 Good luck. Hello, everybody, and welcome to the Latin American webinar of physics. Today is a very nice speaker that we're going to have here in the webinar cycle. It's going to be the webinar 141 of all the stories that we have here in the physics. So the speaker today is Valerie Donk from CERN, and she got the PhD from the University of Hamburg. And after that, she has done postdocs in SISA, in Trieste, and in APC in Paris. After that, she was a junior faculty at DESI in Hamburg, and currently, since 2020, she is at CERN. So Valerie that is here is going to talk about the asymmetries in the early universe. So, Valerie, welcome to the physics, and you can start your webinar whenever you want. Thank you. Thank you for the invitation for the opportunity, and also thank you for the nice introduction. Okay, so let me tell you about the symmetries in the early universe, and let me start by telling you what I even mean by these words in my title. So normally, let me first introduce you to the standard law about asymmetries, in particular about barion and lepton asymmetries in the early universe. So the standard thing that you'll hear is that we know very well the barion asymmetry, both at Big Bang nuclear synthesis and at CMB decoupling from the indirect measurements that we have at that time. And from these measurements, we know that at that time, the barion asymmetry was very small about on the order of 10 to minus 10. And now in the standard model, B minus L, so barion number minus lepton number, and B plus L are conserved below the electric phase transition. In fact, in the standard model B minus L is always conserved. And B plus L is conserved at low temperatures, and at high temperatures we have the spiral processes which drive B plus L to zero. So if you take together this information and you say okay well I know my barion asymmetry is small. I know that I have a dynamical mechanism that drives B plus L to zero, then you would conclude and say okay but then the lepton number obviously alters to be small right and can be at most of the same order of magnitude. So that's kind of where the standard discussion stops right, the standard conclusion is that any asymmetries in the universe or meaning any imbalance between particles and antiparticles is very small. And in particular is bounded to be of the order of 10 to minus 10. And these asymmetries, this imbalance between particle and antiparticle is directly violated or directly related to the amount of CP violation that you have in the early universe. So that's the standard story. Now I want to question a bit the hidden assumptions in this standard story. And they're actually quite many hidden assumptions. Because there's many caveats to the statement asymmetries in the universe are small. The first caveat is very obvious right the first caveat is that the B plus L asymmetry can easily be much larger at earlier times. And then okay we have this dynamical mechanism which drives it to zero at later times but maybe at the very early times, it could have been very big. And the question is, did that leave any imprint in the evolution of the universe. Then the statement that B minus L is conserved is true in a standard model. Strictly speaking, but as soon as you introduce right hand neutrinals, which you kind of want to do anyway to give masses to the neutrinos that we observe. You basically automatically introduce B minus L violation. And then again these these statements as I phrase them above here are no longer true. So given that one can then wonder if we have independent probes of the asymmetries in the early universe, which do not rely on these assumptions. Or maybe what's appropriate symmetries at different times. And one thing that we can check is the asymmetry in the electron neutrinos. Particularly during BBN. So during BBN we have the formation of the light elements and the formation of the light elements involves electron neutrinos in order to convert between neutrons and protons. And so having changing the amount of electron neutrinos versus anti electron neutrinos. This is this is a change to which BBN is very sensitive to. So we can check just from the BBN measurement alone without making any other assumptions. What is the sensitivity to an asymmetry in the electron neutrinos and actually the bound is surprisingly weak. So from from BBN and seem easy even weaker. Well, it's at a similar level so from BBN and seem the observations without making the assumptions that we made above. So we can just conclude that the asymmetry in the electron which we can parameterize by by chemical potential is smaller than about 10 to minus two, which is much weaker than the 10 to minus 10 that we had up here. And even that still has a caveat, because this is only true under the assumption that there's only an asymmetry in the electron neutrino and not in any of the other neutrino species. So if the asymmetry is also in the other neutrino species, then I will have my train oscillations, which will set in just before BBN. So at the time of BBN. The asymmetries will be relatively evenly distributed among the species. So I can imagine a caveat where I have the total asymmetries in all summed over all neutrino species to be zero so total left on number to be zero. I could still have relatively large individual left on flavor symmetry so I could have larger symmetries in the electron flavor, and then the opposite, but same value larger symmetry into me on flavor. And in that case we could not use this bound at all because the neutrino oscillation would have would have pushed these asymmetries to zero. In fact, you can check how strong is the bound from BBN on this case, and it's really only order one. And order one here like telling you telling me that the asymmetry is order one mean the chemical potential over the temperature order one really just means that there's there's no bound at all right because kind of an asymmetry like this this is expansion of the chemical potential doesn't even make any sense. It is it is numbers not smaller than one. So what I want to say here is that despite this kind of standard law that, okay, asymmetries in the in the universe or smaller 10 to minus 10 is actually not true. Right, or that there's cavities to that statement. And in fact, we can relatively easily construct scenarios where we really have very large asymmetries potentially order one asymmetries in the early universe. And that's kind of where my talk is heading today is is kind of wondering. Okay, is that actually true is it really true that we could have a completely asymmetric universe at early times. And we would not know about it today is is that really a true statement. And that's what I want to dig into a bit during during a seminar. So, why is that an interesting question to ask at all I mean one. Okay, it's simply kind of the question what can we actually observationally say about the early universe before we go into any any model building exercises. Then going to model building. Once, if you have this this possibility of having large asymmetries in the early universe that has consequences for barogenesis that have consequences for CP violating BSM physics that has consequences for face transitions because larger symmetries tend to change the temperature at which these face transitions happen. So it has knowing how large these symmetries can actually be in the early universe has consequences for a bunch of BSM models, and also, if you want to chase an ambulance or you can actually even chase a two ambulances here is that our recent hints, I would say, from from BBN and from CNB, which may point to large asymmetries in the early universe. So that kind of has made this a bit of an urgent question to understand what actually are the other asymmetries in the early universe. So the goal of the stock is the following so I will first talk about a bunch of relatively old stuff and the sunset I'll tell you about the ingredients that I need in order to make the argument that I want to make. And all these ingredients by themselves have been known for a while. I mean, some of them for a couple of years, some of them for 20 years. So I first kind of talk you through all the different ingredients separately that I need. And then I put them in the second part of the talk is the following so I will first talk about a bunch of relatively old stuff and the sunset I'll tell you about the ingredients that I need in order to make the argument that I want to make. So I'll tell you about some of them for a couple of years, some of them for 20 years. So I first kind of talk you through all the different ingredients separately that I need. And then I put them in the second part of the talk I put them together. And I show you how from that we get new bounds on the left of flavor asymmetries, which will mean that actually what I said beforehand that we can have these lot or the one asymmetries will turn out to be not true with just standard model physics we can put a new bound. And I'll also briefly touch upon implications for barogenesis. Okay, so let's start as I said by by a couple of ingredients that I need to introduce. And the first ingredient that I need to introduce is the standard model. And in particular the interactions and the conserve charges in the standard model. And as you probably will know this in the standard model above the electric phase transition this tree exactly conserve charges, which is hypercharge and the tree flavored be my cell asymmetries. But if we go to really the very early universe on top of these exactly conserve charges we have approximately conserve charges. One of the reasons is that, as we go higher and higher in temperature, means we go to faster fast expansion rate of the universe. And at some point to different interactions meaning the do cover interaction that this follow run process cannot keep up with the expansion of the universe. And so what this plot on the right indicates is the difference standard model interactions as a function of the temperature of the thermal that when they come into equilibrium meaning when they become efficient. So at very high temperatures, barely no interaction is efficient the top is the first to actually become efficient compared to the Hubble expansion rate. Over many orders of magnitude, all the standard model processes become efficient until the last one which will be an important one is the election you cover, which becomes efficient at about or we say it becomes into equilibrium at about 10 to the five GB. And that means that at any given point in this diagram I can basically separate my conserve charges or sorry my my effective interactions from my ineffective interactions. And for every ineffective interaction it means I get an additional conserve charge, or at least an approximately conserve charge in the limit that that interaction is zero. It means I, I turn off an interaction meaning I have an additional conserve charge in the system. And this just means I can rewrite this this plot as a simple linear algebra system, telling me kind of which interactions which efficient interactions relate the different charges and which charges on the other hand are conserved. So concretely, here, what I'm showing here is for different temperature regimes going from from cold to hot. Now we here have the different interactions that all the different standard model interactions, and the check mark indicates that the interaction is efficient so in the 10 to the five GB, everything except for the electronic cover is efficient. And every time when the chart something is not efficient right instead of the check mark I write the corresponding conserve charge. When we go up in temperature we get less check marks, so less interactions are efficient and we get correspondingly more conserve charges. And this is really just a linear algebra system right so the number of conserved charges, plus the number of linearly independent, equilibrated interactions, has to match the number of total total number of particle species which is 16. So what this means is that if I start at high temperatures, and I put by hand some asymmetry into one particle species, then I need to kind of crunch my linear algebra system. And this asymmetry that I put in one species will, following the, the constraint equations that I have in the system will be distributed among other charges in the system and then as a temperature evolves as different interactions become efficient. So there will be a constant reshuffling of the charges that I put in. This is really just this standard model at work. Okay, that was the first ingredient. The second ingredient that we need is the so called chiral plasma stability. So this is an effect in chiral magneto hydrodynamics. So the system that I'm studying here on the slide is I have a hyper gauge field so you want why I have a thermal plasma of particles. And now for asymmetry is in these particles PC so I will allow for chemical potentials. And I'm describing this in a very coarse grained way, hence the word hydrodynamics right so this is really an effective theory I'm not tracking the individual particles but I'm really describing this as a fluid. These in this MHD how this works is you basically couple classical Maxwell's equation with an effective current with sources is classical Maxwell's equation. And his effective current has the term you would expect, which is conductivity times electric field that's just the standard arms law current that you would expect. And the current also has a contribution, which couples the which is sourced by the velocity of the plasma and the magnetic field, right you can imagine if I have a magnetic field and I and I have the velocity then just the Lawrence force right in that that will give me a current. So this is basically what this term is is telling you. And then, finally, we have this last term, which is called the chiral magnetic effect. So this is a contribution to the current, which is proportional to the chemical potentials a particular linear combination of the chemical potentials which is called the chiral chemical potential. But basically, what I'm what I'm doing here is I'm summing over all the chemical potentials of all my particle species. Every factor here is the helicity, the multiplicity of that species and hypercharge of that species squared. This is the definition of the chiral chemical potential which enters in this equation. And this current here is proportional to the magnetic field. Now that is maybe with surprising right I mean normally you think currents are you understand normally currents are proportional to electric fields right or currents by the Lawrence force right come with a cross product with the magnetic field. So that might at first seem a bit a bit unusual but what's actually going on here is that this is the chiral anomaly equation. This is how the chiral anomaly equation appears in an effective theory of Maxwell's equations in this kind of fluid type type description. Okay, so this is this is the effective current now we plug this into Maxwell's equations. So now I'm going in the first step. Just for the slide I'm going to neglect this term here going to neglect the fluid velocity. And then you get a closed system of equations which contains the helicity, meaning that basically the magnetic field here, the energy in so this is the yeah so this is the, the helicity of the magnetic field, the energy density of the magnetic field, and then also I will have an equation for the chiral chemical potential, which I'm not showing here. So let's look at the two equations for the magnetic fields or hyper magnetic field. So, either here is just a conformal time. And in both cases you have, and I'm doing this in forest space so hence the index k. So the first term in both cases is the diffusion term. So this is what we expect or you expect that I have a plasma. The small scales diffusion is efficient meaning I will have some term which comes with a minus sign so it tends to erase whatever is there. And it comes with a case squared indicating that it's particularly efficient for small scales. Then however due to this caro magnetic effect. I also have a second term here, which is proportional to this caro chemical potential. Depending on the sign of the caro chemical potential right which kind of I designed depending on the asymmetries that I put in in the beginning. This term can have the opposite sign as determined front. So what that means if you, if you solve this equation is a couple of equations right but you can you can rewrite it as a as a just an evolution equation with with a math effective mass matrix. For each possible sign for each of the two possible signs of the caro chemical potential, there will always be one mode, which can become negative with what the effective mass squared term can become negative. So we can have one of the helicity modes, which in a certain range of k modes on a certain range of scales below like so scales above a certain value meaning k values below a certain value, given by the chemical potential. They become tachyonically unstable right and tachyonically unstable again means that they have an effective negative mass squared. So what this means is that you get if you have a system where you have a non zero chemical potential. You can get an exponential growth of magnetic fields. And this this is the current plasma instability right so the name instability comes from the fact that you're happy or something, which is a negative mass squared. So, you get an exponential growth of the corresponding gauge field. And so we can now estimate. How much gauge fields we can produce in this way. For that, we'd actually need to the second equation I'm not writing here so there's also an evolution to close the system we need to also know how this mu y five evolves right in this mu y five. Just evolves according to the caro anomaly equation so the change in the chemical potential is just given by ff dual so basically by by the helicity. So when you plug all of that in together what you what you understand is that as long as this caro chemical potential is non zero, it will source this tachyonic instability. So what happens is that whatever caro chemical potential we have in the beginning it will be completely converted into a helical magnetic fields. And this is given by this relation here so these these factors of temperature and alpha alpha is the hyperfine structure constant. So this is the hyperfine order one factor. They just come from these coefficients and these equations, but basically, and dimensional analysis more or less but essentially this this caro chemical potential will be fully this initial caro chemical potential will be fully converted into and because we can see here we have a differential equation from this differential equation we can extract a timescale, a timescale at which this conversion will happen and this timescale we can convert into a temperature, which is what I'm giving here so this temperature the CPI temperature is the temperature at which this process becomes efficient so at which we convert the chemical potential into helical magnetic fields. And this temperature is given by, okay, here we have just some constants which are the standard model values. But importantly, this temperature is proportional to the caro chemical potential squared. And for values of the caro chemical potential of around 10 to minus three, we find that this CPI temperature is about 10 to the five GV, which is the value at which the electron you cover comes into equilibrium. And that will be important in a second. So, we learned on the previous slide that if I put a particle, if I put an asymmetry somewhere in my system, it will be redistributed across all the particle species. And now we see that this asymmetry can moreover be converted into helical magnetic fields. Okay, then this is the second to last ingredient so this is the inverse cascade so in the previous slide I neglected the fluid velocity. And that because if I put in a fluid velocity back right so this Maxwell's equation is a priori linear equation. But if I include this fluid field which is in turn sourced by electric and magnetic fields, the system becomes nonlinear. And I can no longer solve it with linear methods. But of course, reality doesn't care about that right so in reality we have this fluid velocity. But what happens if I put this fluid velocity back in the system. So, what I said on this slide is kind of all true as long as this fluid velocity is small, which is initially typically the case, but then eventually when this process starts when I have this current plasma instability. I generate large magnetic fields they intern source this this velocity, and hence eventually I will come into the case where I need to take this into account. However, this, this fluid velocity, it does not only make like complicated it also has a very, very interesting effect. And that is called the inverse cascade. So, what the fluid, as I said this fluid velocity term and introduces nonlinear mode couplings, which means you can now transform energy from one mode of your gauge field into another mode. From thermodynamics logic without even solving any equations. You know that the system will want to go into a status where it minimizes its free energy. So we'll want to conserve Felicity because Felicity is an approximately conserved quantity in the system. So we'll want to conserve Felicity but minimize energy. And the way you do that is that you go to very long way like modes because long way like modes have the minimal energy per unit of Felicity. So the inverse cascade basically tells you that as soon as this fluid velocity becomes efficient becomes large, you can convert. You can kind of push your your energy and push Felicity to very large way like modes. And this is something. Okay, this is now very kind of hand wave the argument but people in particular these these authors here have simulated this in great detail on the lattice where of course you can account for all these nonlinear actions. And this is indeed what they find so they find that as soon as your your your magnetic fields are above a certain threshold, which in turn and triggers a large fluid velocity, this inverse cascade is triggered. And the Helicity is pushed to very large scales, which means is protected from diffusion because diffusion was only efficient at small scales. So we saw previously, asymmetry can be distributed among different particle species, it can be moved from the particle species into the magnetic field. So once it's in the magnetic field, it can be pushed to very large scales, avoiding diffusion and hence it can survive for very, very long time on cosmological time scales. Okay, and then the last ingredient that we need is that if this magnetic field survives until the electric phase transition, then we get a source of baron asymmetry. And the reason for this is basically that the current anomaly, so the the ABG anomaly, which on the left hand side of this current anomaly you have. Yeah, the change the change in in baron number left on number. And on the right hand side, you have the Helicity of the of the magnetic fields. And but now what happens at the electric phase transition and here I'm talking about a completely standard crossover electric phase transition is just because you project from hyper charge to electromagnetic charge, you're changing the number associated with the magnetic fields you associate with the master's you want to feel that you have in your system. And that means you're changing one side of this anomaly equation, but that means because the anomaly equation always has to be true that you always have to change the other side. Right so this is a kind of very high level view how to how to see that if you just have helical hyper magnetic fields present at electric phase transition. That will have to lead to a B plus L asymmetry produced during the electric phase transition. Now, you're producing this at the electric phase position was precisely the point in time with his fellow runs the couple. So if you produce this asymmetry much earlier, you wouldn't care because this fellow runs will just wash it out. Now you're producing it just at the time when his fellow runs are decoupling. So there will be a competition between a source term, which is driven by these helical fields and a wash out term which is driven by this fellow runs. And this competition is encoded in this in this in this pre factor here, which I'll talk about in a second, but up to this, this, this pre factor which really depends on the details of the electric of how exactly the electric phase transition happens. This means that the entire Helicity present will up to some order one factor the entire Helicity present at the time of the electric phase transition gets converted into a binary symmetry. Now we can use the. So here, now I'm just plugging in some numbers. So this this term as I said it depends between the competition of the source term and the wash out term, and there's actually some significant theoretical uncertainty and that I would say plus minus. One, two orders of magnitude, at least, but taking the kind of the central value for this for this number, and just plugging in the constants here. We see that we can, we expect to get a binary symmetry, which is about 10 to minus six times the Helicity in units of temperature. And then we use the previous expression how we related the Helicity to any initial chiral chemical potentials. And we see, so this was just to remind you this was this this expression here. Now just plugging in some numbers. And I get a factor 10 to minus four here. Meaning, if I have really order one chemical potentials this equation tells me that I expect a binary symmetry of order 10 to minus four. This would be ginormous completely going against observations. So this this is kind of the logic of what I'm going to be presenting in a second right so as soon what the take home message here is as soon as you have chemical potentials which are larger or particle asymmetries which are larger than 10 to minus six at any early time in the right, it can be way before BBN way before CMB. Then this equation tells you that you are at least in danger of massively over producing binary symmetry. Now, and that's to be contrasted with what I told you beforehand right that I was setting for that kind of current bounds basically telling you, you can have order one asymmetries and and there's no constraint right so here we're seeing okay once we actually take these different ingredients together, it potentially is a constraint. So let's have a have a closer look at this issue. So, so just to recall the the ingredients that we have so far right so so far we said, okay it's done a model interactions reshuffle particle asymmetries, the carol plasma instability converts these asymmetries into electricity. Then with the inverse cascade the solicity can survive until the electric patient position and at the electric patient position, it can generate a potentially large burn asymmetry, potentially contradiction with observations. Okay, so now let's use this concretely actually now set bounds on asymmetries in the early universe. So the situation. Okay, so the situation I want to focus on just for simplicity is the temperature range. Just above the equilibration of the electron your cover, you can also do this in any other temperature range right and you can also look at any other combination of the symmetries. But let's for some simplicity this is some this case let's focus on that. I can compute the carochemical potential at that point where this is just the formula taking into account the hypercharge and the multiplicity of the particles and all the, the interactions that are efficient or not efficient. And this is what I get right so there's, at that time, there's two exactly conserve charges in the standard model which are the two, the sort of this tree right the tree B minus ellisometries and here, because they come with the same coefficient I've combined them right so this is the B minus ellisometry electron and this is the B minus ellisometry in the mu and plus town and then I have one approximately conserve charge which is the electron itself, the right hand electron. In principle, of course, I will have hypercharge right but I said hypercharges Europe because I do want an electrically neutral university and and now importantly we see that the coefficient in front of the electron B minus L and in front of the mu plus tau B minus L is not the same. And the reason for this is obviously that the new cover couplings associated with mu and tau one equilibrium and the new cover coupling that this current plus my stability happens before the electron goes into equilibrium, because once the electron goes into equilibrium, this equation no longer holds. And in fact, then, once all the standard model actions are our equilibrium. The, the, the interactions then dictate that this kind of chemical potential is way zero. So I can only have this car plus my stability above this temperature. Once kind of the would be temperature falls below this value which just means it just doesn't happen. But that's one condition but I gave you earlier I gave you a formula for the CPI right so this this temperature formula somewhere here right and we saw. It's this is why it shows this benchmark value right and now we see it was proportional to mu squared over 10 to minus three. So clearly I need to, in order to have this temperature above this value I need mu five above this value. So going back to now our complete example I plug in the numbers. And I find, as, as you would have just expected by looking at the previous equation that I can, the carousel plus my stability happens. If, and only if the chemical potentials in the individual B minus L flavors are above 10 to minus two. So that's one condition. And then the second condition is okay let's actually overproduce bionic symmetry right so now let's actually compute this bionic symmetry right so this is this, this expression here, a plug in the numbers here. Okay, we overproduce if this value is larger than 10 to minus five. So, clearly, this is the is the stricter constraint, right. So the statement here is, if the carousel plus my stability happens, meaning if the chemical potentials are above 10 to minus two. Then we massively overproduce binary symmetry we overproduce binary symmetry by several orders of magnitude. Right, which is also why we don't have to care in great detail about this uncertainty in this father on processes and the production of this symmetry right because we massively overproduce as soon as we hit this threshold we will produce. So the conclusion from here is that this is the bound one should consider. And that we cannot actually have order one asymmetries in the flavors in order one flavor symmetries, but as soon as the flavor symmetries are bigger than 10 to minus two. This is actually ruled out from just our observation of binary symmetry. So this is a bound which is two orders of magnitude stronger than the than the beyond bound for this particular case of a b minus l symmetric universe. Okay, because it's a nice result I put it again. I put it without the implications of this. So, as I said right so did this bound always applies independently of if b minus l is non zero or zero. If it's non zero. It's the bound is of similar strength than the bound that we already had from bbm just on the electron neutrinos. But it applies in a completely different temperature range and it's derived in a completely different way so in that case it's just an independent bound, but often similar strength. In a particular case of b minus l is zero. Then actually it's it's a factor hundred stronger than the previous bound. It applies the previous bound applied at bbm temperatures right or at CB temperatures. These applies at temperatures larger than 10 to the five GB registers really constrained on a primordial symmetries. So even if you have larger symmetries, which are then washed out over the course of the universe and they're completely washed out by the time you get to bbm, then bbm will tell you, you have no problem. But here, yes, you could still have a problem right so even a symmetries which are only present in the early universe and then get washed out via this mechanism because we kind of hide the symmetry in the magnetic field, in which it's very well conserved that can still cause issues by overproducing burner symmetry. Then now the helium anomaly that I was mentioning so the bbm anomaly suggests right I mean really suggests there's going to be even a slightly too strong word right so this. I mean this helium anomaly keeps on coming and going coming and going every five to 10 years right so not sure how seriously want to take it and I'm not not an expert on the observational observational data here. But if you take it seriously the simplest explanation to explain the data face value is to introduce an asymmetry for the electron neutrinals. And that would require an asymmetry of 10 of four times 10 to minus two, which is slightly above the bound that we put right so I would at least say we disfavor this explanation. However, there's a caveat right because here you need this asymmetry at the time of bbm, we only put a constraint a temperature above 10 to the five TV. So if you generate this this asymmetry below 10 to the five TV we have nothing to say on it. So that I'm not saying that is completely impossible to explain the helium anomaly with chemical potentials but I'm saying if you do want to explain with chemical potentials you have to make sure that you generate them below 10 to the five TV. The bound also disfavor some models of left the flavor Genesis where the idea is that you have larger symmetries in the individual flavors and then they basically leak slightly into some final be my total be minus a little symmetry, but that you need large initial symmetries in the individual flavors and again is in tension at least with this bound. You can of course, I mean, you can like I talk about bounds right because I think that's the more the most robust thing that you can do with this results but you can of course always play the game and say okay well if I have one region of parameter space where massively over produce. And then I also have another region of the parameter space where I obviously underproduce where just if I take this asymmetry to zero. It has to be physics as continuous right so there has going to be some regime but I'm just marginally satisfied is bound, but I can theoretically use this to get the correct burn asymmetry. Now it's probably going to be a pretty horribly fine tuned model, but in principle, you can you can think about building by Genesis models in this way. So we are the result is very sensitive to the exact dynamics of the car plus visibility but is less sensitive to the dynamics of the electric phase transition because as soon as we trigger the CPI, we are pretty confident that we massively overproduce. And on a more conceptual level. What we're actually doing here is if you think where the current where bound on the minus L violation comes from a bound on B minus L violation comes from combining our knowledge about solar ones which while a P plus L with the observed by an asymmetry. This is kind of the standard. How we constrain total B minus L. And now what we're doing here is conceptually actually very similar but instead of using the non perturbative as you to processes we're using the non perturbative you want why it processes, meaning this the CPI. So, if you combine these processes again with the observer and symmetry, you get a bound, which is again a bound on a linear combination of chemical potentials, but it's not the linear combination which is B minus L it's a different linear combination. Here I'm using it to constrain the flavor B minus L symmetries, but you can use it to constrain whatever right I mean it just a bound on some particular linear combinations depending on the temperature of chemical potentials. Okay, so that was the, the first two points, which is actually what I wanted to spend most time on me just more briefly talk about possible implications that this could have for for barogenesis. And the first model I want to start with is this axogenesis model. So the in the axogenesis model. The idea is you have an axon like particle, which is rotating in and rotating very rapidly in some side of Mexican hat potential so you start at large field with values with a large initial velocity, and you're kind of zooming around until then finally you you go down and you you land in the in the rim of the hat but you're still, you're still going in circles. And then eventually at the QCD phase transition, kind of little QCD potential will show up here at the rim of the hat. And then you get back to the to the to the. And then you kind of start producing axon dark matter and these things. So you can get in this in this model here is that you can you can have two interesting consequences of this so one you can produce once we're in the room of this hat and once the QCD potential potential appears to add to QCD scale, and you can produce axon dark matter via the kinetic misalignment mechanism so it's called kinetic misalignment because we have this high velocity in the game. And also because you have this axon like field, which is rotating very fast, which means it acts as an effective chemical potential to the fermions in a game, you can also generate barogenesis to this this mechanism of spontaneous this. So simply true the coupling of the different fermions species to this rotating axon field. And this model is very simple because all you do is add an axon like particle with a specific initial condition. And then in principle you solve two problems to solve axon dark matter you solve by an asymmetry. However, in the simplest model you can't get both simply quantitatively you cannot right so either. You get the axon dark matter right but then you underproduced by an asymmetry, or you get this right but then you overproduce dark matter. There's ways ways to fix that right but in a simplest model this is a story. This model has two regimes. Here up here right when you're before you settle into the room and once you settle into the room. What is important for our purposes is that as soon as you have this rotating field. That's a degree of spontaneous CP violation right it induces chemical potentials and all the particle species and hence it can trigger the carol plus man stability. And if this rotating fields. It's supposed to continue for a long time right it's supposed to continue rotating way all the way down until the QCD phase transition because otherwise it can't generate the axon dark matter. So that means contrary to what I discussed before and right before and I said okay let's put some God given chemical potentials in the universe and see how things evolve. I have an active source term all the way down to the QCD phase transition. So I can in principle trigger the CPI now also below this magic number of 10 to the five Jeff, just because I have an active source term in the system. So this this makes us think that. Okay, here this this model definitely is one of the models that are at risk of triggering the carol plus man stability. So we expect that there should be constraints on the parameter space from the fact of not over producing burn symmetry. So that's what we did. So, yeah, so we, we distinguish two phases right so first at high temperatures before the settling temperature when this inspire phase and then below the setting temperature we're in the local minimum to make Mexican hat. The dark matter production happens around the QCD scale which will be lower than this setting temperature. And the amount of oxygen that you produce is just directly proportional to kind of the initial velocity of the field that you put the carol plus man stability on the other hand happens is most efficient at any time so before the settling temperature. So we can use the formulas I was showing you beforehand to compute the the CPI temperature for this particular model. And we can do the goal now is so previously I said we can avoid the CPI. If we go to temperatures below the equilibration of the electron you cover. It's definitely different right because the electron you cover temperature doesn't actually matter because we have this active source, but we can avoid the CPI if we go below this the settling temperature. But if we're both the settling temperature the CPI will happen. And then what we find again is similar to what we found previously once the CPI happened is just so efficient that it tends to just overproduce the burn symmetry in the entire parameter space. The constraint that we will set is basically this condition here. Does the carol plus man stability happen before this field settles into the room or does it not right and if it happens before that parameter space is going to be dead and if it happens. If it doesn't happen before then you're safe. And this is what this looks like in this parameter space of this model so here you have the the axiom decay constant and the mass of the the radio degree of the Patrick Quinn field. For some particular actual model right in this case the supersymmetric ksvz model. And the white parameter space is the allowed parameter space. This green constraint and the purple constraint are constraints which were previously known. And our new constraint from the overproduction of the binary symmetry to the CPI is this red region here. So, as expected you find that part of the parameter space is going to be excluded, which tells you you know that there are models out there, which were not invented with this in mind right but were invented just to do barogenesis. In principle, the parameter space they automatically come with such large chemical potentials such large CP violation that they actually violate the bound that we put. And, again, you can in principle you can play this game right and say okay if you're exactly on the boundary of this line. Then, in principle, you get the binary symmetry, exactly right. But it's going to be very fine tuned situation, but given given that this model kind of shines because it's it's very minimal. So, for a careful choice of your parameters you can with a very minimal particle content right meaning just an accident like particle nothing else, but very specific initial conditions and very specific parameter choice. You could in principle get both dark matter and barogenesis right. So you'd have a fine tuning problem you definitely have a fine tuning problem. But in principle you can do it with a very minimal particle content. Okay, I think, I think I maybe stop there. I'll give it more time for questions. So let me jump to my summary. So, what we saw is that any spontaneous CP violation in the early universe be it by chemical potentials that I put by hand right or that I put by some pre-barogenesis mechanism I put for example by gut bar, gut barogenesis. So these these types of chemical potentials or also some rotating field, which violates CP all these types of spontaneous CP violation. They can trigger this kind of responsibility, which then together with the inverse cascade leads to a production of binary symmetry that can be good that can be your model barogenesis what can be bad because it overproduces. And using this we set a new bound on the primordial B minus L conserving left on flavor symmetries of 10 to minus two. And we also see that we can get constraints on this axogenesis model or more general constraints on the axon kinetic axon kinetic misalignment mechanism. And, but in a broader sense I mean this I really just see this as both both things that I explained I basically see just as examples right because this is this the framework that we're using is I think much more general. The framework tells you if you have any model which is any sort of large symmetries in the very early universe, then you can use this to put constraints and potentially constrained part of your parameter space or maybe also turn it into viable by genesis model. Okay, thank you. Thank you very much. So, we're going to start with the question we have a couple of questions in the, in the YouTube channel. So, in the meantime, just remind to the people that you can follow us in the YouTube channel just to click the subscribe button to keep updated with the latest webinar that we are going to be programming during the, the, the year in this season. So, let's start with with some questions I don't know if there are questions from the audience here Alejandro has a question. Please, go ahead. Thank you for this very nice talk. I come from a very different field so my questions are perhaps more conceptual so if I say my question is tonight please apologies. Is there a way to understand physically that efficiency versus like how many charges do you have I think that you said like less efficiently means you have more charges. Is there a way to understand this. Yes, yes, so just imagine. This is what you're talking about right. Right. So, so imagine you have, you have a linear algebra system of, of equations. Right. And you simply have a number of equations, right which relate, which linearly relate your charges and set them equal zero right so basically I don't know an interaction of all involving I don't know a hex, turning into whatever let's say a neutrino going to a Higgs lepton doublet right would that written as an equation would mean a chemical potential of the neutrino minus chemical potential of the Higgs minus chemical potential of the lepton doublet equals zero right so very very simple type of equations. So just it's going to be some linear combination of my chemical potentials equals zero when that interaction is efficient. And the more interactions are efficient, the more equations you have simply and if the interaction is not efficient you just remove that equation from the system. And now you have a fixed number of particle species. So the number of equations that you're imposing in your linear algebra system is changing. And simply the fewer the fewer equations you have right and the system is on a constraint, and you just have more parameters in this case more chemical potential that you can just really choose. And something that you can freely choose is in this language a conserve charge. Okay, but so so so my my second and last question then related to this I was trying to think about this exactly is, you know, like this chemical potential in some sense are associated to something that that a number density of something in some sense. Yeah, that doesn't mean that the cattle charge is conserved. And if that's not the case then this cattle can potential. Is it really a potential. I don't know, sorry, I did this is not what not well posed question. The question is more about the origin of this carol potential. If it's associated to a carol charge, and if this is not conserved, or if it is. Okay, yeah yeah okay so the carol chemical potential is a linear combination of the chemical potentials of the individual charges. Right. Okay. So, the chemical potentials are only conserved in this manner right so they only conserved within. So within a given given temperature regime right so say I'm here 10 to the age, GB right, then I have a set of interactions which are completely efficient, and a set of interactions which are completely inefficient. And as long as I stay in that regime, or the individual chemical potentials are conserved, and hence also the carol chemical potential is conserved. But then when I cross one of these lines, I add a new interaction into the game, then all the individual chemical potentials will change and correspondingly also the carol chemical potential will change. So every time you cross a threshold here, you kind of will go down like we will be some sort of step, step function type function. I see. Okay, thank you. Thank you. Thank you. So, before that, if there are other questions from the audience here in the Zoom session, we have a question from YouTube from Adila Afzal, he said hi thanks for the very nice talk. Can you please comment that during the process of exogenesis, do we have the domain world problem? Ah, yeah, that's a very good question, right? So here, okay, so with the domain world problem, it depends when you break the, when you break the petroquin symmetry associated with the axon potential versus inflation. Right, so that's always the story. So in this case, the idea is that we first have inflation. What, sorry, the idea here, okay, the idea here is that here we have, we never restore the petroquin symmetry, right, so let me go to the plot. Right, so here we never discuss the situation where the PQ symmetry is restored, but we always really just work in the picture where the PQ symmetry is already broken. Right. And then in that, and so kind of our initial conditions are really when we start outside here in the room of the Mexican hat. So in that sense, so I don't know we have we have anything new to say on under the main wall, a problem here right so it depends of course on the on the on the number of the main ones that depends how you align, how you do the time watering right of inflation and this mechanism, but we don't have anything new to say on the issue here. Okay, thanks. I'm later maybe Adelaide is going to say some comments about something later. Okay, I don't know if there are questions. I have a question about the, when you were discussing about the role of action in the mechanism of the exogenesis, let's say, what would be also the possible role of other type of particular particles in the, in this scenario I mean, is it possible to generate the same asymmetry with the, let's say, my room from related with the left arm, left arm. Yeah, yeah. Charge or other role of other type of action in granularity five theories or something like that. Yeah, yeah, totally right so I think so from the from the simply from the point of view of generating particular symmetries. And then from the point of view potentially triggering the carol plus for instability and so on right it doesn't have to be the actual QCD action right I mean, and then I think this this goes to me then you know if you have any particle right then you have to specify what how exactly you are going to come into the center of particles. And your constraints will depend on on how what those couplings are. But then the that is not at all specific to the QCD action. I think what what is nice here is why I mean the motivation to use the QCD action is then okay you'll kind of get the documentary for free. You know it's solved the petty Quinn problem right. But that's really just out of minimality and all the more conceptual questions of generating an asymmetry and how does asymmetry propagates from a different phase of the universe. You don't at all need this to be the QCD action for that. Okay, thank you. Yeah. Okay, the idea of the, I understand that the, the best scenarios to talk with the minimal to start with the minimal setup with this. So I don't know if there are other questions in the adela he said thank you to you for the for the answer. I don't know. Joey, if you have a question. I have a question. So, so, in principle, if you. So here you're assuming standard cosmology right but if you assume a non standard cosmology and Roberto will laugh because we've been discussing this elsewhere. If you have like, like entropy injection, right. Could that decrease your, your bound, if you have like a scalar that will decay some matter domination part that will be came to radiation could that a decrease your, your bounds. So, okay, so in the. So in print. Okay, let me first answer in the more general way right so let's forget about axogenesis and just kind of talk talk about the whatever this bound here right. So here in, in principle, yes, right because I mean here, we're saying we're overproduced the problem we're overproducing binary symmetry right. So of course that's a problem you can you can try and solve by by entropy injection. Though you do need to kind of check how the scaling of everything goes with with temperature right because it's all the same. It's all about right because then, like, you'll be. Because then then then you have to see is this actually, I mean, then you would you would what I'm saying is you also have to take into account the entropy injection when you, when you discuss of course how the asymmetries evolves. It's all about time right so there's kind of going to be the actual symmetry in the early universe and then there's going to be kind of the symmetry at later times. And you need to connect, connect it to. Right, but so definitely depends right definitely here we're assuming a standard cosmology right and if you have entropy injection that that would change a picture. In the exogenesis model it comes a bit automatically because in the exogenesis model you can have a phase of matter domination inclination domination. So they're so the individual calculation we have to actually go beyond the center cosmology right and really check explicitly the evolution of the quantities and really check explicitly to two different scaling regimes how the boundary symmetry evolves. Okay, I'll think about that. Thank you very much. Okay, so okay in YouTube we don't have any other question I guess also for the for the time of the, for the length of the to keep consistent with the, without previous webinar, we are going to start finishing here the webinar so first of all, thank you very much for the, for the interesting and for all the people that are following us in YouTube, you can, of course, you can explore our YouTube channel and check the previous webinars and also to continue to to assist into this to attending to these webinars in the future. So, I hope everybody is going to be fine and see you in the next time in this physics webinar.