 Okay, we are live again. So welcome everybody to the Love Physics webinars. So today I am the host, Roberto from Universidad Catolica del Norte. Today is a very nice webinar indeed because the speaker of this webinar is going to be Luca Bicinelli. He's postdoc at the Grappa Institute in the University of Amsterdam in Netherlands. But before he was postdoc at Nordita at the Stockholm University. And he got the PhD from the Utah University. So Luca, he is present. He's gonna talk about the astrophysics with action, mini cluster and action mass. Action starts, sorry. So Luca, please you can start your webinar and welcome to the Love Physics webinar site. Thanks Roberto. Thanks for the organizers of Love Physics. It's a great format that I love to follow and I'm glad to give a talk today on my developments and my research. So I'm going to start sharing my desktop and you should be able to see my presentation now. Is that correct? Yes, Luca. Okay, very good. So I go, hello. Okay, good. So I'm currently a postdoc at Grappa and today I'll talk about action mini clusters and action stars, which are topics. First of all, I would like to give an advertisement. So I just finished a review on the QCD axion on models of this elusive and hypothetical particle. They were just very interesting particle to be studied along with Luca Diluzio, this person on the right. Maurizio Giannotti, who's professor in Berry University in Miami and Enrico Nardi, who's a chief scientist in Frascati near Rome. So basically if you have any question on what the QCD action is, this review now is out and we just submitted it to physics report. So this is my outline. I would first spend roughly 10 minutes on the QCD action as a dark matter candidate. I'll also review briefly what dark matter is. Then I'll focus between 10 and 15 minutes on action of astronomy, including action mini clusters. And then I'll spend five to 10 minutes talking about what we can learn from gravitational waves. I decided to condensate the talk in 30, 35 minutes. So there will be enough time for questions that might arise from the chat, our discussion. These are the papers from which I base my talk today. So we know that we have overwhelming evidence for the existence of dark matter at different scales in astrophysics and in cosmology. First of all, we know that the rotation of velocity curves of galaxies differs from what we expect from the visible disk. Instead, we have a rotation curve that doesn't match what we would expect just from looking at the luminous content on a galaxy. But we have, in order to match with data, we have to assume that there is way more mass than what we see. This is the dark matter interpretation of this mismatch between the theory and the observation. We also have evidence at different scales. For example, when clusters of galaxies merge, this is, for example, a bullet cluster where we see there's more than one gravitational potential which is in line with what's expected from the existence of dark matter which basically would pass through each other and maintain their potential wells as opposed to gas which sticks in the middle. We also have evidence from cosmology. So we see that the peak in the cosmic microwave background are fit nicely. We assume that dark matter is already playing its role and depending the potential well at the time of recombination. We also need dark matter in order to see structure formation later, even at the time for the galaxies as we know to form. So what does this have to do with the axiom? Well, for this, I have to jump into particle physics from cosmology and I first have to discuss what the axiom is. So we know that the QCD sector of the standard model allows for a term which is of the form of the trace E dot B where E and B are the electromagnetic counterparts of the blue on field. Alpha S is the strong force coupling and the theta bar is a new parameter which we expect to be of order one and it controls the matter-antimatter symmetry in QCD. This is why it has some effects that are visible in principle. For example, it would give the neutron electric dipole moment which we don't observe. And this is why we can place upper bound on the absolute value of this quantity which has to be smaller than one part in 10 billion. So we can live with this or we can dig deeper and look for us why one quantity which in principle is of order one is now constrained to be less than 10 to the minus 10 by experiments. This is the axiom solution. So for the QCD axiom to get to the QCD axiom, we first have to promote this field, this parameter theta to be a field which roll to zero dynamically. So it's the dynamics itself that constrain the field to be zero, to be observationally small. This is the solution first proposed by Pachei and Quinn in 1977. And it was then realized that, okay. It was then realized that this theory comes with a quantum which is the axiom. So this was actually independently proposed by two Nobel Prizes or two currently, Lorraine Weinberg and Wiltschappel in 1978 and then showed that the Pachei-Quinn solution of the strong CPU problem comes along with a new boson which is called the axiom. And then the Lagrangian when we saw is a legitimate from the standard model actually converts into this Lagrangian in which the axiom field pops up, makes it present. This is a dimension five operator. So it has to be, it comes up with a new energy scale which is called the axiom energy scale. It's this quantity F. The axiom mass is inversely proportional to F as we see in this box here. The axiom mass is of order of the lambda QCD square. So the QCD confinement scale square which is of the order of 200 MeV over the value of F. Since we expect experimentally F to be larger than 10 to the nine than to the 10 GV, this pushes the axiom mass to be below the milli electron volt. So extremely light particle. This is a one parameter theory and it's falsifiable. So this is a plot that comes from our review that just came up, but this plot has been proposed and already in different other different reviews and it shows the axiom photon coupling on the Y axis in units of inverse GV as a function of the axiom mass in electron volt. So we see that there are different constraints that can be placed on this parameter space with the solid, the constraints bound by the solid lines being experiments that have already placed bounds, whereas dashed line border proposed or future experiments, future reach of our current experiments. The axiom photon coupling comes from this anomaly diagram in which the axiom couples to three level two fermions. And then this fermion can close and make a loop, a fermion loop. And it's required that this fermion is also coupled to photon. So we have an axiom photon photon coupling. We can distinguish between the roughly we can distinguish between vertical lines here which are experiment that exploit cosmic axioms. So axioms there are dark matter which I will explain more in a minute. So, for example, ADMX or a clash. So these are axiom heloscope. They use the axioms that are in the galactic halo. And they look for them by trying to convert them in a magnetic field, which is one of these two photon and making, looking for a signal. So the other photon in the Feynman diagram. Instead, the horizontal lines are axiom heloscope. So they look, they don't rely on the axiom being the dark matter, they look for axioms that are produced in the sun. For example, IAXO is a proposed experiment that would be designed for this. Looking for this particle being produced in the sun. So QC, the axiom is one particular line for which the axiom photon coupling is proportional to the axiom mass. So once you choose your theory for the axiom then you can compute this diagram here. You discover that G, the axiom photocoupling is proportional to the axiom mass M. This draws a line in this diagram. And then we can look for this particular model. We can hope that our experiment is sensitive enough so that we can probe this model. And the interesting axiom model lie in this yellow bound here. So far, AGMX has been placed bound on this. And there are many other experiments that also propose to search for this particle in the near future. So let's see how do we now account for the axiom as being the dark matter particle since it's so light. First of all, we had to embed it in a higher dimension theory. So for this we have to introduce a Pachequian field, psi, phi, phi of which the axiom is the angular variable here. It appears in the exponent. Normalized by the axiom decay constant F. Then the radial part can be split into what is the vacuum expectation value, F, plus a radial oscillation about this value, F. So this is exactly as the X-mechanism is a similar idea. In fact, we expect that the Pachequian potential develops a Mexican heart potential well in which the radial mode sits at the bottom of the true potential when the minimum develops, when the temperature of the universe versus of order F. And then the axiom is the angular variable. It sits anywhere in this circle. So it takes, and the value of A over F takes any value between zero and two pi. And in fact, it doesn't appear in this Mexican heart potential. What then happens, which is remarkable and peculiar just for the axiom is that at even lower temperature, so when the universe cools down at the order of the QCD energy scale, we have additional effects. We have non-perturbative effects that come from the interaction of the axiom field with the gluons, which tilt this Mexican heart. So now all of these values between zero and two pi are no longer equivalent. There is one true minimum in which the axiom fields would start to move to roll down. And in this movement, it would oscillate. It would then oscillate about this true minimum. And it is these oscillations that store the energy density that behave as the dark matter. So this is an idea which is slightly different from the WIMP mechanism. So from the other archetype of dark matter. For WIMPs, the energy density is stored in the mass energy of the particle. For the axiom, the energy density is stored in the oscillations of the axiom field. The details at which this additional potential from the QCD interaction is turned on are still debated and rely on lattice simulations. What I just described is known in the literature as the vacuum realignment mechanism. So it leads to this equation of motion for the axiom in which physically resembled that of a damped oscillator. We have the acceleration of the axiom field, a damping term where H is the Hubble rate and we have the mass act as the frequency times a sign which makes this oscillations non-harmonic. So at very early time, where for very early we mean when H, the Hubble rate is larger than the mass of the axiom. So we can put a place of watershed between the moment in which H is much larger than M. So for times smaller than T os in which the axiom dynamics is frozen and the energy density is constant. And the moment at which the axiom mass starts to matter and for which the axiom field start to set into motion and the energy density scales as the scale factor of the universe to the minus three. So as the inverse volume, it behaves as dark matter. The history is even more complicated than this because there are topological defects. We are talking about a complex scalar field. And in this regime, we expect that the field develops a string network. So we develops the main walls, strings and other topological defects. Already when the petroquin symmetry breaks, this because if inflation doesn't play a role in this scenario, the petroquin symmetry breaks in different ways, in different patches of the universe. So the axiom field takes different values in different patches. These patches would then attach to each other and at the borders of these patches there would be a potential difference. We see this in numerical simulations. This is from my colleague Javier Redondo in which we have a 2D slice of a 3D simulation. The axiom field theta takes any value between minus pi and pi, where minus pi and pi being white, while the value zero, the minimum of the axiom field would be black. And we see that as the time evolves, there are regions like this region here that I highlighted, in which the axiom field takes all of the value going from white to color to black, color then white again. So it ranges all of the values between minus pi and pi circling around this dot. This dot, which I remember is a dot on a 2D slice of a 3D box. So this is actually a string. It's a 3D string, which is a compact localized energy distribution, which we cannot get rid of if not for the dynamics. We see that when the axiom field acquires a mass at the temperature of the order of the QCD phase transition, this string network is dissipated by the formation of the main walls. And during this evolution, the string network constantly evolves and radiates axions as guanta of the field and modifies the energy density of the axiom dark matter. So this mechanism has also to be taken into account when assessing the value of the axiom field. In dark matter today. So now let's go to our compact objects, axiomunic clusters. We see that if we compute the energy density stored in the oscillations of the axiom field, for example from the picture that I showed before, there are spikes. So there are regions in which the energy density is large compared to the mean value of the energy density. These, so these are two these lies from this paper by Kolban Tachov in 1996, which studied this phenomenon numerically. These spike of energy density would later at matter radiation equality collapse gravitationally and for what are known as axiomunic clusters. So these are dense structures, dense objects made of axions, which have a typical mass of the order of the asteroid mass, 10 to the minus 10 to the minus 11 solar masses. And the radius, which is comparable to the distance between the sun and the earth. So you would think this is a quite dilute object, not diluting an asteroid over a volume equal to the volume that has a radius of this size. Yet this energy density is 100,000 to one million larger than the average teratomatter density. So even if these objects are so dilute, they're still, they still store a larger fraction in energy density than what we expect from the local dark matter abundance. These objects have been recently studied in numerical simulation from embodied simulation. So the idea is to take the simulations that I showed earlier for the Pachequine field as initial condition at matter radiation equality and then follow the evolution of this over density as structure formation evolves. And this leads to whole statistics of these objects. So we discovered that this is not the monochromatic spectrum. It's not that all of the axiomini clusters have a mass of the order of 10 of an asteroid mass. This is actually upper bound. And mini clusters are formed in all mass ranges with some halo mass function. And then structure formation would form even larger axiomini cluster by hierarchically merging these building blocks together. This is the idea that comes then for what I'm working on which is axiomini astronomy. This idea has been used already to study the conversion of galactic axiom. So axioms that are not bound into structures into mini cluster, but they just make up the ambient dark matter that we see. And since this particle convert into photons in the presence of a magnetic field, why not use the magnetic field that's hosted by a neutron star? So neutron stars are environments, possess an environment in which dark matter axiom would fall and convert into radio waves that are potentially observable at Earth. Why radio? Because this is the energy of a photon associated with the rest mass of the axiom which basically we can say it has a mass of the order of the gigahertz if it is the dark matter. We know that for a neutron star, well, there are models for the magnetic field around the neutron star. The most studied of which is the Goldreich-Julian relation which is a self-consistent relation tells you what the magnetic field is and what the number densities of charged particles around a neutron star. So both of these quantities are inevitable around the rotating neutron star. And axiom photon conversion would happen when the plasma frequency associated with the distribution of charges around the neutron star would equal the axiom mass. So we expect if we look at a neutron star, we expect to see some radio waves coming from it if there is axiom dark matter falling into the environment of this neutron star. This is the setup. We have a neutron star that rotates around its z-axis with some magnetic field oriented in some m direction. We are at Earth at some distance from this neutron star and we see this signal. So we can place a bound on the axiom photon coupling versus axiom mass space that I showed earlier. We can place a bound based on the sensitivity of radio astronomy that we can exploit. A similar idea can be used for, not for ambient galactic axiom, but for axiominiglasters. So for this, we have first to assess how many axiominiglasters are there today. So the M-body simulation that I discussed before give us what I call the initial helomass function. So we know how the number density of axiominiglasters is deep-series with their mass in the case in which we have an axiom-only universe. I think in this universe, there is also stars. There are different potentials that in which the Milky Way evolved. And this would disrupt these floppy environments made out of axioms. So for this, in order to assess this, we run an M-body simulation in which our axiominiglaster collide with ordinary stars in the galaxy. And we see as a function of the galactocentric distance, how many of these axiominiglasters survive to date. We see that so given this dashed vertical line as the position of the solar system in the galaxy, we see that in our model, most of the axiominiglasters have survived to date in the vicinity of the Earth. But then as we move towards the galactic center, the survivor probability quickly drops to zero and within one kiloparsec from the galactic center, there are no axiominiglaster because there are just too many stars. All of these axiominiglaster have been swollen. They have been disrupted tidally by the encounter with nearby stars. So if we are looking for a signal from this object, we can only look in the vicinity of the solar system. So my collaboration includes Thomas Edwards, who's currently a postdoc in Stockholm University, Bradley Kavanagh, who's currently in Spain and Christopher Eniger here in Amsterdam. On top of the survivor probability, which is the blue line, we also have the interaction probability here, which is the orange dashed line. What is this interaction probability? Is the probability that a neutron star interacts with an axiominiglaster, given some cross-section that depends on the relative size of the two and the gravitational focusing that they might have. And we see that because of the shape of the survivor probability of axiominiglaster, this interaction probability peaks at the radius, a galactic center radius of the order of a few kiloparsec around the three kiloparsec. It then drops for inner galactic center radius because the survivor probability drops. And it also drops at larger values because there are fewer neutron stars. So the chance that an axiominiglaster hits a neutron star as we move far away from the galactic center radius, so far away from the disk. The center of the disk is more and more faint. Okay, so we see how these encounters are distributed. Most of the objects of the neutron star are distributed in the galactic disk, so which is this line here. Whereas the axiominiglaster make up the halo of dark matter, so they are distributed spherically, evenly over the whole sphere. We see basically that we come up with a donut-like, ring-like shape, which is placed on the galactic axis, in which we have basically the most chances to detect axiominiglaster neutron star in encounter. In our simulation, we also check what the duration of the encounter is as a function of the peak flux. And we notice something interesting. So we have basically two populations of axiominiglasters that give rise to two different types of signal. One population gives rise to relatively short and bright signals. And these are due to the axiominiglasters, they are the most dense, the densest one. There is also a population of axiominiglaster that gives rise to a signal which is fainter and lasts longer in duration. Coming from axiominiglaster, which are less dense. This is because some of the axiominiglasters have been disrupted and they make up this second population, so they have lost some of their mass. Whereas the axiominiglaster have not been disrupted, still there in the halo, when encountering a neutron star, give rise to the most bright fluxes that we can observe. So these are the ones that we hope to observe in the future if some search of these objects with axiominiglaster, the astronomy would take place. I have here a video that would show this. So now I'm going to do something that shouldn't be done, like getting out of the presentation, but I want to show you how we expect one of these encounter to look like. So this is a very preliminary simulation again. We expect to have a background of a signal that with time, that gives rise to some signal in Mikoyansky due to the fact that we have many low density axiominiglasters. So these are puffy and the neutron star take a lot of time to transverse them, but we also have from time to time some encounter with some much denser and so much smaller axiominiglasters, which also gives rise to these peaks that we can hope to observe. Let's go back to the full screen presentation. Okay, so I just now want to talk about another topic, which is gravitational waves from these cosmic strings. So I showed you that in simulations of our petroquin field. Let me take a seat. In the simulation of this petroquin field, a complex field, we expect a network of strings to develop. This is actually fairly known already from the 80s, from just from simulation of complex color field that don't necessarily are the petroquin field. The petroquin field. So what happens here? We have at all scales strings, so strings with the length of the order of the horizon, the Hubble horizon constantly enter the size of the horizon and are sliced up by the fact that they intersect with each other and they might also form closed loops, which vibrate, they have some vibration modes that radiates energy density away in depends on the theory in golden bosons or axioms or and gravitational waves. And this makes these loops shrink. This is observed in numerical simulations of the string network. And this would make basically the string network lose energy into both axioms and gravitational waves. In the theory of the QCD axiom, the amount of gravitational wave is subdominant with respect to what the strings radiate into axioms. So you never hear about gravitational waves from the QCD axiom string network. Moreover, the string network of axioms dissipates as the QCD phase transition because of the main walls. So it doesn't last until today. And this makes this amount of radiation even less predominant because then whatever is left from this radiation is redshifted as the inverse power to the fourth of the scale factor. So much faster than matter and we don't observe it today. Now, is it really true? Is it really true in every cosmology? So let's see, what do we know actually about the standard cosmology? We know that there is some plank air in which inflation might occur. So I've got the area in which inflation might have occurred here, but then our inflation ends. We enter into a reheating stage that goes into the radiation part of the universe in which relativistic degrees of freedom take place. And these particles would cool down because of the expansion of the universe. We enter into nuclear synthesis. And then when the universe cools down again, we allow for the nuclei to form. This is the last scattering surface. This is where our CMP forms. And now we enter the era of atoms which clump and make galaxies today. And here we are. Point is that we have a direct evidence of this picture only up until the first three minutes. So we don't know what happens in the first three minutes of the universe. So what happens before big bank nuclear synthesis? This is a big black box from which we don't have relics. We don't have evidences. So we can say that our standard cosmological scenario in which we have a radiation-dominated universe that transitions into matter-dominated universe and then to our present one which has a considerable amount of dark energy. Only we can have this fiducium of this fiducium model only up to some temperature T max. So maybe, oh, maybe this T max is 10 MeV, maybe it's 100 MeV, maybe it's 10 GV. We don't know how much we can push this picture up into this black box. So we can think about other possibilities, other non-standard cosmologies in which this T max varies. This has been done, for example, by considering the spectrum of gravitational waves as a function of their frequency and considering how much gravitational waves are shed from, are released from a cosmic stream network. So in this plot, we have a stream network that radiates gravitational waves, mainly gravitational waves, up until today. In the standard cosmology, we would see this black line. So this black solid line is the expectation of this model in the standard cosmology. But if the universe is standard cosmological model only up until some temperature T max of the earlier one GV, then this spectrum would cut. Following instead this dashed line. And if the T max is even lower than MeV, the spectrum would cut to this dot line. So these three scenarios, standard or some modified cosmology that takes place before when the universe was hotter than T max, can be actually brought in the near future from gravitational wave detectors, such as LISA or BBO. They would be able to tell what the spectrum of gravitational waves from possible cosmic stream network is the nice thing, the sensational thing is that this can be done even for axioms. So this is a project that I've done with a master student, Niklas Vangles in Uppsala last year. We see that basically under certain conditions, we can also see, we can hope to see gravitational waves from axiom streams. So this is a network of axiom extremes. So it's fundamentally different from what I discussed in the previous slide into key factors. First of all, these are axiom extremes. So they mainly radiate into axioms. You don't expect a large amount of gravitational waves. And the axiom stream network only lasts until more or less the QCD phase transition, so around 200 MeV and then it dissipates. Yet there is hope to detect the amount of gravitational waves that comes out of this model. If the universe is non-standard cosmology down to temperature of one MeV or five MeV. So if we really push the parameter space of this model. Okay, so these are my conclusions. Basically there is a lot to do in these models for the axiom, for the scalar fields in general. We have to keep working on details, making estimates and push for collaborations, even larger collaborations that would take together researchers in the theory and in the observation together in order to look for these particles from alternative point of view, not just from the laboratory, but looking for these type of different imprints that are complementary. Thank you. Thank you very much, Luca, for your webinar. It was, for your seminar, it was very nice. So for those that are following the live streaming of the Luca's webinar, please you can start to write the questions. We're gonna go there soon to address that. Don't forget to the people that is following the webinar from the first time to subscribe to the YouTube channel and also to follow us in the different social network like Facebook and Twitter. So we go back to Luca and we'll start with some few questions first from the audience that is here. I don't know if one of the participants, if some of them have questions. Otherwise, meanwhile, I'm gonna be checking what is in the YouTube chat. That's one question I'll come to you soon. Okay, Javier, please. Yeah, well, maybe I'm getting completely round the scales because I don't have any kind of intuition of how big are these objects, but how do they compare to usual dark matter shut-headers that you see in body simulations and related to that, probably they are much smaller and they had a smaller tidal effect, but is there any possibility of serving these kind of things through these reactions in stellar streams like things like Gaia or things like that or they are too small to produce anything? Okay, yeah, so there are different scales. So in terms of whims, we expect the whims to form this type of clumps at larger and heavier scales. Because the whimp form from clumps through the free-streaming length. The free-streaming occurs at the tens of MEV temperature in the early universe. In that case, the mass enclosed is much larger than what we expect for the axion because just because they form at, for the axion forms earlier than for the whimp. So I'm not talking about the seeds for a whimp called dark matter, but then besides these lengths, both the QCD axion and whimp would behave at a larger scale as a cold dark matter. So you would not see the difference until you go to such a low scale, so such a high K in mode, which means that the halos, 10 to the 5, 10 to the 6 solar masses that you observed cannot distinguish between, for the particle perspective, in case of cold dark matter. Okay, well, I only take another question. Yeah, yeah, you can open. It's related to this last strings given to observable gravitational width production that you were talking at the end. So this is also QCD axion or is it a completely? Yeah, yeah, I just used QCD axion. In this talk, I just showed results for the QCD axion. Yeah. Okay, but then if you are able to observe gravitational waves, I mean, you will have also a bit, or a larger contribution into radiation. And is that not violating any kind of bit by neutral synthesis constraints on the amount of radiation? Okay. So let's see. And then I would say no, because we still have the QCD axion as the dark matter. So, okay, you have a basically, something I didn't discuss. The axion can come also as a hot component of the universe, depending on its mass. So if the mass of the axion is of the order of tens to hundreds of microelectron volt, the dark matter component, the cold component is predominant over the dark energy radiation component. Since we are in that ballpark, the amount of dark radiation would still be negligible in these models. Then of course, if you consider axion-like particles or the QCD axion, which is not dark matter and you want to push to heavy axion masses, then you have to be concerned about what fraction of dark radiation would, you would get out of this model. And then you would also get into bounds from an effective or delta-ineffective. Cool, that's it, that's it. Okay, thank you. If there are any questions from the audience, let's wait a bit because we are gonna start. I have one. Okay, you go. So it's related to your previous slide where you showed the gravitational wave. So suppose you have a detection in one of these observatories, there's no way to be sure that it comes from a string, right? From an axion string. Well, yeah, yeah, yeah, yeah. You would, well, if you have a, say you have a Lisa, for example. So you have to match the spectrum. So you have to match the slope of this curve. And this would already be by itself huge discovery because it would tell you we have something new because we have some sort of negative slope that can come up of a string network. Then, yes, I would say you have some sort of degeneracy between different models. Okay, I also want to ask what's the physical meaning of this other maximum? It's giving you some information about something, I guess. Yeah, yeah, yeah. For example, okay. So these spectrum here, in this model, at each frequency, basically we observe, so this F is a sort of, can convert into the moment in which the gravitational wave is released. So this is why we have different slopes here. Basically waves between 10 to the minus eight and 10 to the one have been released during radiation domination. Matter radiation equality, of course, when this kink appears and the frequencies that are smaller than this 10 to the minus eight have been released from the string network after that time. This is why I don't have that type of plateau here. I only observe either the radiation-dominated part or the modified cosmology part. So this peak is basically the transition between the two. Okay, thank you. Okay, so we are going to go to some of the questions that we are getting now in YouTube. So Marvin Flores, he's asking two questions. The first question is, when you say that the theory is one parameter, is this parameter the action mass? Because you show a plot where the action mass is proportional to the action photon coupling. Are the other couplings also present? Yeah, yeah, so basically, okay, so one parameter theory means that, means that the action mass controls the action energy scale, F, just because it's inversely proportional to that, but also the action photon coupling. So one thing is that we have different parameters that appear in this vertex. So how the action field couples to the fermions. This depends on how you embed your action theory into the standard model. So there are additional parameters. Once you choose your embedment, so this E over N basically, then your G E gamma depends just on the action mass. And this is why for a given axiom model, G is proportional to M. This is true also for the other coupling. So the action to the electron and to the nucleons. I hope this helps. Yeah, I think I mean, in the meanwhile, Marvin Flores can write if he like the answer or not. Let's see. The parameter theory wants to know which embedment you're working on. Oh, yeah. So I have a question. I mean, for the moment, I have a question when you were showing these action strings that you were forming in the simulation and by simulation, let's say. This one? Yeah, exactly. That was very nice. But do you expect that the action strings has a large effect in the structure formation or do you expect, for instance, kind of dwarf galaxy to have some population of cause the action strings, action, yeah, extra strings in the, these debilogical effects there, in which you can get some signature, like taking advantage of the same method that people use for standard type and for wind type matter, kind of the centaure galactic center. Okay, the galactic center, you said that it's not possible because you, the population should be very low, but other object like dwarf galaxy or something like that. So the simulation is from Javier Redondo. Take credits for this. But I can tell you about your question, the points that this, the peculiarity of this, of the action is that its first is a massless and then it requires a mass around the QCD phase transition. This makes these string network to leave only up to the QCD phase transition. And all of the actions that are radiated during this period, they get in contact with the population of actions from the vacuum alignment mechanism. So from this mechanism here, and they basically share information and share the distribution, the density distribution, which means that basically they quickly become thermalized between themselves after the QCD phase transition. So you don't probe this string network at subsequent times. So this string network doesn't exist to date, doesn't exist during structure formation or during the CMB. This is gone at 100 and maybe basically. If you consider other string net, other models with goldstone bosons, there are massless or just a string network, then it's a different story. You can make simulations with this type of structures in them. But I don't know the details about those because I never worked on those. Okay, but when you were also presenting before this, I guess the possibility to look for neutron stars interacting with the action that are in the environment. So those are more physically searchable, let's say. Yeah, yeah, yeah. So the story is like basically you have these in homogeneities in the action field. These action field, so these in homogeneities are seen in the energy density distribution. They're huge. And these translate into these dense clumps which are called axiomini clusters. The point is that the axion is a subdominant field during radiation domination because it's a cold dark matter. So if you had instead these type of structures, so these density perturbations in the plasma, you would form black holes, primary black holes. You don't have enough density contrast, basically, to make black holes, so you make axiomini clusters. And they stay, but they collapse at the matraditional equality and they stay to present date given the embody simulations that I discussed. So what is missing now is a embody simulation that takes into account the evolution of the galaxy and the stellar formation and evolution and the merging of the axiomini clusters and how stellar evolution affects this embody simulation. This is not what we do. We basically have embody simulation of axiomini cluster down to some z. We take that result from the simulation of Javier and Egemeyer and Adam, and then we run our model, our Monte Carlo disruption model. So it's the first step towards something more reliable. Something that's not there yet. Okay, okay. No, so these results for the survival probability are not in the literature at all. I see. In terms of Monte Carlo. So there are estimates given some analytic results. They're also valid for generically dark matter sabelos. But the whole literature on what these axiomini clusters do is missing, how many of them are there in the galaxies? And this is a demanding question because, first of all, because of our story, like radio astronomy, which seems to be possible, seems that the signal is actually detectable. But also in terms of lensing and in terms of direct detection. So they would play a huge role and we're just starting to work on this now. Yeah. So let's say, is there any other question from the audience? I don't know. Why? Because it has another one. That's great. No, it's again, it's maybe a bit more technical. When you are showing these simulations by Javier, looking at the plot that you had looks like a field theory simulation. But then you are talking about loops that comes from a Nambu-Coto simulation. There are no loops in these field theory simulations. It's kind of consistent, all the things that you are saying about radiation, et cetera. I mean, so how you can conclude something? I mean, you're like kind of mixing parameters from two different simulations. Yeah, yeah, yeah. Okay. The results that they have on this part on gravitational waves are just, they're not coming from a simulation. I mean, we just did some analytic or semi-analytic model. So we just solved for the equation of motion of the axial field in the non-stellar cosmology. And we estimate the amount of gravitational waves out of formulas. So the results don't come out of simulations. Then is where my problem is kind of coming because you say it's a small fraction before but as you have to plot at least the upper curve is around 10 to the minus eight, but integrated is gonna be a bit bigger. It's gonna be like 10 to the minus seven, 10 to the minus six. And the bounds on radiation or if you want the integrated bound on gravitational waves in the CMV is 10 to the minus five. So the one of radiation should be roughly the same. It's the radiation that you can put in the game. I, yeah, I see. So you're not so far away from 10 to the minus five. I had the impression, but... Yeah. I don't know. My question would be about nuclear synthesis again. I don't know. I have the impression that you're not so far away, but maybe I need to get to know completely about the masses. No, no, no, you're right, you're right. I took those bounds into account. I mean, I computed after word, the posterior in that integral and checked that the result was within the bound. Yeah, but you need the gravitational wave. My question is about the radiation. Yeah. You should get a similar bound for radiation, roughly, not the same order. So for that, I relied on what other people have done in these models and which found that basically the radiation, that radiation is not important at the mass, masses at the actual mass level. I can send you the... I'll send you the link, but basically it's a work of Raffelt. Okay, no, no, it's just my ignorance. I don't know. Again, I don't control the numbers. Okay, okay, yeah, yeah, it's nice to work on that. But yeah, I haven't worked on... I haven't derived the limits myself because working on dark radiation, you have to take into account all of the productions from the blue and brass. So I just relied on what the literature was. Let's... Okay, so we have one more question from YouTube. Percy Gaseves from the book in Rio de Janeiro, he's asking if there are some mechanisms to link the actions from the axiverse to the action string that you show in the last slide. And he is also thanking you for the nice talk. Oh, thanks. Well, these strings are... Yeah, well, these are two different string scenarios, but I would say... Well, if you... Pure string axion, so it's string from the axiverse, basically, if it relates... If you can also relate that to some symmetry breaking, you would observe the same network just at different regimes. So yes, I think, in principle, it's possible... Just that when you talk about the axiverse, you're no longer talking about if you see the axion. So in that case, the parameter space opens so much that it's not easy to give solid answers. So, but in principle, yes, you would have this network just with different... With the different dynamics and different parameters that what you expect for the PCV axion. I see something here. OK. This answers the question. Otherwise, if there are questions, I can answer them on YouTube. OK, so I guess this... We have to stop here to keep the format of the webinar cycle. But anyway, you can follow the rest of the group that is still interested. You can make comments in the YouTube video of this webinar or otherwise contact Luca personally via email or other ways. So first of all, I want to thank Luca for your webinar. It was very interesting. We hope to see you again in a follow-up talk in the future. So for the rest of the people that is following the webinars, let me tell you that next week we are going to have another webinar. But this is going to be by Macarena Lagos that she's post-doc in the Gavli Institute for Cosmological Physics. So everybody is invited to follow the webinar and of course to keep in touch and keep updated with what is happening in higher-energy physics, astro-particle, cosmology and all the topics that we used to cover here in this webinar cycle. So for all the people, thank you all. And see you in the next time. Yeah. Bye to everybody. Bye. I'll stop sharing here. OK. OK, we are...