 Okay, thank you for your life, everyone and welcome to this Latin American series of webinars. So today we have Vasavendu Barma talking about dissecting the dark sector with gravity and so we are super happy to have you here Vasavendu. So Vasavendu finishes PhD at the ITT Guarati and then he has a couple of postdoc appointments, one in this super group in Colombia University of Latin America and then he moved to Warsaw and very recently I think a couple of days ago maybe last week he joined the SRM University in India, right? So now he's a young professor there. So thank you very much Vasavendu for accepting this invitation. So please you can go ahead. Good great, so let me first share the screen, please try to, can you see my screen? Yes. Okay, so yes of course, first of all, many thanks to the organizers for giving me this opportunity for the invitation and it's good to see all the familiar faces all the virtually. So as Nicholas has already introduced that I'm going to talk about something like dissecting the dark with gravity, it's like how one can study physics beyond the standard model utilizing gravity as one of the tools. So this talk is based on a couple of papers which are shown over here which I have worked with different collaborations over last one year or so. So before I really you know plunged into all the details of the models and calculations and show you the plot etc, let me start with a very brief problem just to you know build the framework of whatever I'm going to talk about. So this first few slides will be very very pedagogical, very well known for almost all of us. So this will be a lightning review of whatever we have learned so far regarding a standard model and a bit of beyond the standard model. We know that why the standard model is nearly perfect but not absolutely perfect. And we will ask the question that what happens about dark matter or what happens with the matter anti-matter asymmetry. So these are the motivations of going beyond the standard model. Of course, there are many more motivations that's why I've kept the fourth you know point blank. But I will be talking about mostly about these two scenarios regarding a particle dark matter candidate and generation of matter anti-matter asymmetry. So let us begin. So as we know that this is a recent picture of the standard model of particle physics after the great discovery of the standard model like Higgs boson which perhaps is the only spin-zero boson that the nature offers. And this completes all of the standard model particle content. And we know that the standard model has been tested over and over in different experiments in different experimental facilities and it doesn't want to be robust. So this is a very nice model that can explain the nature to a great extent in a with an unbelievable precision of course that I must say. However, there are still some things that the standard model cannot really do and that's where the requirement of new physics comes in. So it still needs some window open to go beyond the standard model and seek for new fitted signal. And one of the many reasons is of course the explanation of the life neutrino masses as we know that the standard model neutrinos are massless because of the very structure of the standard model itself. But on the other hand we have oscillation experiments we have which have told us that neutrinos are not exactly massless but they have a very tiny bit of mass. So in order to explain this tiny neutrino mass one has to add more particle content with the standard model fields. And there are many ways to generate life neutrino masses as we know. So this is one of the reasons that people seek for for beyond the standard model signature. Another reason being the matter antimatter asymmetry. Again here comes experiments which have told us that there is more matter than antimatter in the universe and that's how the universe created. We do not know exactly when this happened but we do know that the standard model has all the necessary ingredients to explain this matter antimatter asymmetry just not in the adequate amount. So in order to explain the observed amount of matter antimatter asymmetry again one needs to go beyond the standard model. And finally this very crazy pie chart which tells us that only 4% of the universe is visible to us and 72% of course made out of some exotic thing called dark energy which is of course not my area of expertise that's why I'm not going to go over there. I would rather concentrate on this very small you know green region which tells the 24% of matter energy budget is it's made up of something called the dark matter. So these three will be our you know guiding principles for the next couple of minutes whatever we are going to talk about and we will try to explain the matter antimatter asymmetry together with dark matter and also we'll try to address the light new to the mass generation through some mechanism with the help of gravity I will tell you about it. But now let us try to wonder over the fact that how do we are confident about presence of dark matter. We know that there are plethora of experimental evidences which mainly come from gravity and astrophysics cosmology and astrophysics and of course the very earlier evidences are coming from what we know as the galaxy rotation curve which clearly shows that as we move away from the central bulge of the galaxy which is the most luminescent part and go towards the outskirt we see there's a deviation from the predicted nature from theory of the rotational velocity of the stars from what we observed and this tells us that well there are indeed some exotic matter which are non-luminescent maybe non-varyonic and these are playing the role in influencing the rotational curve or rotational velocity of the stars in the galaxy and that's why we see this deviation from what we expect. The next very solid evidence comes from what is known as the bullet cluster which is formed by the collision between the two galaxy clusters and this really tells us that the dark matter is non-interacting at least at the scale of the galaxy cluster and if you look at the picture that when the two galaxy clusters collide then the baryonic matter which is highly interacting is basically concentrated in the middle and that's create this shock or awake kind of a shape while all the masses which are contained with the dark matter are actually lying outside which one can find by napping the whole thing with the help of gravitational lens and at the fourth the most important evidence of the matter energy budget comes from the cosmic microwave background radiation which are nothing but the really photons that are coming to us from the very early universe maybe from the big band and one can measure actually that the very tiny amount of temperature and isotropy in this microwave background and this tells us that well indeed there is only like only the 4% of the universe is visible and 24% of the universe is made up of this exotic candidate which is called the dark matter. Now from all those evidences of course we do not know exactly what sort of particle if at all dark matter is but we are we are sure about some of its properties for example it does not coupled to photon or coupled to photon very very very very frequently that's why it's kind of dark of course it talks to the gravitational forces and that's why you see the rotation curves are deviating from from our expectation and since we can measure its relative density so it's still around today which makes it super stable at least at this at the at the at the lifetime of the universe. Now as a particle physicist we always try to explain what kind of particle nature the dark matter can be and we go back to what model we have already at hand which is the standard model and we try to see that if any particle within the standard model can can can be a good dark matter candidate and in order to do that the that candidate has to you know satisfy these three properties that I have listed below and we see that when the standard model neutrinos exactly have all those properties they're basically light they only have weak interaction and they're stable however there are there these particles are so light they they cannot make up all of the dark matter abundance that we see today and and there is a even more important drawback of having all the dark matter neutrinos which is the structure formation because neutrinos are typically known as for dark matter candidate so they have a very large free streaming length which means that they erase all the small scale structures so the large scale structures in the universe start forming earlier and then the small scale structure formulated and this is against our observation typically from the n-body simulation we know that all the small scale structures form first and then they qualifies through through gravitational interaction in the large scale structures form so in order to have the right structure formation and also the adequate amount of dark matter metallic density again one needs to add some one needs to have some cold dark matter candidate therefore one has to have some candidate beyond the standard now the question is that what sort of particle this dark matter can be the beyond the standard model particle and what can be its mass range well it can be anything between let's say a pin and an ellipsoid so it can be as light as 10 to the minus 22 ev given that it's it's kind of a boson it can be as large as 10 times the solar mass if it's a primordial black hole and anything in between these two scale can can be a good dark matter candidate as long as it has those two properties intact however if you look at this WIMP kind of a scenario this these these things are these particles have been you know stealing the show for for couple of last decades because of the fact that WIMPs give the hint of new physics around the weak scale due to the fact that the WIMPs produce the right amount of density through a weak scale cross section and that's sometimes called the WIMP miracle and that's that's made all of us excited because the weak scale is something that we always want to probe we always search for new physics around the weak scale however tremendous experimental efforts have been put you know in order to search for WIMPs but typically WIMPs are people have been looking for signature of this kind of weak literate massive particles through what is known as data detection experiment where you have some experimental facility having some inert nuclear sitting on the earth and the WIMP from the local hello of dark matter comes and you know collides with it and we measure the recoil velocity and that recoil recoil velocity to recoil energy that gives us the number of such events but no significant number of such recoil events have been have been found so far and that is why we do not have any evidences of of WIMP kind of dark matter in the nature also in the on the collider frontier we do not see any sort of missing energy excess at least in the in a in a in a significant level which can give a hint of new physics around the another weak scale or typically the weak so therefore it will happen looking for alternative dark matter production mechanism and many have been proposed one of which which I will be talking about mostly is called freezing and the difference between freeze WIMPs and and particles these are freezing these are called pimps is the fact that if you look at this this this plot in the in the in the left panel that this black graph shows how the relic abundance or the or the yield or rather the number density of of of a WIMP kind of a particle evolves over time so these particles are actually in equilibrium in the early universe at some point of time the interaction rate falls below the Hubble rate and then it saturates on the in the contrary this FIMP kind of particles are never in equilibrium so they are produced gradually from the visible sector through some interaction depending on what sort of model you build and and and at some point of time they freeze in and produce the observed relic abundance but because you have to you know assure that these particles never come in equilibrium so the freeze in or the FIMP kind of particles have very very people interaction with the visible sector and that makes them very challenging to detect of course not entirely impossible but one important fact is that since these particles are produced out of equilibrium they always carry a memory by memory I mean they they have an information of the background cosmology or or the error at which they are produced unlike the WIMPs because they are they you know equilibrate at very early stage so they lose the memory of their production mechanics this I will I will you know explain in a so now going ahead so as I was telling you that there is one more reason to look for physics field you know physics beyond the standard problem and that isn't being the the barium asymmetry and again the evidences comes from the tiny measurement of temperature and isotropy of cmv or the measurement of the light element abundance around the big bang with this emphasis on pbn and both gives you the same result that there is more matter than the antimatter and of course this cannot be an initial condition for for the universe to begin with because we know that there there was a time when the universe went through a phase one inflation which of course solves other puzzles that that that I'm not going to talk about but due to this first expansion whatever the whatever the asymmetry that you produce in the very beginning that we washed away so it must have been produced dynamically at some point of time and this dynamic generation of barium asymmetry needs to you know satisfy three conditions which are known as saccharic conditions which tells us the underlying the the model or the framework has to be you know barium number violating then which is understandable because they're producing more barium than the antimarion so this charge has to be violated it also has to be c and cb violating this is a bit subtle but it tells that well the whatever the rate of the process at which you produce the barion should not match with the rate of the process that produce the antimarion so that you know they cancel each other out and also what about the process that produces barium asymmetry should go out of equilibrium at some point of time because again otherwise it will just wash out if it equilibrates with the standard model path now again if we look at look back at at the model at our hand which is a standard model we know that the standard in point the barium number within the standard body is not it's an accidental symmetry and it is broken by the quantum correction the triangle diagrams so so barium number violating processes are there and this process is actually very efficient and very high end prediction but they exist within the standard model and also the weak interactions violates cb maximum and we know that how to measure it it's encoded with the ckm and we we have a measurement which which is typically known as the charge parking variant but it's too small it cannot provide the observed a signature of course and thirdly this out of equilibrium condition is actually satisfied during uh electric phase transition formation of the bubbles etc but given the the Higgs mass the the electric phase transition is is not of course not strongly burst order but rather it's a it's a crossover and therefore to have a very strong departure from equilibrium a or to have a new source of cp violation b we need to again go beyond the standard body and and need to add some more uh ingredient with the standard model so that we can explain this dynamically generation of adorn asymmetry and one of the elegant ways is called leptogenesis uh which produces lepton asymmetry in the leptonic sector and then shifts to the baryonic sector through some nonpartner method process and that can generate the observed baryon asymmetry but the goodness of this this this this kind of a process is that it also connects the neutrino mass with it so you can you know kill two bars with one stone you can of course explain the generation of adorn asymmetry but on top of that you can also explain how the value neutrino masses can be generated so with all this in our hand let us first try to understand that why we are talking about about all these things all this like discreetly connected things but but they have some underlying uh connection all together so my point here is that you have two numbers to satisfy one is the darker relic abundance which is 0.1 of course another number is the baryon asymmetry at present universe which is of the order of 10 to the minus 10 this can be done with of course with the help of particle physics and particle physics needs basically the uh the interaction which we provide by writing down the Lagrangian which contains uh the couplings and the masses and the particle contained etc and with that you can compute the the cross section which can give give rise to adequate amount of uh dark matter which we can find out for solving the Boltzmann equation that determines how the number density evolves uh with with time or as the universe expands and on other hand the same model you know with the help of the same model or with the help of some more exotic model you know of course explain the baryon asymmetry as I was telling you for for example ellipsoid analysis so particle physics can do both the job but on the other hand inevitably we have gravity because gravity you know has this democratic coupling with all sorts of uh matter particle which is suppressed by blank and that that's why we cannot really ignore its presence of course the standard model does not have has have it but we cannot really say that well it's it's we can totally ignore it so gravitational production is always there whether we want it or not it's always there because it has this uh uh coupling of of of blank suppressed coupling which is which which is uh one cannot ignore so gravity can produce of course the dark matter uh in adequate amount however it does not provide you a source of city violation so in order to have a city violation city violating process you need to you know rely on particle physics but both of the sectors are connected through cosmology because you always produce these particles in in a background in an expanding universe which is you know uh controlled by this Hubble the rate of expansion so what we're trying here is to bridge a gap between particle physics and gravity with cosmology such that we can explain these two long-standing puzzles called dark matter and baryon asymmetry at the same time or maybe different uh one at a time now coming to the observational aspect of it particle physics of course has many observational facilities for example the colliders there are detection experiments there are neutral experiments which not only search for neutrals but but can also search for uh very fibrilli components of states etc but on the gravity sector we have the the gravitational waves and thanks to LIGO we have already detected them and we know that uh the future gravitational wave experiments can be more and more sensitive and detecting even uh low low or high frequency gravitational waves that I will try to show you so my point here is that gravity and particle physics together with the help of cosmology can be a good probe or or or a good instrument to to explore physically under standard model that can that can explain dark matter and baryon asymmetry together this is uh I will try to show you how so now that I have set the stage uh now I will I will start the the discussion of how to explore the the the dark sector uh with the help of gravity and how can we observe uh all such uh you know uh models or at least predict or or put constraint on them so these three these four will be will be my my point of discussion first I will I will start with with a very simple model which utilizes a portal uh provided by by gravity that can help in explaining dark matter and baryon asymmetry that can also be constrained from primordial gravitational waves typically low frequency then I will also also discuss uh a typical scenario where one can have high frequency primordial gravitational wave coming from a different source and and and finally I will tell you how a non-minimal coupling with the gravity can help you to to dissolve these two to to uh uh dark matter and and baryon asymmetry questions uh at the same time and at the end I will I will cut so let us begin so let us first try to start with with a very simple model we of course have standard model which is intact we cannot fiddle around with that on top of standard model we add some singlets by singlets I mean uh singlets under the standard model get symmetry without disturbing the get symmetry at all and these singlets can be scalars and formulas typically we add one scalar and three right-handed neutrinos and and this one scalar will act as an inflator which will be responsible for the inflation of the universe and the end of the inflation will also you know reheat the universe and and these three formulas will be will be our our dark matter and and and the source of uh cb violating asymmetry and then of course once you do that and and if you expand this flat metric uh with a small perturbation if we will always have this uh dynamical field called the graviton and you end up with with this kind of a of a of a finite diagram where you see that all these exotic particles of course you can produce a standard model as well because everything is everything is connected to the through the same gravitational channel in the final state uh and this happened this can happen during uh by the you know annihilation of this of this phase which are typically the inflator but this in initial state one can also have the standard model as well so what I will try to show you that once you produce this right-handed neutrinos neutrinos can be stable and give rise to uh a good dark matter candidate but neutrinos can also decay through this through this trial linear coupling trial linear u kawa typically responsible for leptogenesis and this the further this can produce the better resolution so I will refer n one as the as the dark matter candidate which can or cannot be stable I will discuss both scenarios and with the other two neutrinos we can generate that selection and and and I choose this pi to you know oscillate in the potential which is typically known as the this hyperbolic potential the attractor potential and there is only one free parameter in the potential which is lambda which is not exactly free but can be constrained from same same observations requiring that it produces a you know right amount of e folds so that this can give rise to uh inflation uh so this is my setup so standard model with some significant fields uh in terms of scalars and and functions so now let's let's move on now once we have that if you remember this this k is basically the exponent of the of the field in the potential which goes like find the k so if you produce all the standard model particles let's say typically the heats through only gravitational gravitationally you know uh mediation of this of this graviton then you need k larger than nine such that you can heat the universe above the bbn temperature which means before the onset of the bbn bbn because you do not want to mess up the generation of the light element abundance however with the help of a non-minimal coupling between the hicks and the gravity you can actually you know you can constrain this number and turn it down to k larger than four and this the scale larger than four is interesting because it says that the the generalized equation of state for this for this inflaton is larger than one-third and remember this omega is a ratio of basically p and rho and for for radiation p equal to one-third rho so this refers to some particle which is stiffer than the radiation so one needs a fluid or during the reheating uh the background should be stiffer than the radiation such that one can reheat the universe to the adequate amount and this can this this non-minimal coupling is done through this usual prescription that you write down everything in the in the Jordan frame then you move to the to the Einstein frame so that you can have all the interactions and once here we do that we we come up with this this uh typically this uh five diagrams which tells you that how the standard model and beyond standard model particles can be produced through minimal and non-minimal coupling and minimal scenario is basically mediated by this external radiation of graviton while the non-minimal standard is basically all the four point diagrams which are guided by uh this uh this couplings you see all these couplings have have masses of the fermions in the top thanks to the helicity of the fermions so one can one can uh you know assume that this fermions masses has to be very high so that they can surpass this this suppression from the plant because its eyes have to be smaller so that the part of nature of the couplings are maintained so what we will try to do now is to produce dark matter which are n1 through all these processes and also the the the next uh heavier neutral n2 through again through these channels but we will remember that we will only consider to non-thermal appliances so there is no contribution from standard model in producing these heavier neutrinos and the universe will be heated through the uh pair annihilation of this of this uh uh inflaton to the standard model path typically to the Higgs so before I typically show you the the parameter space it's a try I will take a very small detour because I will I will I will try to tell you the story about this primordial gravitational wave which has stochastic in nature and these waves as we know they are unlike the statistical sources they are generated during the inflation from let's say the tensorial perturbation of the matrix and and and these are basically typically the quantum fluctuations and these fluctuations uh start inside the Hubble and and because during inflation this Hubble radius is basically shrinking therefore they exit during the inflation and at the end of inflation when again it starts rising these these fluctuations or the modes they start reentering the uh horizon and depending upon at what era these reentrance happen these modes can either be scale invariant if the reentrance happens during radiation domination or they can have uh a blue tilted part if they reenter during this stiff upon that that I was telling you which is required to reheat the universe uh according now this blue to less spectrum has a problem the problem is that it's in conflict with the delta and effect delta and effective is a measurement of how much of extra relative degrees of freedom you can allow around the BBN apart from the standard bottom and we know the gravitational wave is basically the scaleless radiation uh once the source is switched off so here just I try to show you the thing that if you have a minimally coupled scenario then all these curves are in conflict with this BBN bound which are which are shown in blue which tells you that the minimally coupled scenario is basically completely ruled out while if you increase this this non-minimal coupling and put some non-zero value you can reduce this this tension and make this scenario available and the reason for this boost is very very simple that this this ratio over here tells you that my gravitational wave the energy is a gravitational wave to that of the radiation are typically proportional to the the the momentum at the horizon crossing which is nothing but the Hubble at the horizon crossing so therefore when the horizon crossing crossing happens during the radiation domination so these are constant which are shown by this straight line if you follow the red curves but if this horizon crossing happens during the the inferior domination due to reheating then you see this blue tilt which is shown by this uh this uh up up going red curves so the point is that I will I will show in the very next slide that if we consider this this minimally coupled scenario these completely rules out a part of the parameter space so so this is basically the the how the parameter space looks like in the bottom left panel I show you the reluctancy the allowed region in in the heating versus k plane remember k is the exponent for this for this inflaton 5 which determines the equation of state for the inflaton now here if you follow each curve then for each curve for each dark matter mass there are two curves because the the reluctance is satisfied twice depending upon whether you are at a low heating temperature or a high heat temperature in the low heating scenario the high scattering dominates at the high heating temperature typically the contribution from path dominance and here you see the dark matter has to has to be as massive as a p e v in order to surpass the plant suppression due to due to gravity and again this blue line shows what whatever I was telling you in the very last slide that it is excessive gravitational wave which is a conflict with the data on the right hand side the curves each curve show the the right amount of ideal asymmetry that one can produce depending on the choice of the mass of this end to however this region is basically under produced because in conflict with this kinematical suppression as I was telling you that we are considering non-thermal leptogenesis so all contribution comes during the heating where a pair of five goes to a pair of n 2s and and as n 2 becomes heavier so at some point of time it cannot be produced again there the excessive gravitational wave you know totally rules out some part of the parameter space due to the conflict with p p n mount so now if I allow this dark matter to decay let's say the dark matter decays through some channel and but the decay decay lifetime is large enough that that it can be as large as the lifetime of the universe so it's still a stable relic so now if I allow this dark matter to decay remember the only channel through which this dark matter can decay is this the tri-linear new power uh l h n so it always decays to leptonic final state typically to to neutrinos and since this dark matter is at least a p v p v scale dark matter so all the neutrinos it produces are basically uh super energetic and we have we know that such neutros have been seen at the at the ice cube experiment and and and we are not trying to exactly you know fit the data etc but we are trying to say here is that there is a there is a provision for this for this uh in in the setup to have a p v neutrino and then have a dark matter which decays through this tri-linear coupling such that they can produce this high energetic ice cube events in at the experimental front end so this kind of a gravitated scenario is not only you know can be tested with the gravitational wave but can also leave their imprint at at the high at the ice cube facility or through production of the high-energy nuclear events that can be found in some of the experiments as well so this is the this is the net parameter space which I I put it in in in the mass plane n1 being the mass of the right hand neutrino that plays a role for the dark matter n2 being the next massive atom neutrino the decay of which produces pattern asymmetry and here each each of this differently colored you know points they correspond to different non-minimally coupling and this typically minimally coupled scenario is is totally forbidden because of bbn bound on delta n effective so one has to go beyond this minimally coupled scenario and and you know uh typically they choose a non-minimally coupled sector and however one cannot go beyond 10 because then the the right hand neutrino becomes so heavy it cannot be produced through the pair annihilation of a pair of uh inflaton to produce the right amount of pyridon acid actually so this is the the compact nature of this of this of this uh frame one so the upshot of this all discussion is the fact that that the discovery potential of for the gravitational wave uh not only can you know provide you a window to look into beyond the standard body physics but can also give you some idea about the early nervous cosmology typically that whether the whether the universe went through a period uh where the the the inferential energy density that shifted faster than the than the radiation which is typically known as the stiff epoch so this is one one one reason uh of of having a primary gravitational wave but typically one can do more with this primary gravitational wave and one can look into the uh into the uh coupling of of inflaton with a pair of standard model particles uh with the help of the same primary gravitational wave originated from inflation and how can we do that so let us consider that uh my my inflaton couples to a pair of uh standard model particle visible sector particle so at the end of the heating it decays part of it into a pair of standard model particles that can reheat the units and now if the inflaton oscillates in a in a steeper potential uh which is not quadratic then of course its mass is not constant but it becomes field dependent and then one can parameterize its decay with typically which looks like over this and and this parameterization is valid uh because of the fact that my mass is no more no more of free parameter but depends on the on the on the time and therefore the scale factor as well and here i here i just put this gamma phi e and beta in blue which are which are completely determined once we specify what sort of you know uh decay channel we choose so this f over here can be any any particle of any spin it can be a pair of uh scalar a pair of uh gauge boson or a pair of funnel so now with the help of this again we can see how the uh energy density of the two components typically the inflaton and the radiation evolves with time uh by solving the Boltzmann equation and one can show that this this radiation energy density uh or the internal energy density depends on two free parameters which is this gamma phi e basically which contains the information of the coupling meaning the the information that that to which final state this inflaton couples to and the other is this n which determines the the slope of the potential due to the heating so there are three free parameters basically in this modeling which is this coupling this n and another one is lambda which is the scale of inflation which has an upper bound from the measurement of scalar to 10 separation and here i just show you one one one example plot uh by choosing this by fixing some of these values and of course here uh as one expects that this uh profile falls faster so such that the heating is the onset uh of the point when the radiation energy density dominates over the internal energy density which is shown by this this red card and the slope of these curves will change once you choose different set of parameters typically sorry typically this n helps so now what we can do with this we can again compute the bluetooth spectrum for the gravitational wave but now this will depend on our free parameters which are this scale of inflation this gamma phi e which contains information of the of the coupling and this n which decides that how steeper this potential can be and therefore one can again uh you know plot this this uh the present day energy density that is contained within the gravitational wave versus frequency and can and one can tell that how large and how small this this coupling can be uh depending on the choice of our few parameters and here you see that i i'm giving an instance here where uh the the the inflat on goes into a pair of scalars and you see that's couplings as small as 10 to the minus 80 is in in in is completely ruled out uh because it it it is forbidden by the plank measurement on the entire effect so again this product is the same parameter gravitational wave which is helping us to constrain or or put some bound on the on the nature of the coupling between the inflaton and the pair of visible sector particles one can further go a bit more one can one can do a bit more one can one can now now now ask the question that what if i i produce a dark matter in such uh in a in such a scenario by such a scenario i mean where the inflaton has a time dependent decay width to to some uh visible sector particles here for example i choose the production of dark matter through some non-puree ramas move operator which typically looks like suppressed by some scale lambda u v and here the production happens through what we know as the even prison of dark matter and remember that the inflaton always decays into visible sector particle and the dark matter production happens through this kind of an interaction which is suppressed by this new field scale lambda u v then depending on the choice of this new field scale together with the dark matter candidate and what sort of uh uh channel for this inflaton decay you choose then depending on which you can produce dark matter starting from let's say an m e v to at least as as large as 10 to the 15 g if you are so so this is also uh uh a way to show that how our time dependent inflaton decay can influence uh dark matter production uh in a scenario where the dark matter is produced by some u v p c and and and just uh a comment that depending on the choice of this of this exponent by which the scale factor uh changes uh one can also show the dark matter production can be boosted that depending on how how large or how small this x is to be taken of course that will control your background cosmology as well as you see over here. Now since we're talking about decays let's let's go a bit far we so far we have only talked about two body decays of the of the of the inflaton where the when an inflaton goes into a pair of standard model particles but if you you know uh introduce uh this gravitational interaction then you cannot also forbid decay in which the inflaton goes to a pair of standard model particles together with the radiative production of a graviton either from the initial or from the final state and this gravitons can be energetic enough because they're producing from the decay of a very heavy inflaton and they can also constitute what is what is known as the of course the gravitational wave and the the source is again primordial because they are getting produced during during the heating from the decay of the inflaton itself. Now in this case typically the gravitational wave is is you know uh is a very high frequency gravitational wave courtesy to the fact that getting produced from the decay of a very heavy inflaton and and in the in the high frequency regime which really do not have much of a much of an experiment that can that can probe this kind of a scenario but of course there are certain experiments which can which can do the job but nevertheless this is also a source of the production of gravitational wave uh which is not you know uh discussed uh uh in in a to to a great extent so this is this is how it looks like so in the low frequency uh the the u desicc is perhaps the the best best uh uh sensitive experiment so far so it still cannot reach but in the high frequency there's only one experiment which can do the job which is the disordering cavity of course I'm not going to the details of of how this thing works but of course uh just to give you the idea that a high frequency gravitational wave is also possible to you know comprehend through the decay of an inflaton. Now since we were talking about gravitational you know reheating or gravitational production of of of standard model particles uh in the in the very beginning here we we first told that well gravitational production is is the production in which a pair of particles getting produced through the external variation of gravitation but that's one way of course to put put this thing but one can also imagine a non-linear a non-minimal coupling between the gravity and the inflaton uh like like this the which which has a which has a coupling strength of psi. Now once one go from let's say the the Einstein from the Jordan to the Einstein frame and make all the interactions you know diagonal of course this phi will eventually decay into all the standard model particles which meaning that it can it can uh read the units. Here we are choosing a phi squared potential which is typically ruled out uh from from cmp data because it produces too large of a of a scale to tensor ratio so that it cannot you know uh in it cannot you know explain inflation in in a in a proper way keeping within the data but thanks to this this non-linear coupling now we can tune this accordingly and and one can see that even with the phi squared potential the universe can undergo inflation maintaining all the you know observed bound on ns and r but on top of that also this inflaton can decay to all the standard model particles such that the reading happens before the ppm and what is important over here is the fact that in this case if only one only considers reading from the decay of a of a non-minimally coupled uh inflaton of course uh single inflaton uh then all of this it depends on only one free parameter which is non-minimal coupling site and and the site can decide what the mass of this inflaton can be how how large the maximum temperature can be or or how large the range temperature can be which is very fascinating because everything is determined by only one free parameter over here. Now one can again do the do the same trick uh as before and introduce more exotic particles more exotic features and say that well what if I introduce singlet scalar on top of the standard model particles or singlet fermions on top of sense standard model particles then of course this singlet scalar of all the singles fermions even can play the role of a good dark matter candidate and in case of a singlet fermion they can undergo uh again the cb-violet in decay and can produce uh the observed matter anti-matter acid energy and here I'll show you the the parameter space uh you see this this branching uh because everything is now happening through the decay of this inflaton so that the inflaton has a branching to the to the standard model to the visible sector which is maximum because you have to repeat it and there's a very tiny branching to the to the invisible sector to dark matter or to or to the dietary neutrinos then depending on this branching and the masses uh one can again produce the right amount of relative density or can explain the matter anti-matter acid battery uh through the decay of this this right element you know so but here so what we're trying to say here is that with a with a simple five squared potential which is quadratic potential of course uh one can again explain uh the the inflation one can reheat the universe and not only that one can also explain the matter anti-matter asymmetry and the and the and the dark matter energy budget uh once we introduce more exotic stuff along with the standard model so this is basically an example where one can resurrect the the quadratic potential with the help of a linear normal coupling. So this is this is at least uh what what I had to really say so I will try to summarize whatever I was I was telling so far so as I was as I was telling from the very beginning that standard model does not include gravity of course but one the the operative gravitational interactions are inevitable uh because thanks to its uh uh the nature of of of having this plan suppressed coupling to everything so gravitational interactions are something one needs to take care of and then only taking the gravitational interaction is not enough one has to also build simple particle models and and they can play a role together they can conspire among themselves and can provide uh the standard model path which is of course the heating they can explain the dark matter abundance depending on what sort of you know new physics particle you are you are adding with the standard model they can also explain the the barion asymmetry again you have to have some source of cb violation for example phylectogenesis and the goodness of this model is that they have very few free parameters you don't have to deal with like thousands of couplings and masses don't you have to you have to tune you don't have to tune them and sometimes they can only have one parameter as I was giving an example just before here for example this is everything is controlled by a single free parameter and that's that's something we always want not not to introduce more free parameters they also can have some observational aspect in the front of gravitational waves because primary gravitational wave can be produced during inflation and depending upon uh the fact that if during reheating there is a stiff epoch which means the the energy density of the inflaton uh you know decreases faster more faster than the the relation itself then you have this two tilted part of the of the primary gravitational wave spectrum that can that can be detected with the help of uh futuristic gravitational waves not only that these gravitational waves are typically you know in the in the low frequency regime in the high frequency regime you can also have something like a Bremstrahland process where an inflaton decays into a two-body final state along with the radiation of a of a of a graviton and this graviton can constitute the gravitational wave uh that can perhaps be detected with the help of more sophisticated you know experiments so finally let me let me discuss some outlooks so so far I have been you know emphasizing on the fact first of all the word part of it if because uh I was you know cunningly trying to avoid more intricate scenarios which are which is known as preheating because reheating precedes preheating precedes reheating during which you can have a past of particle production exponential particle production where this uh part of it if scenario is not part of the approximation is no more valid and one needs to invoke the lattice evolution this is something um I I guess it's a very uh you know dynamic field right now and people are doing uh many many research in this direction there are many packages available for example cosmolattice and etc and this preheating can also give also be a source of gravitational wave uh and that is something perhaps one one needs to you know study in a in a greater detail and there always remains a window to explore more in the in the connection between particle physics and cosmology together with gravity because there are many many experiments in in both front and one should try to you know uh have a complementarity between between all all these searches so that uh they can put some firm ground or some constraint on the new physics scenarios and of course beyond freezing there there are many many dark matter production mechanism for example s imp is strongly interactive as a particle core seam etc and I guess there will be many uh in in in years to come so these this is something again one needs to think about that how to you know break this uh break our uh bias towards towards winds and go beyond the wind paradigm to search for more uh exotic dark matter production mechanism and finally since I am I have been talking about gravitational production although gravitational production is not exactly the truest sense of the term because those who are really pedantic they will be saying that no no this is not gravitational production because it did not take care of the fluctuation of the uh metric you did not consider the boggling water transformation production from the vacuum itself well everything falls in a broader sense gravitational production so I must also you know uh mention the production from primordial black hole evaporation which uh people have been doing for for for maybe last couple of years and that's of course another story this will take maybe another uh seminar all together to to discuss so that's it from my side um thank you very much for your attention so I'll be happy to take questions thank you thank you very much for selling you very nice talk um are there questions from the audience cannot see in the chat well I can start so I'm just out of curiosity so you have this data from colliders and laboratory experiments uh what do you have in mind I mean is this in the context of gravitational dark matter or in general no in general not necessarily gravitational dark matter so let me be more specific for example first order phase transition may be right so it's it can be uh triggered by the presence of some new scalar which gets a non-zero vacuum exploitation value and that scalar can always research at the collider so that first order transition can provide you critical gravitational waves so there is a complementarity between gravitational wave and colliders such as in that sense but perhaps it can also be extended to gravitational production of dark matter itself but I don't don't know that how to how to do that perhaps that's what one can think about it okay thank you for a lot of questions okay I have a little bit so in the uh previous slide or well even at the very beginning so we're talking about these low frequency blue-tilde and gravitational waves yes so in the plot you show at the beginning exactly there for instance next one I think or okay with that one uh do you have uh this for abstract or some particular model for inflation yes I was just wondering how how model independent can be this statement be of course if you have a blue-tilde spectrum of course you you cool we have to be careful but I mean that's a that's a great question I mean the requirement of having a blue-tilde is that you need to produce you need to have this like a stiffer period right so this this equation of state that you have to maintain so um so you always need some sort of potential which is typically let's say polynomial in nature right phi to the k so in that sense it can can I mean well alpha factor is well motivated but any phi to the k potential can do the job as long as you have this period where where this steep up up comes okay yeah nice I see but okay again you say that these correspond to alpha factor right this this typically I I'm taking this alpha factor potential keeping this in mind yes okay thanks uh that may be a time for last question I have a question for what's your name yes so I was wondering if you have any comments about the regarding with the Hubble constant tension in the sense that is any possible explanation between these kind of fields that affect the late time evolution of the I mean not the early universe but just a bit a bit late I get the point but but honestly honestly I I I do not have any any uh sort of idea regarding how to resolve this Hubble tension with the help of uh you know you have to control the the Hubble rate right that how the Hubble rate changes whether it's faster in the early universe and and store in the late universe and so on and so on but I I have seen like many people trying to do it with the help of very uh how should I put it uh like very intricate models keeping you know many particles keeping keeping them together but honestly I I do not know that how how to resolve this issue with the help of this kind of feature with the help of like a gravitational production or gravitational variation I I really don't know thank you and excellent I don't see more questions so let's turn okay if not let's thank you again thank you thank you very much thank you so much thank you so much and let me just remind the audience that next week Wednesday we'll have another seminar by Rebecca Lane so she will talk in um just one hour earlier than usual so next week uh Wednesday so thank you very much and hope to see you next week see you guys ciao ciao