 Hello everyone, and welcome to our next seminar of the seventh series of the Latin American webinars on physics. My name is Federico von der Palen from the University of Antiochia, and I will be your host today. Our speaker is Luca Visinelli from Stockholm University in Nordita, and he will talk about a very hot subject, a very interesting subject, which is actions in cosmology and astrophysics. Luca received his PhD at the University of Utah, and after postdocs in Bologna at CMCC and at the University of Bologna, he moved to Stockholm, where he is currently a postdoc. So Luca's title is the action in cosmology, and we're really glad to have him today speaking about this subject. I hope there are many people interested in this. And so let me remind you that you can be part of the discussion, writing questions and comments in our YouTube live chat system. So now let me pass you to Luca. Luca, no, you have to unmute yourself. Sorry. Thanks for the great introduction and for the possibility to speak today. Okay, so should I start with, let's see, how do I share the screen here, screen share? Screen share, this part, okay. Good. So now you should be able to see my presentation, right? Yes. Go on. Thank you. Okay. Very good. And you can even put it like this. Okay. So today I'll mainly discuss a paper done in collaboration with Sebastian Baum, Javier Redondo, Keterine Fries and Frank Wilczek. So Sebastian Baum is a graduate student here at Stockholm University. Javier Redondo. Excuse me. We're not seeing the presentation right now. We're seeing you. Are you done? Ha. Okay. But now, yes. Now you do. No, no. No? It was for a second there. Huh. Just share and share screen again. Sorry. Yeah. Let me try to... It doesn't allow me to share again. It's going on. Yeah. So let's... What's happening? It was working before. I clicked the green button, right? The second one. But now it's not working anymore. Screen share. So strange. So what should we do? Let me try something else. Yes. Let me try to join from here. Let me see if I can share a screen. Oh, sorry for that. I don't know what's going on. Don't worry. Let's see. I'm sharing a screen right now. It's working. Okay. Let me try from a different browser. Maybe that's what it is. But it was working before. It was working, yes. It was working when we tried. Yeah. That is unexpected result of the live streaming. But don't worry. It's okay. Okay. How about this? Okay. Let's try this. Okay. Now it's working. Perfect. Yeah. Now we can see you on the slide. But we need to close the other browser. Because now we have to duplicate it. I closed it already. Okay. So it's perfect. And we can hear you. Okay. So now it's good. I'm just going to share. Yes. Now what happened? Okay. Here. Here. Share. Good. Fine. Sorry for the problem. I'll speak quicker. So now it's fine, right? Yeah. It's perfect. Very good. So I'll skip the introduction. Basically I'll talk mainly on the paper that came out in 2018. The dynamic collaboration with people here. And with Javier Edondo you already had the pleasure to host him in your webinar series. And my talk will be about mainly about the loot and dance action stars, which is the topic of this 2018 paper. I'll take the lead to also talk about other papers that have done on axels in the past. Because I want also to cover the action as the co-dark matter particle. And as a co-dark matter of candidate. So in my first slide here I speak about motivation for the action. The motivation comes from the fact that in the QCV sector, which theoretically is expected to find to yield the CP violation term experimentally, we don't find such a CP violation. So we have this parameter theta bar, which in principle could be of order one. And then in practice is constrained to be less than 10 to the minus 10. So this is sort of a strong, a naturalness problem. We all in order to solve for this problem, the chain queen into 1977 introduced a new U1 symmetry in which this parameter theta is not a parameter anymore, but it's a dynamical field that relaxes toward the minimal energy configuration, which happens to be the configuration in which theta is equal to zero, which leads to a CP conservation from the QCV sector. This is now called as the chain queen solution in which there's a new U1 symmetry introduced. Soon after this in 1978, we'll check in Weimberg independently into parallel papers, realize that an axiom, so a new particle is associated to the breakdown of this U1 symmetry. And it's called the axiom because it cleans to get rid of the chain queen problem. After this, many models, so benchmark model like the DFSZ and the KSVZ model were introduced. In the DFSZ model, we have additional Higgs fields, while in the KSVZ model, we have an additional Havoc work. So these are sort of minimal models that augment the standard model and also include the axiom. There are sort of minimal viable axiom model and still the benchmark model today. So these are the models that people test and look for axioms in today's research. In the same year, so early 1980s, the axiom was also pointed out as a possible candidate for the cold dark matter. And this is why the axiom is such an interesting particle for its phenomenology, because it could both solve the strong CP problem within the QCD sector of the standard model and provide a solution for the dark matter problem. All of this within basically two orders of magnitude spent by the possible values of the axiom mass. So it's a well constrained problem that people are now trying to address experimentally as I'll talk in my slides later. So axiom coherent oscillation, the axiom is a very light particle with its masses in the range of the 10 to 100 microelectron volt if you want to address the axiom to be the cold dark matter. And to do so, in order to be a cold particle, it has to be produced non-thermally. And a way to produce it non-thermally is through this misalignment mechanism in which the axiom sits at the bottom of a Mexican hat potential. This is through the usual Pachequean breaking. But then at temperatures, at range of the order of the QCD phase transition temperature, non-trivial QCD effect tilt this Mexican hat and the axiom, which could sit anywhere from zero to pi at the bottom of this potential, feel the presence of this additional potential of this additional tilting and start to roll towards the true minimum of the potential. So to the minimum of the potential with a coherent motion. And this coherent motion today behaves as cold dark matter as we see in the next slide here. This is a slide from Javier in which the axiom could sit anywhere between minus pi and pi. It starts to roll down. If you take into consideration the equation of motion and you solve it, you actually find that in any cosmology, so for any given value of the, any given time dependence of the Hubble rate, your energy density of axioms always behave as a cold component, so as a matter. So it scales as the scale factor to the minus three. This is today's perspective and the future searches for axioms in the laboratory. So in the, on the x-axis I've put the axiom, the mass of the axiom in the electron volt ranging from the order one, ten electron volt to ten to the minus fourteen and on the y-axis I've put the axiom photon coupling in the inverse GV. So the solid regions are regions where the searches has already been excluded except for the yellow band, which corresponds to viable axiom models, the DFSZ and KSVZ models I've discussed previously. The hashed regions are future regions that will be in reach of given future experiments that are either underway, like IAXO or proposed, like abracadabra. So the axiom requires an effective axiom photon coupling through a fermion loop, and this is the insert diagram that I've put on this slide. If you compute the value of G through Feynman diagrams computation you actually find that G is proportional to the axiom mass. This is why the line, the KSVZ and DFSZ lines are lines with constant positive slope, because G is proportional to M given some theory. So you choose your theory. So you choose basically the charges that are the vertex of this Feynman diagram and you gauge where this proportionality constant is, where this line is. Okay. So we see that there's a lot of parameter space still to cover. The CDM, okay. So this yellow band here is divided into different, various different regions. I've put the CDM bound here in light red. This is the region, which corresponds to around 10 to the minus 5 electron volt in axiom mass. This is the region in which the axiom is favored to be the cold arc matter particle. So if the axiom has a mass and a coupling constant so that it lies in this region here, it would solve the cold arc matter problem. If the axiom is heavier, it would fall into the subdominant part here. So it would still be a particle, a particle that exists in the standard model and a strong CV problem, but it would not lead to a solution of the cold arc matter. It would be a cold component of the universe, but it would be a subdominant component. The exclude region comes from the fact that if we go in this region here, the coupling constant would become too strong and we would have astrophysical effects, like cooling white wolves or with the same effects coming from the 1987 supernova. All of these regions that I've talked about now assume that the initial value of the axiom field, so where the axiom field sits at the beginning of its evolution, is of the order of one. But the axiom field initially can be much lower, can have a lower value, can have a lower value of order 10 to the minus one or 10 to the minus two. So we can fine tune this parameter in order to have the proper amount of dark matter today. And this is what's called the anthropic region. So basically going lower in mass from 10 to the minus five down to 10 to the minus 13, 12, roughly, the axiom can still be the dark matter. But the initial value of the misalignment angle has to be fine tuned in order to fulfill this requirement. Otherwise, if we start with a value of theta of the axiom angle of order one, so that's too large, we would have too much dark matter today, we would over close the universe, and this would not be allowed, of course, would be against the data that we see. Eligo here is the proposed detection by as you mean, Arvani Taki, and the Planck region here means simply that f would be, will become transplankian here in this region. So I just excluded it. Okay, anywhere else in this parameter space, so away from this yellow band, away from the QCD axiom band, we would still have particles, it's possible that we find actions in these other regions, but these would not be the QCD axioms in the sense that it would not be a strong CP problem. It could be dark matter particles, but they would not be the standard model axiom, the axiom that solves the strong CP problem. They are called alps, axiom-like particles, you know, because the share of similar properties to the axiom, for example, the same effective axiom photon coupling, and there would be pseudo-scarabosons basically arising in various theories. Okay, today a new PRL paper came out and, okay, what's going on? Sorry. New PRL paper came out which is this solid dark blue line here that extends the previous finding of ADMX to a region in which the DFSZ axiom is also probed. So this is basically an expanded region that shows these results better. So basically going back to the previous slide comparing here with the previous result of ADMX here which could barely touch the KSVZ line, the new result extended the DFSZ in a portion of the region that was probed before. So this is a very narrow band that the ADMX work takes actually a lot of time, every time they have to recalibrate the whole experiment, the whole set. So if they knew where the axiom were sitting they would be very fast in finding it, but since we don't know, even in principle what the axiom mass would be, could be anywhere in this micro-electron volt to 100 of micro-electron volt range they have to reset every time the cavity. Okay. Now, this is again from Habir. So what happens here? This is a medical simulation in which the axiom field, actually the whole Pechenkwin field, so the whole complex field is simulated in which the axiom is just the angle variable of a complex field. In this scenario here the Pechenkwin breaks after inflation. So we don't enjoy the benefits of inflation which basically erases all of the substructures and leaves out with a smooth field, but we have to deal with all of these all of these field structures in which the axiom field ranges from minus pi to pi and the axiom energy density varies within the same Hubble patch. This leads to various different features today that are actually detectable, one being the axiom string network so there are regions in this 2D slice in which the axiom field winds up from minus pi to pi around a point and in 3D this point is actually aligned in which the axiom field winds up around this is called an axiom string so it's a high degree of so to high degree of precision this is a cosmic string behaves as a cosmic string so for that reason you want to get rid of that you want axiom strings and other topological defects like the walls that are in this other picture here to wash out otherwise we would see their effect, they would come to dominate the universe today okay and there are actually debates on how this axiom string condensate the case into axioms so these are additional sources to the cold dark matter component of axioms today because they would also radiate and decay into cold axioms and the effect could be of the same order if not more than what we find from the misalignment mechanism another effect would be the axiomini cluster so in some regions the over density would actually be of order one if not larger I think here in this paper by Colvin Kachev who were among the first ones to study this effect the over density goes to be of order 20 so these over densities in the axiom energy density detach from the detach and basically at the matter radiation equality they would form structures that are basically that would lead to some effects to some power spectrum erasing which could be could have some imprints today and I'll talk about this in a slide later if the pressure queen breaks inflation we have the breaking so we have all of this filled with different configurations but inflation singles out a patch in which theta is homogenized so we don't have any of these features we don't have mini clusters, we don't have strings or walls because they have been washed out they've been taken far out from the size by inflation today and we just have to deal with one initial configuration so what's the amount of dark matter today? What is the allowed parameter space? since inflation plays a role here because whether the patch and queen symmetry is broken before or after inflation we have to completely different scenarios, we also have to take into account when inflation ends and this is the Hubble rate at the end of inflation it's a new parameter in the theory this is taken into account here so in this slide, in this plot I've put the HI, the Hubble rate at the end of inflation on the x-axis this in single model inflation is directly related to R which is the tensor to scalar ratio which is a measurement of the primordial gravitational waves the amount of primordial gravitational waves on the y-axis I've put on the left the axon decay constant which ranges from 10 to the 9 to 10 to the 18 gb roughly when the axon decay constant is inversely proportional to the axon mass which is on the right hand side of the y-axis and we see that the axon mass is of the order of the micro to well millimicron nano electron volt so these are the energy scales that are in play here for the axon mass I've put some of the known bounds so for M I've already talked about the upper bound on the axon mass which is the red giant brightness but there are actually various astrophysical constraints that come from either red giant brightness or white dwarf cooling time it depends on the axon model you're dealing with whether the FSC or KSVZ but they pointed around the same order of magnitude for the bound on the axon mass as for HI tensor mode constraints are to be smaller than 0.07 and there are actually forecasts for the next for the next generations that would push this value to being below 10 to the minus 10 to the minus 2 or even 10 to the minus 3 this is the forecast that I've put here without coloring in yellow so this is the ADMX with its forecast result this is the result that we already knew of ADMX the forecast is for the future experiments this is what they want to have covered this is the proposed ADMX and the proposed IAXO forecast some regions that parameter space here would be probed in the next 10 years 5 to 10 years okay this line here FA equal to HI separates the two regions the two scenarios that I talked before the axon field breaks during inflation and this is the scenario on the top left side from the scenario in which the axon field breaks after inflation this is the bottom right side so basically high value of FA is equal to breaking during inflation lower value of FA correspond to breaking after inflation roughly this is because iso-curbiter fluctuations are produced during inflation so the axon would both have iso-curbiter and diabetic fluctuations during the spirit constrained by Planck so we see that we cut out a huge region of the parameter space but we are left with a window here which nevertheless hints at a value of r which is really low so in order to have anthropic axons so axons for which the initial value of the misalignment angle is small is equal to 10 to the minus 3 in order to have the correct dark matter abundance we need r to be less than 10 to the minus 9 10 to the minus 10 so of course this is even a theoretical challenge because r can be well there are many sources of primordial gravitational waves that could hint that r in order 10 to the minus 3 we will know soon in the next 10 years would be really problematic to have an axon in this window let's turn our interest to the other end to the other scenario in which the axon is produced after inflation so omega a larger than omega cdm is the bound for the overclosure so you don't want to produce too many cold dark matter axons and this sets a limit from below on the axon mass the parameter alpha here parameterized the amount of axons that come from strings from topological defects that come from the misalignment angle so alpha equal to 1 means they have the same contribution from these two effects to alpha to 100 meaning we have 100 more times axon from strings and other topological defects other than the misalignment mechanism so the alpha equal to 1 or the alpha equal to 100 which debate in the literature of what's the value of alpha this actually is not quite settled so semi analytically there were two different sets of paper debating about whether alpha equal to 1 alpha equal to 100 or 200 even numerical solutions of the string condensate hinted that alpha equal to 10 although more recent results hinted that alpha equal to 1 even for a numerical solution so this is not settled yet and there is a lot to say now I want to talk more about mini-classes and dilute stars so mini-classes are over one over densities on the initial spectrum of axons so the mass is the mass enclosed within a Hubble rate when the axon fields start to oscillate which correspond around to the QCD phase transition while the radius is fixed by the density given at the matter addition equality these are the computation that I've done for an axon mass of 100 microelectron volts this is for a sizable contribution from axon strings the masses of the order of 10 to minus 16 solar masses for a mini-classes but you can go and have axon mini-classes that are up to 10 to the minus 12 minus 11 solar masses it's easy to tweak these models here and the radius is of order the astronomical radius so the Earth to Sun distance so the problem with the mini-classes is if most of the axons are in mini-classes and we don't know today we don't know what the fraction of axon actually contents into mini-classes we would have very few encounter with these objects so we have like one encounter every million year of 100,000 years so it would be very rare and if most of the axons are in these structures we could this could affect the direct detection of axons or even if axon mini-classes are not mostly condensed into the structure still we would have to take into consideration the structure in any case even if we find the axon to be the code because at that time then we would need more precise and refined measurement coming from the density distribution from the energy density of the axon and this would in any case have an impact so we have to take out the fraction of axon that goes into mini-classes if we want to make a precise physical estimation of the cosmology of the axon if this particle is ever found and it is the dark matter now what are the axon stars so this is another piece of history missing and requires further a lot of studies this is what I think so axon stars are well are boson stars where the boson is the axon boson stars have been known since the late 60s so these are well studied objects in which the self-gravity which is the first term in this u in this potential energy is counterbalanced by the kinetic pressure which is the second term m2v2 so for axon stars the kinetic pressure is provided by the fact that you are packing a coherent currently oscillating field into an object of a size r which means that is the Heisenberg uncertainty principle that gives you the required motion of the particles, the uncertainty momentum spread which gives the kinetic pressure in addition to this we have added the third term u which is the axon self-interaction not only the poetic potential but the whole cosine potential that the axon feels when the Mexican had potential so we have added all of these terms in our analysis in the paper so for the paper that we have cooked up we do not talk about the formation of these objects in a cosmological environment or a physical environment, we just talk about how axon stars would look like today because even that was a missing piece and there was some literature we were not actually satisfied with and we were criticizing in our paper the formation of axon stars is a completely different topic and today there is still a lot of work to do we think that axon stars could form cosmologically inside the axon mini clusters so if you are able to produce an American simulation that is refined enough to look at the mini cluster and look inside of it you should be able to distinguish the axon star or this is what has been done in 2014 with ultralight axon that self-interact this object could also be formed hierarchically but this is not what we covered in the paper we only covered the hydrostatic equilibrium which is given by this plot here on the x-axis I put the mass of the axon star in these fancy units which is f2 over m we use these units because they are so universal profiled it is not only good for the qcd axon but also for axon-like particles this is against on the y-axis the radius of these objects in units of 1 over the axon mass so let's start from the top if I okay so this line here negative slope line represents the first two pieces so we just neglect the self-interaction of the axon and we look at the hydrostatic equilibrium of the objects in which the connected pressure is counterbalanced by gravity so for this branch here which we call the valued branch in the paper the self-interaction is actually negligible so we put the self-interaction into this region of development space this interaction can be safely neglected these are stable configurations in the sense that the second derivative of the potential is positive which also means that if you displace a little stable configuration from this blue line dynamics would be such that the axon star stable axon star configuration today they would survive to today if they're not stripped away by tidal disruption or if they survive further mechanisms what happens next so what happens if you increase the density so if you increase the density you move along this line and this is given by these arrows here if you increase the density you basically arrive at the point in which the self-interaction can no longer be neglected and actually overcomes the effects of the self-gravity so you have to remember that both self-gravity and self-interactions are attractive that's why they can counterbalance the effect of the kinetic pressure which is repulsive okay so if you do the computation you find that the radius is proportional to the mass that's why the slope now is positive but the second derivative is negative which means that these axon stars here in this configuration cannot be existing they either blow up and go back to the dilute configuration or they collapse to what so black holes maybe these other branches that blow maybe let's see what happens what's important to see is that there is a kink here between the dilute and this red slope branch and you cannot find any axon star that has a mass larger than the critical value that's given at this kink here so this is a sort of cut-off value which for the QCD axon is of the order of 10 to the minus 12 solar masses above which axon stars in this simplest configuration don't exist now if you keep increasing the density of your axon star so if you keep cramming axons into this axon stars and you actually end up to a configuration where you reach basically the value of the axon field to be over there one in this region here what we criticized in the previous literature is that they would still use a normal relativistic approximation but now axons in this configuration are relativistic so you have to use the whole Klein-Gordon equation actually the Sein-Gordon equation if you use a Sein potential for describing the self-interaction what we found numerically is that the density is constant which explains why we find a relation between the radius and the mass as given here are proportional to the one third because this would yield a constant density but the important thing is that these objects are metastable so an axon star in this configuration would radiate away relativistic axon shrink until it goes back to the kink and then collapse which means these objects also don't exist this was the original motivation of the work I was reading about these dense axon stars and I was checking if they could also give a signal in gravitational waves like from spiraling merging or other types of signal but while redoing the computation I found some discrepancies and this is the outcome of that actually the whole picture what the axon stars do is the outcome of this curiosity there is a lot more to do there is the whole picture the whole history has to be defined people still don't know because the numerical simulations start to be available and accessible now this is basically what I want to do in the following months and years ok so come to the conclusion which basically I hope I showed you that axon are well motivated it's nice to know that they are also falsifiable because there is just a couple of orders of magnitude in which the qcd axon could live it could take decades but still we would get there at a certain point we need a lot of work on understanding mini-classes and axon stars from the first principle and to actually be able to give a number for the fraction of axons that today is condensing to streams and mini-clusters that's all ok thank you ok thank you very much for this very interesting talk about the axon axon landscape and prospects of understanding the structure of axons now let me remind you before we pass the questions that you can take part of the discussion writing questions and comments on our youtube live chat system so first I will pass you to the questions in the audience yes I have a question for Luca I was very I mean I got my attention about these axon stars that we were talking about at the end so one question would be how do you expect that these axon stars radiate photons I mean let's say because at the end axon emits decays into two photons let's say when they are in vacuum we are not this over-density but do you expect that these kind of could be mistaken like a regular star or just like a star that emits monochromatic photons or monochromatic plus some dispersion because some extra effects or something like that ok if it just looks like a star I would not because well think of the Feynman diagram that's an axon that goes into two photons so you would need so what can you have you can have an axon decay into photons and that basically is we know that for the axon this is too long it's many other magnitudes larger than the age of the universe the frequency of the axon of the photon that would come out would be a fraction of a millie electron also would be very hard to detect if ever so for for the axon star per se I would say no but we don't know what's the distribution of this axon stars and also mini clusters because the mini clusters are the objects that are actually out there the axon stars are just the cores so what would happen what if these objects encounter a magnetic field then things would come interesting because then you would have a conversion of these axons some emission it would be eaten up by this magnetic field probably I don't think this has been done much so this could happen definitely for the signal you would first need to identify where this region of large magnetic field is I'm thinking of a neutron star now but the cross-section would be too small the cross-section between a neutron star and an axon star would be too small or even a mini cluster would be too small to give a probability for this encounter I think so you need first to find a galactic environment and then make a computation of this I would think but in that case it would be possible but continue with the question because I'm curious about this axon star an axon star made only of action could be kind of rare for the start as you were saying wouldn't it be an extra signal if these action stars are surrounded by variants and there is an interplay between a small component of variants so you have like a a neutron star I call them stars because of the hydrostatic equilibrium maybe that was the first thing to say so there are stars in the sense that you have a balance between the self-gravity and the kinetic pressure there was a study on the accretion of matter like hydrogen from these objects from the dense branch but they were using the previous results in which these dense stars were stable and the stars are not stable because the action is relativistic inside of them so you have to basically basically today the second and third branch don't exist you only have actions in which the gravity and the kinetic pressure are counterbalanced and these are boring because they are not dense enough to produce any interesting effect in the sense of gravitational waves or in the sense of accreting material they could be interesting for other reasons like when they get stripped or if the earth goes through them but not for these other effects that you are asking okay, thank you I don't know if there are any questions for other people no, yeah, that was my question about the stability yeah, that was my question only the first branch is stable thank you the third branch would be stable in the classical sense like if you do the classical stability analysis but you have the relativistic effect and the quantum effect also that come in the quantum effect being this release of an action or relativistic actions thank you Luca like a question from someone who is ignorant on this subject I didn't really catch up what's the largest structures that these stars can have of these creations can have and I was wondering if that could have any effect on dwarf galaxies but I guess you answered that they don't well, you have to remember that these are still, these are dogmatter candidates the axon is a dogmatter candidate if they clump into mini clusters if most of them clump into mini clusters then the mini clusters become the building block it's like having particles it's like having the wimzilla basically you don't have a coherent field of axons anymore you have these objects that then undergo electrical structure formation so first you form the mini clusters and then at the time of structure formation you form halos of mini clusters so the thing is the mini clusters are much smaller than the pre-striving length that you would find with wimz so you find a structure formation that's different from what you expect with the dark matter this is another aspect that has not been really covered and that I really want to address in the near future as well so there are some papers on structure formation with axons but there's still a lot more to do especially in view of the new numerical simulations that you can perform with the pre-striving field it depends on the axon model on the model of the axon and on the mass what I said before is one AU that's for the most interesting case for the QCD axion that is the dark matter but you can think of ultrawide axions you have basically two parameters to tweak the value of the axon mass and the decay constant which for an axon-like particle are not related with the axon they are but the axon-like particle are not ok thank you are there more questions? so last chance well if not let's thank the speaker again and we learned a lot at least I did and we'll see each other in our next webinar in two weeks and so thanks again thanks, thank you very much bye bye everybody