 One, two, three. Hello everyone and welcome to the Latin American webinars and physics. I'm Nicolas Bernal from New York University in Abu Dhabi. So I will be your host today. So today we have a young Shu. So young PhD in the University of Bonn in Germany. And he recently started his postdoc in Mainz. So young will talk about the rotational waves producing during the heating by brain striving process of the graviton. So you're super happy to having you here, young. So Shu, you could start sharing your screen. Okay, let me try. So can you see the screen? Yes. Okay. Yeah, so thanks a lot for the introduction. Yeah, I also want to mention that though I did my PhD in Bonn, but Nicolas is the co-supervisor of my thesis. Yeah, so it's a great pleasure to speak here. And I like the philosophy of law, physics a lot. And I'm a follower of it. So it's really a pleasure to talk something about my research here. So today I'm going to discuss a recent project in collaboration with Basbendu, Nikolas and Oscar regarding gravitation wave from graviton-branched atom during inflation reheating. So the purpose of this talk will be two folds. First, I will show that there is an unavoidable source of gravitation wave. We are branched atom during inflation reheating. And secondly, I will show that the branched atom gravitation wave can be used to say something about the physics of reheating. So this is a two-purpose of this talk. And the scope of this talk will be the following. So in the textbook, there are many, many sources of gravitation wave. For example, during inflation, you have a inflated atom fluctuation and where the Einstein equation, you have the fluctuation of the metric. So this is one source of gravitation wave. Or during reheating, you have some inhomogeneity of modes being produced. This can also source gravitation wave. Or you have this transition, you have the collation of bubbles, which can also source of gravitation wave. But today in this talk, I will focus on the direct gravitation emission as a source of gravitation wave. So the setup will be the following. It's very simple. First of all, we consider a perturbation of the metric along the flat one. And this is the excitation of the metric, which will correspond to the skin-to-graviton field. So now, if we plug in this perturbation or expansion back to the action, we get an effective coupling between the graviton and the energy momentum tensor. So as you can see from this coupling, you see the emission rate of the graviton suffers a suppression by one over m-plunk square. So in order to get efficient gravitation emission, we need a very large energy momentum tensor. And I want to mention that inflation-reheating is a natural source to give rise to such large energy momentum tensor. So this is the scope of the talk. And now I want to briefly give some ortho-line for this talk. First, I want to briefly mention cosmic inflation and the reheating. Then I will discuss the graviton-branched column as a source of gravitation wave D and ring reheating. Then I will discuss the contribution of the graviton to the delta EFF. Then I will discuss the gravitation wave spectrum. And then finally, I will summarize. So yeah, so inflation correspond to the exponential expansion of the space in the very early universe. And the dynamics is usually driven by some scalar field slowly looks down some light potential. So due to inflation, the universe can be driven from very tiny scale to a big scale. And this explains why we have a big universe. Also, because of the quantum nature of the scalar field, there will be some fluctuation when the field are moving along the potential. So this fluctuation will source the inhomogeneity which we saw in the CMB map. This is also the seeds for the structure formation. So inflation solve many problems. And so after the inflaton moves from the flat part, the inflaton will start to oscillate. And at the same time, it will transfer energy to some radiation so that we will have a thermal universe. So the energy transfer stage is usually called the reheating. And it can be perceived via the inflaton decay. For example, the inflaton can decay to some bosonic particle like the standard model Higgs or from a monoparticle. So in general, the reheating can be very, very involved. For example, you could have some non-perturban preheating. Let's for example, look at the bosonic channel, the verify this particle. And this is the equation of motion for the bosonic particle in momentum space. So here is the case of momentum. You see, due to the trinear coupling, the mu phi by sphere, once the inflaton oscillates and move on the left, this part of the minimum. So this part is negative. So if you move this part to the right hand side of the equation, you get the exponential production of the particle. So this kind of tachanica instability tended to make preheating very, very efficient. But in our setup, the doctor particle or bosonic particle phi, small phi, will be the Higgs, which features a sizable self-coupling. So once you produce a lot of Higgs, there will be inversion, the variance term, once you plug in the Hartree approximation. So you say there will be a effective positive mass. This effective positive mass will count react on the negative mass making preheating less efficient. So this is for a bosonic case. And for the fermionic case, due to the polyblocking preheating in general, it's not efficient. So the remark will be the preheating is not efficient in our setup. So in the following, I will mainly focus on perturbative reheating. Then we can write down the decay rate for the bosonic channel or for the fermionic channel. Once you have the decay rate, you can further estimate the reheating temperature here. So I have mentioned the two setup. One is effective coupling between gravitan and the energy momentum tensor. The other one is a perturbative reheating. So once you have these two, we will have direct gravitan emission during perturbative reheating. So these are the four possible diagrams. For example, here the phi is the initial infallown field and the F is the doctor particle. And the h nu nu is a gravitan field. So there will be four possible channel because the gravitan can be associated in the initial state or the final state here and here or on the vertex. So one of the main tasks in this talk is to estimate the emission rate of the gravitan. Well, in other words, we have to calculate the matrix element. But before we do that, I would like to briefly mention the polarization of gravitan because the gravitan is massless. So there are two physical states or two polarization states. And the gravitan polarization tensor satisfies a set of conditions. First it has to be symmetric, then it has to be transverse, then traceless and also on the mole. And you can choose a frame where the gravitan moves. For example, here I just choose gravitan move along the x direction. So once you have a momenta, you can try to construct the polarization tensor. So here are the two possibilities. It's easy to check that this polarization tensor satisfies these conditions. And I also would like to mention that if you choose different frame where the gravitan moves, you will end up with different polarization tensor. But in the end, it doesn't matter. So here I just choose it for convenience. So here I consider a inflation decay to a scalar final state. And these are the four Feynman diagrams. And the M1 correspond to the matrix element for the first diagram and so on and so forth. This is M2, M3 and M4. And I would like to first mention M4. You see this is just the trace of the polarization tensor. As I mentioned before, the gravitan is traceless. So this matrix element has to vanish. On the other hand, you see that the gravitan can associate in the initial state where the momenta is air or in the final state with momenta P or here. You see the result is very, very symmetric. If it is associated in the initial state with momenta air, you have air nu nu times the gravitan polarization tensor. If it is associated with P, you have P nu P nu and the polarization tensor and so on and so forth. So a lot of important point is that because here the in-state time decay at rest, which means that only the first component is not zero. So if we go back to the polarization tensor of the gravitan, the only non-vanishing component is a loss of two here and here. So you say the M1 vanish. So in the end, we will only have two matrix elements, M2 and M3. And this simplified our calculation a lot. So we now just need to calculate the square and the cross. Here I want to show you how the emission rate looks like. So here the E omega correspond to the gravitan energy and I define a new variable for the X and which is scaled by the inflator mass. So the result looks very, very simple and instructive. Of course, you have this face-based factor, 64 pi cube. And this is a coupling square. So a nu correspond to the trinium coupling between the inflator and the stocked particle. And you also have a one over M long sphere due to the gravitational coupling. So you say if X goes to half, then this differential rate goes to zero. So physically the reason is that because the gravitan could at most carry half of the inflator energy. So once you cannot go beyond that, this is a reason why you have a cutoff. On the other hand, there will be a divergence when X goes to zero. This is actually very, very similar to the IR divergence in the 2ED case. And if you want to resolve this divergence, you would have to consider the vertex and the self-energy diagram. So this is a differential rate for the scalar case. And now I briefly showed for a fermion and the vector case. The result is very, very similar. You have a coupling square. And you have a feature that when X goes to zero, the differential rate goes to zero. You have a feature that when X goes to zero, there will be a divergence. And the only difference come from that fermion case, you have to do the spin sum. And for a vector case, you have to do the polarization sum. This is the main reason why we have different terms compared to the most simple scalar case. So yeah, so we have now have the differential rate and now we are ready to study how the whole system evolved by the whole system. I mean, we have the inflate time, we have some radiation and we have gravitation wave. So this is the evolution will be governed by a set of differential equation. So here the gamma zero correspond to the two body decay without the gravity time. And gamma one correspond to the three body decay with gravity time. If I set the gamma one to be zero, you have the U-year Boltzmann equation. And now if I insert gamma one as we are looking down here, you see we have new terms. Now I will explain why the new term looks like this. For example, let's first look at the evolution for the gravitation wave energy density. Here the E omega divided by M correspond to the fraction of the energy goes from inflate time to gravitation wave. Because as I mentioned before, the graphite energy can goes from zero to half of the inflate time mass. So you have to sum over all the graphite energy. You see a reason why you have a integral here. And the rest part of the energy goes through radiation and similar way have to sum over all the graphite energy. And this reason you also have an integral here. So with these three equation, we can get the solution for gravitation wave. And the solution look like this, it's also very instructive. And first this first term looks like the differential branch ratio. And the second piece correspond to the energy fraction in each decay. So if you integrate over the solution, you will get the whole energy stored in the gravitation wave. So, yeah. And gravitation wave effect will also behave like a dark radiation. So it will possible to the effective number of species of neutrinos or the so-called data EFF. So in this plot, I show you the data EFF versus the mass of the inflate time. And the different line correspond to, for example, the black line correspond to the vector, the inflate time decay to vector. And the blue line correspond to inflate time decay to fermion. And the red line correspond to inflate time decay to scalar together with a extra graviton. So you say, unless you have very, very massive graviton, it is almost not constrainable even by the future CMB experiment. And after that, I would like to mention the topology of these three line. The main reason why the black line is on the top because for a vector, we have three degree polarization, three degree freedoms. And for fermion, we have two spin and scalars. We only have one degree freedom. So this is the reason why the black is on top of blue and the blue is on top of scalar. So now we can move to the spectrum for a gravitation wave. And we can, this is just a normal definition of the gravitation wave amplitude. And it's proportional to the differential rate of the gravitation emission. So we can use the solution from the Boltzmann equation. We can estimate what is the gravitation wave amplitude looks like. It is very similar to the other gravitation waves for steering reheating. The amplitude will be proportional to the reheating temperature then proportional to also the frequency of the gravitation wave. And the gravitation wave frequency is related with the gravitation energy via the Einstein relation where the energy equal to the long constant times the frequency. Here I said H bar to be one. This is the reason I have a two pi. And the gravitation after production will redshift. This is the reason why I have some skill factor. And you can treat this skill factor with respect to temperature by using the fact that entropy is conserved. So we also mentioned before the gravitation energy could only be half of the infotainment mass. So this also means that there will be a upper bound for the gravitation wave frequency. You say if you have Planck scale inflate mass the frequency can be very high. So now I show you how the spectrum looks like. And here are the y-axis correspond to the dimensionless stream parameter which is defined here. And in this plot I choose two benchmark parameter. The first one, I consider inflate mass around 0.1 times Planck mass. And reheating temperature correspond to the current upper bound from the CMB. And for the second one, I consider smaller mass. Also the black line correspond to vector and blue line correspond to fermion and red line correspond to scalar. You say if I decrease the inflate mass and reheating temperature, the signal gets decreased off as expected. So from this figure, I also show several experimental bounds in the future, the DCGO or the cavity experiment. You say in order for a signal to be detectable we need a very, very large inflate mass and reheating temperature. And it is not clear how to construct a realistic inflation model given in rise to this kind of a parameter but it's not impossible. So far we have only considered a inflate mass oscillate around a horizontal potential. So what if for the inflate town potential is deeper than quadratic? For example, we can consider inflate town oscillate around potential with a five power n with n larger than two. And this kind of setup is very, very well motivated in for example, the alpha track Q or E model. So once we consider n larger than two, you say the inflate mass or namely the second derivative of the potential becomes field dependent. Now, if you look at, if we recall the definition of the two decay rates in the Bosonic case it is a one over M five. And for a fermion case it's proportional to M five. So due to the field dependent mass of the inflate town you say in a Bosonic case the decay rate can be suppressed because we transfer the energy from inflate town to radiation via the decay. If the decay rate is suppressed which means that the Zohar or the radiation energy can also be suppressed. If you recall the definition of the gravitation wave energy density it is inverse proportional to Zohar. So if Zohar is smaller the spectrum can be boosted. So physically this means that if you have less entropy dilution you can further have larger amplitude for a gravitational wave. So here I show the evolution for the energy density for radiation and inflate on energy density. I consider for example in the first panel I consider n equal to two. And now I increase and you say now let's first look at the n equal to two. So we are mainly focused on the black line namely the radiation. So it's here now you say if I increase the n in the Bosonic case the black line the slope become slower, become smaller compared to n equal to two case. And for fermion case the slope become even larger. So this means that in the Bosonic case the radiation can be suppressed as I explained in the previous slide. So now we are ready to study the implication of the evolution of radiation through the gravitation wave. So here is the results. Here I consider inflate on also laid free ground or around a quadratic and with n larger than two free ground n equal to four and n equal to six. Here you say if I increase n the signal can be significantly boosted due to the fact I mentioned before. And in the Bosonic in the fermion case we don't observe any boosted feature. So a lot of important information I would like to mention that in this plot I consider very very small parameter like free ground might consider inflate on mass around 10 to 13 GV. And this kind of parameter can be realized in many inflation model. So now we may ask what will happen if the future detector free ground so resonant cavity do not see any signal. If it does not see any signal which means that those Bosonic reheating scenario free ground n equal to six are ruled out. So in this sense it seems that the future gravitation wave experiment could potentially help to prove or pinpoint the dynamics of reheating. For example, it can tell us the shape of the inflate on potential when it oscillate. Also the type is Bosonic or fermionic. So I now are ready to summarize. So in this talk, I have shown that due to the unavoidable coupling between the metric and energy momentum tensor the gravity can be produced via a branch tunnel. And it will further, this gravity can further give rise to a gravitational cosmological gravitational spectrum. And the spectrum depends on firstly the shape of the inflate on potential during reheating. Also it depends on the type of the inflate on to matter coupling. So we have also seen that for quadratic potential we need a very large inflate mass and the reheating temperature in order to make the signal detectable. However, for potential deeper than quadratic the gravitational wave in the Bosonic case can be significantly boosted. And even it can be detected even with very small inflate on mass and the reheating temperature. So I think this is something very important. So the conclusion will be reheating. Uranus is a black box, but our study via Graviton branch tunnel hopefully offers a new venue to explore the physics of reheating. So I think this is all I want to share today. Now I think we can discuss. Yeah, thanks a lot for your attention. Thank you. Thank you very much, Yung. Very nice talk. So are there questions or comments here from locals? There's one in the chat. So someone is asking about reheating. So sorry, preheating. So you mentioned it at the very beginning, but could you maybe elaborate a bit more the fact of preheating in this case? Yeah, so, yeah, for example, like for example, we look at the preheating produced the Bosonic particle Phi by default will be the Higgs. So here, due to the trinitial coupling there will be a tachymic resonance which tend to make preheating very efficient. But once you produce a lot of Higgs, this will give rise to some back reaction due to the Higgs self-copying here. So this back reaction will counteract on the tachymic mass make preheating less efficient. And for Mianni channel due to the poly blocking you momentum space, you cannot have a number density larger than one due to the poly blocking. So this is the two thing, two fact that's why I mentioned preheating our setup is not efficient. But in general, the preheating can be very, very efficient if you don't have this self-copying or back reaction. Yeah, I hope I answered the question, yeah. Further questions or comments? The YouTube chat, maybe locals? I have a question. So at the very end, you present plots for scalars and fermions, so that your very last plot but not for vectors. Do you have an intuition what could happen in that case? Well, I mean, for example, because I mentioned before for vector, you have more degree freedom. So if I use the same parameter, the gravitation wave in a vector case will be larger compared to the other two case. It is similar to the angle two case simply because for vector we have more degree freedom. Yeah, but in terms of the boost, do you think it will be more like the fermion, like a small boost or like a scalar with a larger boost? Well, for fermion, sorry, for vector is also a, I would expect it's similar to the bosonic case because effectively, the vector is also bosonic, right? So there will be also separation for rate. So I expect the signal in the vector case can also be boosted. But we don't observe this boosted because the rate, decay rate in a fermion case is proportional to and not inverse proportionate. So if something, if you have a model where the decay rate is inverse proportional mass, if you can suppress a mass, sorry, if you can make the mass larger, you can suppress the decay and further suppress the entropy relation, you can enhance the signal. So I expect in the vector channel, you can also have a boost. Okay, thanks. So I have a question. So in principle, you have shown that different potentials for the inflaton give different rotational wave signals. So does this leave any imprint on any other cosmological parameter or something that we could observe? Very good question. So for example, like as I mentioned before, this kind of setup are motivated in some offer tracking model. For example, indeed, if you consider for example, the N, we have considered N equal to one or two or N equal to four or N equal to two or four. So if you consider different N, the inflationary parameter can also be changed. So this is one, the other change for the cosmological aberration. So by the parameter we have chosen, it satisfies the inflationary constraint, which is assumed by the current flank plus bicep data. And do we expect to measure this to improve these constraints or maybe exclude some N? You say actually here the N, actually I forgot to change it. The two N correspond to our N, which means the N equal to one here will correspond to N equal to two and N equal to four, where we'll correspond to N equal to here. You say, I mean, this is a kind of bound. This is the blue region is a kind of bound for a tensor to scalar ratio. If in the future this bound can move lower, in principle, this can also help to constrain the parameter we have chosen. Yeah, but I think the future, so here the counter bound for tensor to scalar ratio is around the 10 to, still around 0.035. In the future, it will be like a CMB stage four, it will be around 10 to minus three by still, it's far from some of the parameter space. Okay, okay, thank you. Maybe I last question for Yung. Okay, maybe I have a small question or a comment. So I was just thinking that we know there are many sources of high frequency gravitational waves, right? For example, they can come from, for example, they can come from the evaporation of primordial black holes, right? The gravitons coming from the primordial black holes, they can also constitute a gravitational wave, which has a high frequency. So I'm just thinking that if there is a detection of a high frequency gravitational wave in future experiments, so can we disentangle that the sources, like, yeah, yeah. How do they distinguish? Ah, yeah, yes, yes. Can we really have a handle on that, that if it is coming from Blamestalung, or if it's coming from like the primordial black hole evaporation, can we distinguish them? Perhaps not, I'm not sure. Remember, if I remember correctly, you say for our Blamestalung, the spectrum is very broad. If I remember correctly, for the gravitational wave from the primordial black hole evaporation, the spectrum is lighter. So I think in general, this is a very good question. How do, in the future, if we see some signal, how do we distinguish the source of signal? I think one possibility is the various shape. If the shape of the spectrum is very well studied, we can, in principle, disentangle the different sources. Yes, yes. Okay, thanks. But it's difficult to detect these guys, right? Yeah, it's also very difficult. Grampo, this detector is proposed and in reality, it's not exactly yet. Okay, yeah. I don't see any further questions. So we'd like to thank you, Young, again, for this super nice talk. Thanks. And yeah, so we'll have another webinar in a couple of weeks, right? So I think it's beginning of June. So let's reconvene a couple of weeks here again, the same time, same day. So thank you very much, guys. And thanks again, Young. Thank you. Thanks for your location, yeah.