started to oscillate with a decreasing amplitude in each given patch so that the oscillations first took place in effective aquatic potential so that the energy density of the field at first was scaling down proportional to the scale factor to the power of minus four. Effectively, the field at that point constituted radiation in cosmological sense, but afterwards, when the field had relaxed towards its minimum and started observing the quadratic part of its potential, recall that we also assumed a mass term for the field and when that happened, when the quadratic term became larger than the quadratic term due to the relaxation of the amplitude of oscillations, the field started acting effectively as cold dark matter. Its energy density can be shown to have scaled down proportional to a to minus three from the point onwards when it started observing the vicinity of the minimum of its potential where the quadratic mass term dominates. And the final abundance of dark matter then can be shown to be given by the expression that you can see on the screen right now. It depends on three parameters lambda and m that characterize the potential of the field in which it first acquired fluctuations and then later on where it's oscillated and age here the Hubble scale during inflation characterizes the typical size of displacement together with lambda, of course. That's why the weird potential for lambda. However, that is only true if the field did not fragment due to its oscillations. The field can fragment much in the same way as the inflectant field fragments into particles at the end of inflation during reheating also here with this type of spectator fields the fields do their oscillations about the minimum of their potential they can fragment into particles in this case we assumed that there are no other particles that there are no couplings to other particles however the oscillations may not have remained coherent and the field may have decayed into particles of the same field of the chi-field and these particles may have then thermalized among each other so instead of having a coherent scale a condensate that oscillates and constitutes dark matter today it may so have happened that there was a condensate at first but that fragmented into chi-particles and these particles might have thermalized among each other before the eventual freeze out of chi-particles before the eventual freeze out even so called dark matter cannibalism may have been possible in the early universe dark matter cannibalism refers to a situation where dark matter particles annihilate themselves where they are eating up their own number density due to these number changing processes which in our theory here can happen by this 4 to 2 number changing interactions when the dark matter particles were in thermal equilibrium they have maintained these processes for some time in the early universe diluting the dark matter number density and affecting that what size the energy density of that dark matter component today is in our paper on this we took all these possibilities into account and found that obviously in all cases the final dark matter abundance is proportional is some function of these 3 parameters that characterize the model lambda the self interaction term of the chi-field the Hubble scale during inflation and mass term for the field alright so far so good it can be shown that this is how one can generate dark matter number density all of dark matter that we observe in the universe due to this random walk of scalar fields during inflation this is in some sense gravitational production of dark matter because the field I mean it's a phenomenon that connects gravity to quantum field theory the initial energy density in the field is generated because of behavior of quantum fields in the cedar space but what about dark matter perturbations then it was noted that the dark matter energy density is position dependent in each patch after the end of inflation at the end of inflation the field had slightly different energy density depending on what was the field value in the patch at the end of inflation and that means that there are perturbations in dark matter energy density and a big and very important question is do these perturbations in dark matter energy density overlap with those in radiation that is are the dark matter perturbations adiabatic or iso-curvature perturbations what is meant by iso-curvature perturbations it's really the simplest thing in this case because iso-curvature between dark matter and radiation can be defined to be the difference between density contrast of dark matter and density contrast of radiation weighted by some equation of state dependent factors which imposes this 3 over 4 pre-factor for radiation density contrast and this quantity what it physically tells is that it describes how much the dark matter perturbations differ from those in radiation there's no a priori reason in this case to assume that perturbations in dark matter energy density would overlap at all with perturbations in radiation energy density and that is because the perturbations in radiation energy density were sourced by the inflatum field by its fluctuations whereas this field chi which is never thermalised in this model with radiation it acquired its own perturbations during inflation and perturbations in this chi field are completely uncorrelated with perturbations in the infatum field and hence because both of these fluids dark matter at a later stage and radiation inherit the perturbation spectrum from these two fields there's no reason to assume that there wouldn't be iso-curvature the reason that I'm talking about this is that there's there are very stringent constraints on the amount of iso-curvature perturbations however before discussing them in more detail let me say that an important quantity in cosmology is the power spectrum of perturbations and in the case of dark matter iso-curvature perturbations the corresponding power spectrum can be shown to take the following form it is essentially of power law form with an amplitude of the order 10 to minus 11 and spectral tilt of the order 1.5 times square root of lambda square root of lambda enters here because it characterises the steepness of the potential in which the field was gaining fluctuations what this power spectrum tells is essentially how large where typical fluctuations typical perturbations at a given furry mode at a given physical scale corresponding to that furry mode k here is a furry mode whereas k star is a pivot scale in the case of cmb observations 0.05 inverse megaparsecs and indeed the reason I'm talking about this whole thing is that cmb the cosmic microwave background radiation and fluctuations in it would look very different if these iso-curvature perturbations would be very large what we see here is the usual plot of cmb perturbations essentially temperature fluctuations as a function of angular size on the sky the observed peak structure of cmb would look very different if there were large iso-curvature perturbations that is all these peaks would be enhanced and shifted from the observed positions if there were large iso-curvature large dark matter iso-curvature perturbations so from that one can conclude that the perturbations at least on the largest observable scales where measurements of the cmb can be made the iso-curvature perturbations must be small that is perturbation spectrum of dark matter must be close to the perturbation spectrum of radiation and that imposes constraints on the model that I have been discussing here on all these type of scenarios that gain fluctuations during inflation but which is never thermalized with radiation after inflation and the constraint the most important constraint that can be placed from the non-observation of dark matter iso-curvature perturbations in the cmb is that the power spectrum for dark matter iso-curvature perturbations at the Planck-Pivots scale is smaller than 4% times the curvature perturbation power spectrum at that scale and that imposes a constraint given that Pz for curvature perturbation it has been measured and given that we know in this context what the power spectrum for dark matter iso-curvature perturbations is it imposes a constraint on lambda it is a lower limit on lambda on the steepness of the potential and in particular it can be shown that the model avoids all iso-curvature constraints if lambda takes a value which is larger than of the order 0.1 or which is of the order 0.1 to show you a plot about that in the model parameter space the allowed region is what is shown in green here mass what is self-interaction coupling parameter space different shades of green here show different production mechanisms accounting for thermalization and eventual cannibalism of dark matter particles however in all cases the very source for dark matter energy density is this production during inflation these quantum fluctuations of this chi-field during inflation the model parameter space is bound from the left by the non-observation of iso-curvature perturbations in the CMB and you can see that it imposes a lower bound on the self-interaction coupling which is of the order 0.4, 0.5 roughly speaking the green region is also bound from below by the non-observation of tensor modes in the CMB that is the tensor to scalar ratio has not been observed, there are only upper limits on that and that in the context of single field inflation imposes a constraint on the Hubble scale during inflation and because the abundance for dark matter in this context is proportional of function of Hubble scale during inflation we obtain constraints from the non-observation of tensor modes as well the green region is also bound from above and from the right by internal consistency above the green region the field was not light enough to acquire fluctuations during inflation and on the right hand side of the green region the self-interaction coupling is not perturbative anymore however one can see that there is indeed a big chunk of available parameter space in particular the mass range where this field can constitute its all dark matter goes from roughly 1 GeV to 10 to 8 GeV that's the values for lambda that make it possible for this field to constitute all dark matter range from roughly 0.4 to order 1 so far so good this field can constitute all dark matter that we observe and all cosmological constraints can be avoided what about testability of this model can it be tested in any way given that we have assumed that this field does not couple fields at all of course it's hopeless to assume that it could be produced at the LHC or observed by direct detection experiments however with cosmology and astrophysics interesting things can be learned about this type of dark matter because so far I have only discussed constraints on say the dark matter isocover to perturbations and tensor to scalar ratio constraining the Hubble parameter during inflation but let's say that either of these or in the best possible case both of them are actually detected if say this beta parameter shown in this plot that characterizes the amount that characterizes essentially the ratio of dark matter perturbation spectrum and curvature perturbation spectrum at the Planck pivot scale if it was observed to be of the order say 1% then in this model parameter space the observed dark matter abundance is satisfied the criterion for that is satisfied on that blue diagonal solid line if on top of that tensor to scalar ratio was measured to be of the order say 0.01 then that means that the abundance of dark matter is obtained on that dashed blue line and together these observations single out a point in the model parameter space so this is a very minimal model for dark matter and interesting things can be learned about it by making discoveries either in cosmology or astrophysics however there's also a way to falsify the simplest type simplest version of this model which is by detecting dark matter self-interaction cross-section divided by mass of dark matter particle currently there are constraints on it which are of the order 1 or 0.1 cm2 per grams coming from astrophysics in particular bullet cluster however if in any foreseeable future this dark matter self-interaction cross-section divided by dark matter particle mass was detected then that must mean that in this model one should lie on one of these dot dashed lines in the lower region of the blood and you can see that it's not in the Korean region at all so simultaneously in this model one cannot explain observation of dark matter self-interactions of any sizable size that can be measured in any foreseeable future and the dark matter can that one cannot account for dark matter number density simultaneously however the model indeed is testable and falsifiable in that sense that then brings me to my conclusions as shown in this talk dark matter may have been produced during inflation by amplification of fluctuations of quantum fields the model can avoid all cosmological constraints and there is more to follow we are now working on this together with Artur Rajanthi and Tomi Markanen in Imperial College London and with Steve and Stofira in University College London so stay tuned that's basically all I wanted to say thank you very much thank you very much Tomi for this nice talk and for the super fancy slides are there questions from the audience I can start at the very end Tomi you say that you want Dharma to be completely coupled from standard model in particular you didn't add Higgs portal copy that's right however when you were talking about the dark matter content say decay you said that this dark matter content into radiation right yes but not radiation that is constituted by standard model fields like in the simplest possible case where the Higgs portal coupling is set to zero there's obviously no standard model particle production originating from oscillations of this chi-field but the chi-field can nevertheless fragment into chi-particles so that instead of having this field that oscillates you relax the field into its minimum but produce a bunch of chi-particles it's much in the same way as in the context of standard model Higgs when it's oscillating off the inflation if it had quite a large fluctuation spectrum during inflation then there's a Higgs condensate it oscillates about its minimum and produces all kinds of standard model particles including Higgs particles okay I think I see are there more questions I've had one but I okay so what is the difference with this because I remember this paper in quintessentially inflation these pebbles and ratra or pebbles and bilenki I don't remember now in which they were doing exactly the same thing so only that matter was quintessentially inflation but I think the analysis of the idea was roughly the same so what is different from that right so you are right with that ratra or bilenki I don't remember but these pebbles for sure yeah that's right they have many papers on topics that touch this issue pebbles and bilenki have a paper I think it's called non-interacting dark matter and in that paper they really presented the foundation for this they they showed what the fluctuation spectrum is here we have improved the analysis accounting for all these different new constraints on dark matter is a curvature on tensor to scalar ratio and so on and so forth but also we accounted for the fact that the field can fragment that is something that pebbles and bilenki didn't discuss but the model is roughly the same apart from the constraints it is that's correct great are there more questions are you from the youtube chat I don't see any I still have another question so you're talking about dark matter evolution you say that first it scales like radiation like A-4 and then like dust but we just want to know when this transition happens I mean why do you have this change of behavior sorry can you say that last part again why do you have this change of behavior A-4 and then A-3 what's basically happening there so it is just you see at the beginning of the inflation right after inflation the field has a very large value so when it starts oscillating the potential is very well approximated by the quartic term of the potential only but of course the mass term is very big but let's assume that it's fairly small and the fluctuations were large in a given patch where the field started oscillating however the amplitude of oscillations essentially the field value is decreasing all the time due to the expansion of the universe and at some point the amplitude of oscillations has has decreased enough so that you cannot neglect the mass term of the potential anymore and the fields the field starts seeing the potential which is first a sum of these two terms quartic and quartic term and then when the amplitude of oscillations has decreased even more then the potential becomes well approximated by the quartic mass term only so that is what happens so effectively you have this transition from radiation like behavior to metal-like behavior okay, I see, thanks any more questions? I have a question for Tommy Tommy, very nice to talk but I was wondering if there is any possibility to connect your spectator dark matter with dark energy some feedback between the two sectors um maybe that's all I can say really can you elaborate on that that's what you had in mind? No, just by curiosity since inflation is one of the mechanisms and there are some models that try to connect dark matter and dark energy via the same inflationary process so I thought maybe you were also thinking to to push in that direction in some sense right, we haven't really thought about that but the first thing that comes to my mind regarding your question is that while it might not be feasible in this model where you have only one field that gains fluctuations during inflation you can have multiple fields gaining fluctuations during inflation and all fields gain a perturbation spectrum of their own so it is conceivable I guess that one of those fields acquired a perturbation spectrum which has um elements that are required for that field to constitute dark energy at the labor stage how fine tuned those models maybe that I do not know about but with multiple fields I wouldn't be too surprised if you can achieve something in that direction as well okay thank you you're welcome okay thanks, I can see one question from the youtube chat so I think he saw that I was asking what is the question of state for the dark matter condensate and how does it evolve so equation of state parameter the pressure over energy density is essentially 1 over 3 at first can be shown that whenever there's a scalar field oscillating in an expanding universe in a quadratic potential the field behaves effectively like radiation so its equation of state parameter is one third and for a field that oscillates in quadratic potential it can be shown that its energy density is scaling down as that of cold dark matter so it's equation of state parameter vanishes okay thanks are there more questions for Tommy okay so just out of curiosity so in your model you completely neglect the possibility of having a Higgs portal model Higgs portal sorry but what happen if you switch on that coupling do you expect the phenomena to change a lot right so what does change obviously is that if the portal coupling is larger than roughly 10 to minus 7 then this field can thermalize can and eventually will thermalize with standard model particles and of course if that happens then you lose all information about the initial stage so the particles just thermalize with standard model radiation and then that is as if there was no condensate in the beginning whatsoever you lose all information about that however you are willing to introduce a coupling which is smaller than 10 to minus 7 then the dark matter particles do not thermalize with standard model particles and you do not lose all the information about the initial stage however via this Higgs portal standard model particles can decay and annihilate into standard into dark matter particles so it gives you an extra channel for dark matter particle production and more dark matter so that certainly changes the part of the parameter space or the combinations of different parameters that are required to give you the observed dark matter number density in this model so those things change okay I see thanks any further questions for Tommy okay maybe have a very last one show the very beginning in your I think one of your second slide when you were talking about the appetizer so you say that the model was natural or I don't remember exactly what exactly you say but you mentioned I think natural the model was natural so play this what were you thinking about like hierarchy problem or something like this or what what do you have in mind of course natural is not very well defined term so indeed it was just an appetizer but what is really meant by that is that you don't need you don't need to fine tune the parameters within the dark matter sector all too much I mean there's a wide range for for masses where the field can constitute all dark matter and its energy density can constitute all of its all of the observed dark matter and the value for lambda that you need is of the order point one but of course we did assume that the field is not coupled with the standard model so I mean if you want to define naturalness from that point of view then of course that conclusion may change but that was just what I meant by that okay I see thanks a lot thank you I don't see more questions so let's thank Tommy again thank you very much for this super nice talk and I hope to see you guys in two week time for the next webinar on high energy physics okay thank you thank you bye bye