 All right, so we're going to start. All right, so we're going to start. We are very happy to have Selene. We'll continue with these series of lectures. So Selene. Hi, thank you very much. Hi, everyone. I hope you're okay. And hopefully you digested the lectures yesterday. So we see the second lecture which is going to be focusing on mostly on the evidence for dark matter and the type of requirement that it has to follow. So the one thing before I really start the lecture, I just wanted to come back on a few things that I said which often maybe were not clear enough or I didn't provide any support. So yesterday I mentioned that if the cosmic microwave background had only one temperature, we would see only one color. So what I meant, if you do the composition is spherical harmonic, you tend to take, I mean, you take basically the first one which is Y00 and that's actually a constant. So that's what I'm saying. It would be just one temperature all across the universe, but it's also corresponding translate directly into essentially one spherical harmonic and that's a constant. So it's one color if you want. Now, if you go a little bit further than you take, you want to bring more details if you want. So you can't just take the first spherical harmonic. You have to go a little bit further. You take the L equal one. And then in this case, you obtain a cost data which is essentially giving you an oscillation. So it's giving you a dipole. There's a second picture on this slide. And in this case, you can have capture of the fact that you can have anisotropies, but they're not necessarily real. In the case of Kobe, which was the first experiment to see the anisotropies, they measure the dipole, but they realize the dipole was actually related to the velocity, our velocity with respect to the universe. So first, the second spherical harmonic, if you want, is good, but it's not actually capturing the anisotropies. So in order to see the fine structure of a cosmic microwave background, you need to go further to add more details. You need to add more multiples. And so you have to compute tons of spherical harmonics. And eventually you will get a map like the third one, which is the one of the most sophisticated that we saw, which convinced everyone, basically that the anisotropies existed. But eventually what we do now is up to, I mean, it's far more than L equal 2000. And that gives you an incredible map, which is the one that you see on the sphere at the bottom. And there you can see all the anisotropies. And so it's really this decomposition. It's a mathematical decomposition of a spherical, I mean, on the sphere, basically. But it's basically this decomposition, which brings all the details in the CMB map. So when you have this, then at that stage, you have enough multiples that you can plot them. And you can, and basically by doing this, you obtain the plot I showed you yesterday. So yesterday, I didn't really explain how we got that plot. And so I just wanted to give you a bit of, well, a bit more details on the maths underlying this. But essentially the plot that you see is really the decomposition in spherical harmonics. Now what we said yesterday is that this plot cannot be explained by using, by assuming that the universe is made of volumes alone. That's just not working. So you need to do something else. And in order to reproduce the plot, I mean, reproduce the data that you obtain, you need to add a component which doesn't dissipate. So what does it mean dissipate? It means that if it clusters somewhere in the universe, so if you have a pocket of matter, then it needs to stay. It shouldn't, it can collapse under gravity, it can become bigger under gravity, but it should not spread and basically become bigger. And any substance that you know on earth tends to dissipate. That's the principle of physics really. Anything that you can think about on earth that you observe will dissipate. So you need something which is not dissipating and therefore it's very likely that we need to add something that we never seen. I'll come back. This is a subject of a lecture today. I'll come back on this, but it's important to understand that this plot can only be realized either by adding a substance which doesn't dissipate or potentially modifying gravity. Now I show you this plot or so. The analysis of that plot tells you that there is about 25% of this new substance which we call dark matter, something like 70% of dark energy and then you have atomic matter. So ordinary matter, it's about 5%. But that plot, the Planck curve, which was, I mean, I should say, actually I didn't mention this before, but Planck was not the first experiment to observe the CMB with a lot of details. In fact, the first three peaks were observed by WMAP experiment. And before that, there were several experiments, but the most famous one was Boomerang and Arkeos, for example, which were starting to measure the first peak. And the first peak, as I tried to explain yesterday, tells you an important information about the number of structure at a given basically one degree. And that helps to tell you that the universe is flat. What all this measurement, so whether you take WMAP, Boomerang, and now with Planck, what it tells you is an information about, as I said, the quantity of dark matter and versus the quantity of ordinary matter, but they also give you more information. So Planck in particular, because it's the most precise, give you an information about other parameters. So one which is very important here is the age of the universe. Thanks to this measurement, in fact, the normalization, if you want of that curve depends on the age of the universe. And if you have precise data like you have with Planck, you have a measurement of the age of the universe. There are a number of other parameters on this, on the table that show you. And among this, you will see sigma eight as eight, but you will also see tau, which is a realization parameter. And you will see something called NS, an AS which are basically the amplitude of the fluctuation and the spectrum associated with, I mean the slope of a spectrum associated with those fluctuations. With all those parameters that you see here, you actually have a complete picture. But in that picture, we're assuming that we have 5% of variance. And the question is, can we actually prove that it's correct? So you get a very precise number using the CMB, but is it consistent with other observation? And there was an observation which was made a very long time, well, it started a long time ago, but the prediction was made actually, I think it was 1948, and it's coming from a primordial nucleosynthesis. So primordial nucleosynthesis is actually telling you how the primordial elements have formed in the early universe. Now, you can see on the right how to form, I hope you can see because I'm kind of blind, but I hope you can see everything. But there is a picture starting with hydrogen, I mean protons and then hydrogens and going with deuterium and so on and forming helium. So you basically by having those interactions, you form more and more complex atoms and eventually molecules. Now both of those primordial elements, you can measure them because they come, they basically have been produced in the primordial universe, but you can also, I mean, they are emitted by stars and so on. So eventually you should be able to measure them, which people have done. And so there is a very famous plot which is on the left, which was, I think the first person to do this plot was Schramm, was a very famous, let's say astro-particle physicist. Maybe at the time he was calling himself a cosmologist, but this plot is extremely famous because it does predict the abundance of those elements. So you see on the y-axis, you see the fraction of helium, deuterium, helium-3 and lithium-7. The bands so far, the helium-4, it's very narrow, the prediction is very good. So you see the purple line is basically the prediction. The yellow band is where the observation are. I took this from the PDG, so you can read the details in there if you're interested. It's accessible online. Then for the deuterium, you see the prediction also and the yellow band. So the deuterium is actually basically, it's very well measured. The helium-7 and the lithium, you can see that the prediction is a little bit harder to make. I mean, there's more uncertainty, but you can also see that the observation is actually favoring a region which is not where the two of our yellow bands are. And so in principle, if you have everything correct, if your theory is correct and you have all the cosmology correct, all the yellow bands should select the same region, which would be basically, in fact, where the CMB vertical line, which is the magenta, I'm sorry, the cyan line, vertical line is. So you have this narrow vertical band where it's written CMB in cyan. That's where the measurement from CMB lie, but you can see that actually the measurement of a deuterium is perfectly aligned with this. And this is compatible with the measurement for the helium abundance. So in principle, you expect the lithium to be also basically underneath, exactly in the vertical line where the CMB is, and that's not the case. So this is often referred to as a lithium problem that evolves. People are trying to understand why the observed amount of lithium is not compatible basically with the prediction or at least the correlation between what is observed for the other elements and what is derived from the CMB. But essentially, apart from the lithium, what comes is that by having those observations by cross-colorilating with prediction, you find a constraint on the number of variants in the universe from a problem of big mechanical synthesis. And this is referred to the parameter eta, which is the x-axis, which is essentially the ratio of the number of variants, the number density of variants divided by the number density of photos. Just a remark, so we mentioned the big bang, and then you have, in principle, eventually you will have particles that are created. Now, if a big bang happens with, as we think, then there must be enormous energy. So all particles, even if they were there at the very beginning, they would have been relativistic. But most particles have a mass. So all of them, I mean, all the ones we know, in fact, have a mass apart from a photo. So all of them will eventually become relativistic at some stage in the evolution of the universe, except for the photon. So the photon, in a sense, is the oldest messenger of, as people has remarked, of a big bang. It's the one which is not altered by anything about being a particle. So the photon's basically the messenger, but they're also the witness of the story of the universe. So by looking at the ratio of variants and the number density of variants to photons, you're actually also making a discovery, to some extent, to what happened to the biomes and the complexity of the story of the universe as it evolves. Now, the point is, because there is a straight line, which is a combination, I mean, the magenta is a combination between what you observed and the CMB, you see that it's selecting a very narrow value. That value you can read it from the plot, but it says it's very small. So what it tells you is that there is a tiny fraction of a number of variants, that's just the number of photons. In other words, the variants nowadays, and so this is also capturing the asymmetry between biomes and anti-biomes, which I didn't mention yet, but basically it tells you that there are not so many variants today. And in fact, there is a huge asymmetry between the biomes and anti-biomes. So there's almost no anti-biomes anymore. I will come back to that when I explain the dark matter, the particle side of the dark matter, but what you need to retain for now is that there are not so many variants compared to the number of photons. And I'll come back to that because in question of densities. Sorry, sorry. There are a couple of questions. Yeah. The one by Julian Bolling should be able now to ask. Yes. I just want to ask, why is it so difficult to observe helium-3 in the universe or why isn't there an observation? Yeah, so to be honest with you, some people are measuring it. I'm not an expert, so I'm not really sure why the, I know that there are measurements. I mean, I'm pretty sure I've seen them. I don't know why it was not put, it's not very obvious, but in principle, I'm not aware there is a discrepancy. So I have to say it's not my expertise here, so I would check. Maybe I can answer tomorrow. I was meant to answer that question and I didn't have time to look into it, but I'm pretty sure there is an agreement there. So I'll come back to you tomorrow. Great. Then there's another question by Hishikesh. I'll activate him. Okay. He should be able now. Yeah, hello. Hi, so my doubt was pertaining to the mass fraction. So why are all the mass fractions evolving linearly, except for lithium? And what governs these, the dynamics or the variant of photon ratio? Yeah, so it's just a prediction of how you form them. So you can see, actually, for this prediction, you need to use a code. And that code was actually the first one, I think, who made it was actually people's. But this is just because of a way you always need, sorry, you're meaning for the detail in Manila, right? You were referring to the detail in Manila. Is it correct? I think it's... Anyway, I can continue with this. And so I think that's what the question was. But yeah, it's just because you need, I mean, you always needed to tell him, I mean, it's just the way it's formed. Yes, it was a digital one. So there is this bottleneck, and that's why the evolution gets this way. Oh, lithium is more complicated. Again, that's not really my area, so I've never put my hands in the code there. But I think both a measurement and prediction are difficult to make. I mean, you can make the prediction, but the uncertainty, I could, I should do, I dig it. I try to do that for tomorrow. Actually, I think I lost. Do you still see my screen because I lost it? No. I don't know. There must be. It went out now. So you can try sharing again. Yeah, I just stopped it to find my presentation again and disappear. Same thing like yesterday for whatever reason. This is very bizarre. Share again. So you should see it now, hopefully. Yes, it's working again. Yeah, so I'll dig a bit of the details. I can try to answer tomorrow. All right. I mean, so tomorrow, just to summarize so that I remember for tomorrow, I'll explain why it's difficult to make the lithium prediction and why there's so much uncertainty. And I'll check my explanation for the linear evolution for the terium and helium and then tell you why there is no observation for the helium. There are no more questions for the moment. So we can continue. So what I wanted to tell you, so we have this measurement and in a sense people, nucleosynthesis was very important, I would say until 2000, probably 2010. But then as the CMB became more precise, people tend to forget it. The reason why I spoke about it and that's why I'm not so much of an expert of it because in a sense for me, it was always like, okay, there is a prediction from nucleosynthesis which is actually that you have about 5% of volume in the universe. And that was consistent. That's always been consistent with other measurements in particular the CMB. And so from that moment it's like, okay, the story of the balance is simple. There's 5% of balance in the universe and that's it we can move on. The rest is unknown to us. So the 5% exists on earth, they find earth but the rest doesn't exist on earth. So we never seen dark energy in an experiment here, not yet at least and no dark matter again yet. So it is very peculiar situation where what constitutes us, so the basically the atomic matter is penis in the scale of the universe. There's nothing, I mean, we're an exception. And yet everything that constitutes the universe doesn't seem to make earth, doesn't seem to be actually on earth. So it's a very peculiar situation. And yesterday we were mentioning that maybe as a problem comes maybe we will discover that we have to revise the whole picture. It may be, I mean, it's hard to know at that stage but just the sheer fact to say, well, we are constituted of a type of matter which is essentially nothing at the scale of the universe is very weird. The fact that most of the ingredients of the universe actually are not represented on earth is even weirder I think. So we will see what it means. But in the meantime what was very interesting is while the BBN prediction is in agreement with a CMB, it turns out that when you try to observe the balance you don't find them, you don't find the five percent. So five percent is not a match. But for many, many years people, well, many decades people were saying, well, actually we can't even find five percent. So again, I'm not an expert on this but I wanted to show you a light development which is as you can see the publication which has actually was in nature a year ago. And this paper, unfortunately the lead author, GP Makar, passed away tragically. But this is, I think, one of the groundbreaking publications because what they have done is essentially found the missing biomes, that's the way the problem is referred to. They found the missing biomes and they found them in the filaments which I mentioned yesterday. The way they found them is fairly peculiar because they use, there is, I think, three years ago the telescope that you see on the picture there which is actually a telescope that Sydney University of Sydney, where I am, that's our telescope, it belongs to us. That telescope found for the first time a fast, what we call a fast radio burst. And if you ask for the definition, basically the best definition is given by Wikipedia at this stage. They say it's essentially a transient radio burst and a flint which varies, so we don't really know, but actually, many a second, it seems to be one of the most record. So the thing which is very puzzling is that some of them repeats and we don't understand what is the source of those fast radio bursts. Now at some stage there was speculation and all sorts of speculation, including at some stage some people were mentioning aliens to explain it. The reality is that it's probably a good astrophysical source which we didn't identify yet, but it's probably nothing extraordinary apart from an astrophysical object. But what is really interesting is using the fact that they saw those fast radio bursts, they could actually identify their position and they tracked them back to the filaments. And you see this in the picture at the bottom of the screen, you see every blue, I mean, it's an artist impression, but every blue kind of star is basically a fast radio burst and you can see the correlation with the filaments is absolutely remarkable. So they never fall in the void, which is normal because obviously you expect material to be in the filaments and not in the voice. However, by seeing this, by doing this map, they could track the dispersion measurement if you want. So they could track the distance of those objects and they could track using the formula which is at the bottom, they could have an indication of both in principle the cosmological parameter as measured with a CMB, so H naught, the age of the universe, omega matter and omega lambda. And by doing this and combining with other things, but by doing this, they could find a measurement for omega variance and they determine it to be 5%. And so that's remarkable because no one could find the 5% before and now with this, we know where the values are, not so surprising they are in the filaments and we know that indeed they found the five, I mean, it seems like there is 5%. Now, any analysis, you know, any scientific paper is always, you can always question them so I wouldn't be surprised if there's a number of hypotheses which you can alleviate to some extent and you can find some different values, but it's a fairly robust analysis and what is really important, I think, is we can say now we found the variance so the picture is really complete, variance are not making the whole universe and that is really surprising. So there is something else, whatever it is, whether it's a modification of gravity, it has to mimic the fact that it's 95% missing and we need to understand that. So it's a very puzzling situation. So just to end on what I was mentioning yesterday, so this picture I gave you 25% of the measurement. Kim Saini, there's a question on previous slide, okay? Yeah, yeah, I'm sorry. So by Anna, Anna, you are... Hi, thank you. I was meant to ask if there were any sort of conjectures of what the high energy astrophysical process causing phosphorado bursts could be? Yeah, so I think there is... So again, I'm not an expert at all to have a list. I know that now there are some... People are starting to investigate whether they could be related to the fast gamma ray burst. So you have your observation in the radio. The question is, can you correlate them with the gamma ray burst, for example? I think this is a start. This paper was 2020 and the fast radio burst were discovered very recently. So I don't think there is an answer to that. I don't think I'm making a mistake by saying this, but I think now there is... I mean, I can see a lot of work going in the direction of trying to pinpoint towards the astrophysical source. I don't think one has been identified yet, but they probably are correlation. And in fact, now I think there are some specific regions, for example, of the Milky Way itself as we start to know that there are things, strange things happening, and that might be... This is locally, but that might be a similar process as for the things which happen in the filament. So this is a long answer to say. I don't think anyone knows either as correlation with high energy physics, but generally radio means synchrotron emission. Synchrotron emission means somehow electrons with a lot of energy have been emitted and so there should be some gamma-ray signature. I don't think there's been a full... I don't think there is correlation yet. Again, I'm not an expert, so that's something I can check and I can tell you tomorrow. We have some experts here because of the telescope, so. All right. All right, so we have this picture now and this picture I just wanted to remind you as some hypothesis has been obtained by assuming that the metric as a certain form is Friedman Le Maître versus Malka. And we also assume for getting those parameters, we also assume that there is, even though we introduce new physics because dark matter would be some new physics, dark energy would be some new physics, but we assume a certain type of new physics and we are making some assumption here. One assumption which is extremely important to remember is that the dark matter has no interaction. That's the way that fit has been obtained. I will show you what happened when you say this is not, I mean, if you question this hypothesis and you say that the dark matter can have interaction. If it's matter of matter, if it's matter of particles, then it's likely to have interactions. So in a principle, this hypothesis is wrong. The question is how wrong is it? Maybe the dark matter has so weak interaction that you can neglect them. And I will answer this question probably in the last lecture. All right, so just to complete the last thing and then I start the new lecture, I just wanted to remind you. So we're talking about a phase, a big bang phase, then inflation phase, then the life of particles specifically are relativistic, and they become nano-activistic. And at some stage, the biomes, which now we know exist in our firm, the biomes which we're interacting with the photons and by biome, remember, I mean, elliptomes and quarks and so on. At some stage, they will stop interacting with the photons. That is a moment where light is free and light can come to us. And that's the last, basically that's the, if you want the first moment for us that we can observe things. That also means it's a very strong boundary innocence. We cannot see anything that happens from inflation to the moment where the ordinary matter stop interacting with the photon. So we blind, we can only see from that moment where there is, where the ordinary matter stop interacting with the photon and that's called the last scattering surface. It's last scattering because it's the last time the ordinary matter with scatter of the photons. But then after that, the photons are free so they can come to us. And that's the moment we can see everything happening and we can see basically the history of the universe from that moment to nowadays and we can see the complexity of the universe. So when I mentioned BBN, BBN is well before the last scattering. So even though we don't see light coming from it, the fact that we are able to measure the quantity of balance for BBN is critical because it's absolutely amazing because we don't see anything. We just see the results, but we can still infer what happened at a stage where actually light is not coming to us. So I hope it's clear and I hope you appreciate how special the BBN is actually for reconstructing the history of the universe. But the main thing is what we can learn is from the moment where the ordinary matter stops scattering with the photons and then up to now. And as I told you, once you have initial conditions, you can make all the predictions and that's tons of simulations. You have a large panel here. The latest one, as far as I know, is the Apostle for example, illustrious and so on, Eagle simulation, all of those, they all show the existence of the filaments. And as I told you, the whole question would be when you put the dark matter physics, the micro physics, if it's made of particles, are you really reproducing what you observe? So this would be the key essential. So for the lecture today, I really wanted to go back and explain why we think that having a dark matter hypothesis from the CMB is not completely crazy. So as I told you, it's a very weird situation of basically saying what constitutes us is not the main component of the universe. And that's because we observe a CMB. And now you may say, well, the CMB is, I mean, it seems correct, we fit the plot, but as I told you, the hypothesis. So you may say, well, we need of a probes of this, I mean, we need of a probes which allow to indeed say that the dark matter exists. And so I wanted to go through this. The first thing I wanted to just remind you is dark matter, whatever it is, again, manifests as absolutely all scales. It's not just the thing that you see in the CMB, you see it in cluster of galaxies, you see it in galaxies, and even smaller galaxies like dwarf galaxies. You see them when you use observation, which I'll detail later. You actually see them in the filaments and you see it, in fact, in the Milky Way. And I'll tell you something just after that. But first of all, I wanted to show you a film which is a reconstruction of its data stack, basically, by the Sloan Digital Survey. I hope you can see the filaments here. You just, you know, you're traveling through space and you can see the origin of emptiness, which avoids. But hopefully you can see the filaments being drawn in front of you. So this is a distribution of galaxies in the universe. It's just incredible, I mean, to me, it's incredible. You know, this is what we can achieve and now we can achieve them in there. So this is what we need to describe. There is no doubt we have a data and we should be able to exploit them. But we have to exploit them and we have to explain them with something that we don't know anything about. And that's really the problem here is how do we get something so precise because we do succeed in explaining the CMB and structure formation, at least at first order. With something we don't know anything about. And it's a kind of a little bit tricky situation, but at the same time, for me, it's always like the most magnificent success of physics. This is what physicists are good. This is basically what the greatest achievement is. To make prediction with basically models which contain very little parameters with very rough hypothesis and yet managed to describe nature. And that, I think, is a celebration itself. So now that you've seen this film, I hope you can see it's, you know, when I speak about filaments, it's not just a prediction from simulation, it really exists. All right, so who spoke about dark matter first, actually? So everybody mentioned Zwicky. I'm sure you must have heard about his name. Tell that that captain was one of the first. There are many people actually who contributed to maybe the term dark matter, but also, in fact, the concept of dark matter. This paper was 1922, and you can see that, so in the yellow region, I mean, what I highlighted in yellow, he was mentioning random rotational velocity, the nature of equidensity surface is such that the stellar system cannot be in a steady state unless there is general rotational motion. He was starting to look at the motion of objects and starting to realize something was a little bit off. But in the second yellow highlight, you can see that there is a sentence. It is incidentally, so at the bottom, basically, it's incidentally suggested that when the theory is perfected, it may be possible to determine the amount of dark matter from its gravitational effect. Now, it turns out that dark matter here is not really referring to assistance that we would have never seen, but it was measuring the fact that it was indicating the fact that something was missing and people felt like there were some anomalies and they needed to explain it with a form of matter. Now, Holt also, in Room 32, mentioned this by looking basically at both objects. So I guess I will read it again, but maybe I would prefer to read the second part. So if you look at the bottom, you will see, it's not necessary to conclude from this that the absolutely bright stars are relatively less frequent in the center or that there is a greater percentage of nebulus of all dark matter in this region. We might reserve, sorry, we might reverse the argument and conclude that some 85% of the light of the galactic system is obscured before it reaches us. So somehow, Holt was saying, well, there is a problem, we can explain it, but there is a problem. It turns out that there is a thing called the Holt cloud and clouds are basically obscuring the light from stars everywhere in the galaxy and further away. So clouds are a real thing. They're not necessarily dark matter. They're actually kind of biomes or gas, if you prefer. But I think all those people were starting to realize that the light, I mean, basically objects can be faint and you may not detect them, but you can observe them indirectly by looking at the rotation curves of objects, for example, galaxies. And so that's where the revolution came in a sense, or at least we accepted evolution. So in 1933, Fritz Wickey started to basically think that there may be really some problems. In this case, he was looking at Nebula. And so you can see the abstract of this paper, which is in this case translated. So I think he was a German, a Swiss German. And so he gave, in the abstract, he said, this gives a description of the most essential characteristic of extragalactic Nebula, as well as of a method used to investigate this, right? And then he said, in particular, the so-called redshift of extragalactic Nebula is discussed in detail, various theories which have been proposed to explain this important phenomenon are briefly discussed. Finally, it would be indicated to what extent the redshift promised to become important for the study of cosmic ray. So I highlighted this because it was already, it was noticing that there were issues. It was noticing that maybe there was a question of redshift. And you remember for example, the supernovae we were mentioning redshift. And clearly already people were proposing various theories at the time. So ferretician were doing that job. But the critical paper was 1937. And in that paper, which is really explicit on the mass of Nebula and of clusters of Nebula. So basically, I mean clusters of stars, if you want, you can see that he had an estimation for the mass. And then he said, I mean, maybe I can just refer instead of reading the text, perhaps you can read the text, but the thing I want you to look is the mass to light ratio, which is critical information. So mass to light is the quantity of mass that you can infer from an object divided by the amount of light that you receive. If there is nothing anomalous, then the mass should fit the light. You measure a certain amount of light and you deduce, so you measure a certain amount of mass and the two should be in agreement. So the mass to light ratio should be one. In this case, it says no, actually it's 500, which is major discrepancy. And he said, in this case, as compared with about gamma prime equals three for the local captain stellar system. So he's already basically there is telling there is an issue and there is more mass than there is light. So in other words, the object that is looking at is producing light, but it's not correlated to the mass. There is something else which is giving the mass of the object. It's either that or as before, the light maybe like all was suggesting the light could be completely obscured by something, but this something obviously is there. And the question is, is it ordinary matter or something else? Now as Wiki went on, I'm sorry, maybe I should stay here, but Wiki went on and say basically there's something new and that's basically the dark matter because you can't see it, but it has to be there. And I have to say I will trust but people describe in the literature, but essentially everyone was very septic of his explanation. And often people use a picture I put on the first at the top, you know, where he doesn't look like a nice man. So often people say, I was a bit of a grumpy man and so on. So there was a bit of, I think, some prejudice against him, maybe. But in reality, it seemed like he was able to smile so when he was taken in picture. And I think it was reflecting the fact that for me it's a message to you really, when you propose something new sometimes it's not necessarily accepted, which is probably a good thing. You have to define your idea, but in some cases it might take a lot of time. And in the case of Wiki for various combination, it turns out that it took a very long time before actually people accepted that his explanation was correct. And in fact, it took until 1970s and actually 78, we've been that you see in there, we've been on the top. And then there is also a contribution which is rarely mentioned, but from Bosma at the bottom was a, almost before, I mean, I will explain the story a bit better, but at the same time, let's say, both of them contributed to understanding the fact that indeed there is an anomaly and indeed it's very likely that there is more matter in objects like a galaxy than expected. And so what they've done, so in this plot that you see, you have let's say a galaxy, so something like the Milky Way and then you have the radius of the distance toward the center and then you have the rotational velocity on the y-axis. What you see is you have two curves. There is one which is expected if you have only bionic matter. You remember bionic matter dissipates, it has interaction with photons, so it will obviously eventually, it will not rotate forever, it will dissipate, so the rotation velocity from variance should fall eventually as you get further away from the galaxy. If you're not convinced with this explanation, well, you can see on this photo, for example, of a galaxy, you can see that that galaxy doesn't shine forever. At some stage, you don't see any more stars, you don't see anything. So eventually it becomes dark and that's because eventually you don't have in principle the variance inside that object. So it has, the rotation curve has to fall. Yet when you do the observation, what you see is that the rotation curve actually increase as you get further away. So it's extremely puzzling. Now, there are being contributed to the inside of the galaxy to measuring the velocity of the stars within the galactic center. And you can see, so the yellow points are essentially where they are being contributed. But then afterwards, a lot of people contributed to the fact that you don't see stars because as I said, the visible galaxy ends, but not the rotation curve. The rotation curves goes further away than the visible galaxy. And what you see here is people then use other methods, which is in particular the emission line from the hydrogen, the 21 centimeter. And by tracking the 21 centimeter, you actually see that there are things in that galaxy, the galaxy continues, even though it's not visible anymore. And in fact, the velocity, the rotation velocity increase. So BOSMA and all those people were making a strong contribution to the rotational velocity measurements beyond, let's say, 10, 15 kilopart, 10, 50 kilopart. So here is another explanation of what's going on. So you have a visible galaxy. I'm sorry, I put it in a cylinder, but just for you to understand. So it extends, in some cases, up to 20 kilopart sec. But what we understand now is that this visible galaxy is within something much bigger, a much bigger structure, which we call a dark halo. And that dark halo can contain, so as I say, we trace it via the 21 centimeter. So it does contain molecular clouds, which emit 21 centimeter, but we also think it contains something else, which now we think is not related to billions because there are not so many biomes around. And we think this is the so-called dark matter. So the same plot, a bit differently, but the same plot, you see the velocity, the rotational velocity on the y-axis, the radius on the x-axis. And what you see is the disk, essentially to the bionic matter is falling and the rest is continuing. And this means that the velocity associated with this halo is increasing, so that you can obtain a flat rotation curve. So how do you do this halo? Well, you got the velocity. So in principles, you have a velocity. It's very straightforward to go back to understanding the mass, which is contained in this halo. And what you do this, you realize that actually essentially the mass increase as you go further away. But the number density of particles we view is actually bigger in the center. I'll come back on this. I think it's a fairly difficult concept, maybe. So in the third lecture, I think over the fourth lecture, I'll explain in detail. But you have to remember, so the mass is increasing as you get away. And that explains why the velocity eventually looks like a flat rotation curve. Eventually the speed of all the elements in this halo reach kind of a plateau and it's about 10 to minus three times the speed of light. So it's fairly fast. Obviously we don't feel it, but it's not negligible. And I should say the smaller the object, the smaller the velocity, but the bigger the object, like a cluster, the larger the velocity. So on that note of there must be something, then other people continue to make measurements. And a very important paper in the field is actually by Sandra Faber in 1979 and John Gallagher. What, again, I will just read the part which is highlighted, but there that was really where I think people stop having doubts and there was really the acceptance that there must be some form of dark matter in those objects in every basically cosmic structure in the galaxy, in the universe, sorry. So they say, we think it is likely that the discovery of invisible matter will endure as one of a major confusion of modern astronomy. So basically it is, yeah, there is something wrong. Now we can actually prove that there is more mass than like coming from various subjects and in particular for the Milky Way. And so this was really, I think the establishment that there is some form of invisible matter, whatever it is. As I say, we will question whether it's invisible matter or modification of gravity, but there is something which mimics the form of invisible matter. That's for sure. And there are so many evidence now that I don't think there would be ever question. So the fact that there is something missing in our understanding, I think is not questionable. Excuse me. Can I go on it? Yes. Do you think it's a good moment now for the five minute breaks or do you want to do it in a while? Yeah, we can stop now. Okay. But it's already past 45 minutes, so. Yeah, so we can. We do five minute breaks and then we will continue. Perfect. Hi, Selene. Maybe you can assume. There is a question, maybe you can take the question. Oh, no. Well, there was a question in the chat. So there was a, there's a raise at hand by Max. Let me, so. Maybe Max don't have a microphone because I didn't see. Ah, here, okay. You should be able to ask the question now. Yeah. Hi. Can I ask you a question about the previous thing? It was sort of this slide about, yes. Yes, it's about the rotation curves. Oh, you mean this one? Yeah. Yeah, so and so, okay, so, so the, so I'm wondering about, so this one curve, curve, which shows the gravitational potential for the gravitational force coming from the baryonic matter and the other one comes from the, comes from the dark matter distribution, right? Yeah, that's right. The one of the. Oh, wondering, so why is the gravitational potential from the dark matter so much less cheap than from the baryonic matter? I think that if you heard one explanation, who wants that dark matter doesn't lump or something, but I don't understand because I mean, so there's some structures due to gravitational attraction, which should be similar in the case for dark matter and the baryonic distribution, right? Yeah, that's correct. So the best way to understand it is it does clump, but it clumps on that scale, which is very large. And the reason why it clumps so, I mean, on such a scale is first of all, because there is no dissipation. So it doesn't lose energy. So it doesn't fall if you want in the potential. I mean, it does fall in a potential, but not like baryons where there's so much dissipation that they would collapse. That's one thing. The second thing is because you have a six, I mean, you have this extension basically, you can see it as the biggest part of a potential will depend on the quantity of dark matter that you have. So let's say the energy density and the energy density, if it's a particle at least, would be the number of particles termed the mass, okay? So what it tells you is there's a certain distribution of a number density, which explains the distribution. And again, because they don't dissipate, you have to find them distributed. You can imagine that they will somehow cluster with the baryons. So they should be the number of particles, I mean, the particles should be correlated with the baryons, somehow. But when there is no more baryons, they can spread because the baryons are not retaining them. And that's why, because they really don't dissipate and the baryons are not forever, then the dark aloe can be larger, much larger than for the baryons. Does it answer the question? Yes, thank you. And there's another question by Merna. She'll be able now to speak. Yes, hello, excuse me. My question is related to the mass to light ratio. Would you clarify the reason of the mass to light ratio being exactly equal to one? That it should be equal to one? No, well, yeah, I will explain. It doesn't have to be equal to one, but in principle, if you have as much mass, oh, sorry. If you have nothing else than the baryons, the baryons emit light. So wherever there are baryons, you should see them. Okay, so maybe I can bring this one. So wherever you have baryons, you should see the light. And so in principle, there is absolutely no anomaly. You can measure the intensity of the light and so on. You can deduce how much baryons you need basically to explain this intensity. And then you can with the gravitational potential, you can make a measurement of the mass that is contained in the area that you're looking at, which is visible galaxy. So if there is no nothing else, you should be a strong correlation between the gravitational mass that you measure and the light that is emitted. And technically it should be one because it should be a perfect match. In reality, it might not be perfectly one, it might be factor two, factor three, but in principle it should be around one. Above that you start to wonder if there is not so much, there is something bizarre happening. When it's 500, there is no doubt that something is missing. So you don't see either you can say, well, you don't see all the baryons, or you see all the baryons, or there is something else in addition. Yes, okay, thank you so much. So as a question. Yeah, that's one. Let's say one more question by Isben, please. I'm mute. Now he works. Okay, great, thank you. So good morning. My question is regarding the former one. So isn't it possible that there are suns, so stars that are much, it has much more mass, but do not emit so much light, such that mass to light ratio is far, yeah, I don't know, larger than one or smaller than one? So if you speak about stars, yeah, that can be, to some extent that can be, it depends what you call by star, if it's a living star or a dead star. If it's a dead star, like a supernova remnant for example, you could say, well, that contributes to some extent, but you always see those objects in some ways. So back in the 30s, you could have applied, you could have actually assumed that that was related to something like a star. Nowadays we know those objects emit cosmic rays or generally in gamma rays and so on. So we have a map of those gamma rays and of a wavelength. So we have a good understanding where the matter, things like what we know, like electrons and so on, where they're distributed and that doesn't really correlate with what we see in those observations. But just to, I mean, basically what I was going to say is that if you're not talking about stars, but you're speaking about an object, which is not necessarily a star, but is a compact object, then yes, that could be. And I will talk about this today. So stars, I think, unless they are made of new material, so dark stars, like really made of dark matter, for example, yes, they could. If it's a normal star, well, if it's a star that we know, basically, the answer is no. If it's a star which is a different type, we didn't discover them, so we maybe are discovering this, but you will see that it's a bit more complicated and maybe I can even answer that right now. So I told you, this is the evidence that we get with the galaxy, but I told you that we make measurement with a CMB and with a CMB, we know that we need this kind of dark matter. With a CMB, there was no star form yet, because essentially all the fluctuations that I show you, they didn't collapse on the gravity. And in order to form a star, you need basically those fluctuations to collapse. So this strange, you know, this, as you say, maybe you can explain the things what's going on in the Milky Way, but you have to remember that even if you were explaining it, that's 100%, you need to explain the CMB. And with a form of dark star, whatever you call it, that wouldn't actually fit. I mean, star made of ordinary matter, but with a different behavior, that wouldn't fit the CMB. So it's probably not the right explanation. Okay, okay, great. Thank you. Do you want one more question or would you give it for the Q&A? We can, I guess we can take it and then I move on. Let's take one. Okay. So Chris, you should be able to talk now. Thank you. So my doubt is why can't dark matter be explained by something like an asteroid or an asteroid belt that is exceptionally huge? I'm coming, I'm coming to that. All right, so we'll continue then. Let's continue then. All right, so just before I actually touch on this, I wanted to show you this mass to last ratio, which is greater than one in most objects. You can see it in action because if you have more mass than light, the mass hopefully you all have seen general relativity and with general relativity, you know that light is banned basically by mass. So if you have a lot of mass, you should start to see some, what we call the Einstein ring. So you should start to see the light bending around objects. And that's exactly what is illustrated in one of those. This is a cluster of galaxy here. What you see, actually it's a galaxy in this case, sorry. No, this is a galaxy cluster. I was sorry for the confusion I was like. So this is not the most pretty image. I mean, now we have, I'm actually part of a collaboration which has much better cluster, much better data. But what you can see is mostly the arcs. So I hope you can see, again, I can't use my mouse, but you should see really all around those very bright lights. And that's because there is a lot of mass that you don't see so dark basically, but the light is curved by the fact that there is something on the way from the light to you. In the picture on the left top corner, you see close to the arc, you see in fact a galaxy, you see an object which is a little bit distorted. And that's basically clearly an image from a galaxy. The question is you have to see whether this image with galaxy belong to the cluster that is in front of you or actually is an image from another distant object. So that's all I wanted to show. So this is referred to as strong lensing. So this is really abuse here. You can see mostly there's your cluster, but in terms of visible light, you don't see so much, but there is a strong bending of the light which indicates a lot of mass. You have the same effect, but much weaker. And it's called the weak lensing effect. It's much more subtle. So you won't see the rings, but you will see a distortion of the form of the object. So you will recognize an object is the same. It can basically appear in different places, but it would have a strange shape. And that's called weak lensing. That's really subtle. That's really hard. But people are using this to make measurements. And in particular, so the combinations from lensing and weak lensing are helping basically to understand where the dark matter is distributed in the universe. And so a while ago, so focus on the image at the bottom of the screen, a while ago people have mapped the distribution of dark matter with redshift. And they realize wherever you look, basically you can go with different redshift. So you go back in time, and you always see the presence of this form that you can use this matter that you cannot observe directly, but it's very influence the gravitational potential. I also show you, I have to show you, I guess, the bullet cluster. So maybe many of you would have heard about it. The bullet cluster is a strange object. It's not isolated, but it's an object where you measure the gravitational potential and you see, so what is in red is a visible X-ray light. So it's not visible by eye because it's X-ray, but it's something you can measure. And you see that it's mostly in the center of the cluster. And then all around the blue is basically where the gravitational potential is and it's the dark matter. And this subject is a merger, but what you expect is that if there was only some ordinary matter, because the ordinary matter dissipates, everything, the gravitational potential should be basically a line where the emission of X-rays is. So you should see basically the blue and the red connected. And it's not the case. The blue extend beyond the emission of X-rays. So there are the variants merged basically between those two objects, two clusters. But then after the very low of dark matter basically continue to evolve. So pass through because it doesn't interact much. Now, the collaboration which I have this observation, I should put the reference here, but they put a constraint on the type of interaction that the dark matter has. And it's not good. I mean, they made a big fuss about it and there was a very famous press release. But in reality, if you're a particle physicist, I would maybe speak to you. In reality, the cross-section, the constraint is of the order of the Thomson cross-section. Thomson cross-section is the cross-section, the interaction, describe the interaction between electron and photons. That means the light is visible basically. So if you obtain a cross-section that large, you're not told that dark matter is dark. You just say, okay, it doesn't interact as much as that. You're not actually explaining why the dark matter is dark. You're just saying that it's not interacting as much as ordinary matter. So it's a valid point, maybe not as impressive as the collaboration was saying, but it's a valid point nonetheless that we are dealing with something that is not exactly like ordinary matter. Okay, so. Excuse me, there are various questions before we move on. First, where is Ben? Maybe Ben has his hand from the previous question. Sorry, yes, I'm sorry. I think preschool, maybe? Yeah, preschool is a new hand, so. Yeah, probably you said that, and I missed it, what kind of interaction are we talking? Self-interaction or interaction with light? Yeah, so in this case, you can call friend, but you can call friend, but there's an echo. You can, in principle, you can do both. If what you want here is basically saying where you have a two alos, so basically what you're really constraining here is in principle dark matter, dark matter, and this became a famous constraint for self-interacting, dark matter indeed. But in reality, you can use the same argument to say, well, you have variants and they pass through. So in principle, you can put a limit on dark matter and variance. The value will not be very good. And you could do the same with light. The reason why it's hard to do is because even with a galaxy, you know that there is variants and there is a dark matter halo. And the interaction is too weak basically to get a meaningful constraint. So the observations are not good enough to place a constraint. But in principle, you could do it. You just suspect that it would be more like Coulomb interactions than Thomson interactions. I mean, the constraint would be of the order of Coulomb. All right, this is Shivan, I think. Yes, Shivan has a question. He wants to ask. I'm asking to bring out your... Hello. Hi. Hi, how do... Yes, please go ahead. I'm just wondering that how do we describe the possibility that the blue region here is comprised of new trees rather than dark matter? Excellent. In principle, yes. In principle, you could think it could be made of neutrinos. That's right. The issue is going to be, and I will speak about it later on also in the lecture today, the issue is that you have a gravitational potential now. You can measure it and you need to explain it. And while gravitational potential means that you have mass. So now you could infer the mass of the neutrinos to explain what you observed. And the problem is that the mass would be much larger than the constraint that you have for a neutrino mass. So it will not be consistent with the hypothesis, well, not the hypothesis, but the constraint you have on the mass of neutrinos, which is extremely small now. But in principle, yes, that could work. I mean, I will go back to that, but in principle, neutrinos could be a dark matter candidate. So thanks for this question, it's very good work. All right. Let's see, go again. Okay, so just to go back to the question about meteorites. Well, yeah, the dark matter could be in principle meteorite. In fact, there are even some people who propose that it could be a particle with a mass of, sorry, a steroid or whatever. So that's one hypothesis. But again, remember, if it is, then you explain maybe the dark matter in the Milky Way, for example, you won't be explaining the dark matter that we see in the CMB data. So likely not the right explanation. But nonetheless, some people have pursued this hypothesis that the dark matter could be an object, which is essentially compact, massive, and living in the yellow of the Milky Way of any other galaxy. While you're there, you may say, well, actually it may not be something of matter as we know, it could be a black hole. And this is another hypothesis. Now, all of those, again, have to be in the yellow of the Milky Way. So the Milky Way here you see is not an image. It's a reconstruction of, I mean, it's really a reconstruction of data here that you see every single point is the galaxy, sorry, the star. And you know that there is a yellow. So again, you have to feed those objects in the yellow and then you have to explain still what happened in the early universe. So I personally think it can't be the case, but maybe I should bet with you see what would be the answer. But people have looked for those objects. So when I say, I don't believe it, it's also because I kind of know what people have looked for and obtained. But let me take you through this. So in fact, well before 2001, this was really in hypothesis people were not the black hole so much, but the asteroid or whatever, compact, massive compact object was really an hypothesis people were really considering seriously. And if you have those objects, then when they pass through in front of a star, they would induce some lensing. And as I explained before, but actually a very small amount of lensing. So it's called microlensing. And there is two, at least back in before 2001, there were two experiments looking for those. Unfortunately, they have a precious name, especially nowadays, but one is called Eros, the other one is called Macho. So it's just a story. Macho stands for massive halo compact object. So sorry, always invert a massive compact halo object. Both from the same or as we agreed, and there were some candidates where essentially you see this microlensing happening. So you can see here a star is a little bit more deformed, more intense than the other one, comparing the two picture. Hopefully you can see this on the picture. But by looking at those events, they actually managed to put some constraints on the fraction of those objects in the halo or the Milky Way. And so you see here a plot, and again Eros and Macho found more as the same. So I think this is the Macho plot, but it's more or less the Macho collaboration, but it's more or less, they were in agreement. So the halo fraction that you see here is essentially less, everything which is colored is excluded. So what is left is everything that is not in those regions. And so either it's an object which has to be extremely small, so less than 10 to minus eight solar masses, or it has to be bigger than 10 to minus one solar mass. And if it's in that range into minus eight into minus one, the fraction has to be lower than 20%. So as I said, you have a CMB problem, but 2001 we didn't have an answer from the CMB, but there it was already the case that those objects, which is a mass framework, but you need to explain the dark matter, those objects would only constitute 20% of the halo and that you need 100% for the halo. So it's not a possible explanation at this stage. So 2001, that was really the big result from the Macho collaboration and again referrals. And it was clear that the fraction has to be small. In fact, it's more 10% than 20%. So you need something else. Just to give you another magnitude, Earth is treated to minus six solar mass. So it is essentially a Macho, a massive compact halo object and Jupiter 10 to minus three, Sam, and Pluto 10 to minus eight just above there. So those objects are potential coordinates. So you could say, well, there are planets we don't see. So maybe not stars, but maybe there are planets we cannot see. But again, if they are, they're less than 10%. All right, so what about the black holes now? So after the Macho heroes, everybody thought, well, in this case, black holes will not work, small black holes are not a solution. But there is a revival seems probably 2015. So in a particular 2016, after 2015 when the collaboration with you and Diego found basically gravitational wave because not only it says, well, there are events, but then it clear that you have measures. For example, you have black holes merger. So what they observed were fairly big black holes in comparison to what we refer to here as primordial black holes. But the idea was, well, if now that we observe black holes and you know that black holes are merging, maybe you have primordial, so black hole, very tiny black holes, which were formed in the early universe. So we call them primordial black holes. And maybe they actually come together as a pair. So as a binary. And so people have looked at this hypothesis and are still looking at this hypothesis. So there's a number of reference that I put here if you want to have a look. Number of constraints have been put. So the plot in the middle, you see Eros and OGLI, you see some constraints basically. So Eros gives you the indication of where the microlensing is in 2001 and they improve a little bit since. As you can see, there's not much room. Now you look at the plots on the left, for example, there are constraints coming from the CMB and from other cosmological observation, mostly because black holes, primordial black holes could evaporate and they would emit some, I mean, basically they would release some heat and then from that you can put some constraints. They would emit some particles. So they could essentially, for example, they could produce some positons and the positons can annihilate with electrons and forming a 511 kiwi line and so on. So from there you can see that there are some constraints, but not completely, the range is still open. The range in above, let's say a few 10 to 17 solar masses is actually open. And that's consistent with the fact that the lensing is not good for this regime. So this is not the regime where the lensing could have proven. And then you have constraints from gravitational waves themselves. And then you can see the fraction what is obtained from a gravitational wave is going to be small and so on. So there are five or two other constraints. So in principle, it doesn't seem like there's much room for primordial black holes, but the argument is, if you have plenty of primordial black holes with a mass distribution, so not just one mass, but maybe it's a range of value size, maybe you can actually explain the whole dark matter. Then there is a problem of a CMB, but if it's primordial black holes, maybe they were there really early on and you might explain the CMB also. So this is a way, basically a way out. Again, personally, I'm very biased and very skeptical, but maybe this is an explanation. And so there is a, it's interesting because you're going to have a number of experiments which will be able to prove this hypothesis in particular the LISA experiments for gravitational wave. But then you have radio experiments and SKA, which is a set of telescopes and they're actually the part of, most of them are basically in Australia and the government actually just approved the funding of SK. So SK will happen. And so that's going to be very exciting for determining whether primordial black holes exist or not. Okay, so one thing I wanted to say, a little bit slow maybe, but one thing I wanted to say is that there is an issue that is rarely discussed, I actually not discussed. To some extent it's controversial, but I think it's a very valid point. And that point has been made actually by one of my students, Zachary Picker, in the photo here. I should have added the reference to a paper, but I'll do that tomorrow, but the point is the following. So everyone who is looking at primordial black holes, basically treating them like you would treat a black hole. They use a Schwarzschild metric and they basically say it's admitted in a flat empty space. And there's a problem with a mass and you can't really define the mass so they actually assume that is zero, I mean the local mass. But in reality those primordial black holes have evolved if they exist. They evolved with the universe because they were very early on. And so they should be embedded in a cosmological fluid and they should be really embedded in the Friedmann-Le Matroberschen Walker metric. So obviously the metric that you use for cosmology will not be valid within the primordial black hole, but just for describing the structure where the structure of spacetime where the primordial black hole is, it should be basically Friedmann-Le Matroberschen Walker. Then you have a definition of mass, which is essentially a local mass. I will not go into details, I mean I'd say it's even controversial to some extent, but the point we make in this paper, which I think is really important, is you can define a metric which tries to encompass the fact that you have Minkowski within the primordial black hole and you have to get something like Friedmann-Le Matroberschen Walker outside. That one of them, one of those metrics is called the tachyltide metric. We're not claiming is the right one and no one would want to do that even. But the point is if you use that, then you get an interesting consequence on the constraint that I showed you before. So one of the constraints before is obtained by LIGO. And LIGO says, well, if you have those primordial black holes, they probably form binaries and if they form binaries, well, you would see them basically, they would coalesce today. But if you change the metric, and instead of using the Schwarzschild metric, you actually assume that it's in Friedmann-Le Matroberschen Walker, so from maybe the quota or anything else, then you change the number of binaries that you form today. And as a matter of fact, you may actually evade the LIGO limits. So what I'm mentioning this is because I show you plots with limits. And again, it's like what I show you before the CMB, it's always rely on assumptions. And I just want you to be wary that some of the assumption we make may have to be advised. And in this case, it's basically the point of saying, maybe this is the wrong metric people are using, they're making an assumption. And maybe actually it leads to some constraints and maybe those constraints are actually not there. And so it could be that while I'm skeptical about from underbackers, it could be that actually they are because we're not using the right cosmological framework to describe that. So with this in mind, I hope you will basically understand that what I'm trying to tell you is be open-minded and expect surprise and question every assumption that people make to get results. Sometimes you can see a combination of various constraints always lead to something which is consistent and then you I think have the right to believe it's correct. But we never know. And in particular, in this case, I think really the embedding of the metric is and embedding the primordial backers in the right metric I think is going to be key. So with this, I think that Anna and the Shiva have questions. Yes, and I have a lot of questions. First, Anna. Thank you so much. So this is a double sort of question. Could you please describe how the tukota metric differs from the Schwarzschild? Because I don't make much of a difference. Oh, beyond the sign. And then. Yeah, so. You can describe what's called. You see, there is no much difference, but the mass is different. So the mass actually depends. The mass is, I should have written it a bit better. The mass is actually the normal mass that you would have times the scale factor. And that makes a huge difference. There are fellow, maybe I'm sorry, I should have put the reference to the paper, but there are other difference, but you need to read the paper because they will bring me too far from a lecture. But the biggest difference is really the way you write the mass. And also I should say. Okay, thank you so much. So just to make sure you understand, it's not a mass, it's not an equity mass, it's a mass, it's like space time, it evolves, it's just saying it evolves with expansion. It's not saying that the mass, but the mass changing with accretion. So it's a different type of mass if you want. It's just going with the fact that the, you have a parameter of like all living on a space time, that space time is stretched basically with expansion. And so is the mass, that's basically equivalent. All right, thank you, that makes a lot of sense. There are many more questions. I suggest that we keep going with the lecture. Yeah, maybe because it's almost 11.30. And I ask the participants to give their questions for the Q&A sessions, which will be in five or 10 minutes. Yeah, so I probably need 10 minutes if you don't mind, but all right, let's continue with the lecture and later we'll take all these questions all together. Thanks. Okay, so I keep mentioning that, well, it's likely an invisible matter, but it could be some modification of gravity. So what is it? And the first one to mention it was milk home. So it's a bit the idea of, or let's explain the anomaly in the galactic halo. And at the stage we don't need, we didn't basically worried about the CMB. And there is a reason for that, that the paper milk home's hypothesis was in 1982 and we didn't even have a proof of CMB fluctuations. So it was reasonable to focus, it was mostly about rotation pairs of galaxy and it was mostly about trying to explain them. That, as you see in the title, it's a modification of a Newtonian dynamics because that's what it is in my galaxy as a possible alternative to Eden mass hypothesis. So it's very clear what it's trying to do. And you can see again, in, that's basically the abstract, I found that by using a certain modification of a Newtonian dynamic in the limit of small acceleration, both observational aspect of galaxy and galaxy system, which I have looked into can be understood with no need to assume Eden mass. It is basically saying no need to have new particles, it just can do it with gravity. It's a very important conclusion, basically, if it's true because it changes, it tells you what you need to modify. It's not the standard model of particle physics, but it's actually general relativity or Newtonian gravity. So the concept is very simple. It's empirical approach. It's just firing the forces of the mass time acceleration. What about you make a small modification to this? And the modification is by adding a parameter which is scale dependent or acceleration scale dependent. So if the acceleration is basically greater than a certain value, then that parameter is one and you find the normal force. But if the acceleration is small, then the new parameter is equal to the distance where you are, sorry, not the distance, but the ratio of the acceleration to the reference acceleration. What is amazing is that by doing this, it kind of works. Certainly in the 80s, it looked like it could work. When you look at all the galaxies that you have nowadays, where you have done this measurement for the rotational velocity, you see that not really it works, but not perfectly. And there is an explanation, Milgrom would say, and a number of people in that field would say, well, a galaxy is very complicated. There's a lot of fast physics. And it could be that it's a local structure which changes the value for the reference parameter, A naught. So maybe I didn't explain that very well, but basically with Milgrom, if you take it at phase value, A naught has one value and it should be universal, whatever galaxy you're considering, that should be the same value of A naught. You do the observation, you realize it's not quite the case. It's not the same value for A naught, which works for every galaxy. And the counter argument is that maybe it's because of the astrophysical situation of each peculiar, a particular galaxy, could well be. The thing is, as I keep telling you, and that's why I started the lecture with the CMV, is that with this theory, it's an empirical fit. So you don't have a theory really. It's an empirical fit. So with this in mind, you cannot go back in time. You cannot do cosmology. You can explain maybe the halo, but you cannot go back in time and explain the shape of the CMV. You cannot explain why the fluctuations look like what they look like. And so you need, the only way you can do that is having a relativistic version, like general relativity, if you want a relativistic version of this empirical model. And for many years, there was none for several decades. And the first one to propose such a theory, which is relativistic, so which allow you to go back in time, which allow you to do cosmology was Wittgenstein in 2004. And I like saying, this is one of the important moments in my life where I saw this paper, and just to show some of you will recognize themselves. So I saw this paper and I thought, well, it doesn't explain the CMV. In 2004, we had the CMV. So maybe we should try to see if it fits the CMV. And so I'm not at the door. I was a young postdoc. I'm not at the door of a colleague of mine who was also a young postdoc. And I told him, he can't escape the cell damping. They will be seeing damping. So we should look at the CMV and we should see a damping of a fluctuation and Wittgenstein will not be able to explain it. So we cannot really tell. It's going to take us a week. It took us a year and a half. And we prove that indeed there is a damping. So you can't explain with this theory. You can't explain the CMV. But actually it's not so bad. And so what you see here is the curve that you need to fit is the fit I showed you before, which is lambda plus dark matter. So cosmological constant plus dark matter. I put it in gold because this is really basically what you need to achieve. If you just have TEVS, it's a disaster. So just this theory, which is basically a tensor, a vector and a scalar, it's a disaster. But if you put this TEVS theory and you add manually behind a cosmological constant, then you get the dash line, which is not too bad. I mean, it's not working, but it's not too bad. You add the three nodes and then you get the black line which basically fit the golden curve up to the second peak. And then after, you see the seldom thing. Then you see that the fluctuations, the scales, the small scales are being damp because the biomes are biomes that dissipate. And so it was great because on one hand, we could prove that, yeah, there is a sildemping and it's not working, but on the other hand, it's close enough to start to tell you maybe modifying gravity is actually a possibility. I didn't want to show you the latest result from my colleague, Konstantinos Kordis, but basically he had a new theory and it works, actually it fits the CMB. But then the problem is it doesn't reproduce more. So it's always afraid of. So we see eventually if we solve this problem, if I always say the day you can fit the CMB and the galaxies with modified gravity theory and we didn't observe a particle, then I will personally think it's modification of gravity rather than a particle. But we're not there yet. And so going back now, since there is no so far modification of gravity, which fits everything, let's go and see what happens if you think about new particles, whether they actually fit anything. So you know the solar model, squarks and leptons and we've seen also mediator of interactions. We know the gluons, the photons for the electromagnetic force and for the weak force, the W and the Zebo zone. And then we know that what gives mass to particle is actually the Higgs boson. Now we're saying, in principle, you have this and you need something else, which is a dark matter. Now there was a question about the neutrino and I will answer about it. But in principle, you could say, well, maybe we don't need anything else. Maybe we can just use a neutrino. And that's what people thought about in the latest. And just put this for recreation but just to tell you that it's one of those particles which is essentially a node and the problem with this is that the mass range can be anything. So it can be from 10 to minus 20 EV or even less to anything you're thinking. So even 10 to the 60 EV. So the mass range is absolutely enormous. Worse than that is not just the mass, the interactions are unknown. So yeah, probably dark matter doesn't interact as much as a biome, so that's fairly obvious because otherwise we would have seen them. So we know that. But tells us that we don't have electromagnetic interactions not at least like the ordinary matter. So not the one we know, fine. Kind of knew that already. It tells you that they don't cluster apparently. So people have looked for that actually. They don't have strong force as we know in the Stola Voodoo. So as you three forget it, you won't forget it. But anything else like SU2 could work. And that gives you an interaction which could be as weak as you want potentially even zero interaction of a type of Stola Voodoo and maybe just gravity. So among the candidates, you see all sorts. Here I've stolen this slide from Jean-Franco Bertone. You see action, you see stirrer, neutrinos, wins and wins, yeah. That would be the subject of the fourth lecture. But in principle and primordial beckos, but in principle it could be any of these. Now for the neutrinos, people have looked and for the neutrinos, you can see the papers from 1972. So people started to have information about the rotation curve and started to think about hidden mass. And one hypothesis was, well, maybe the neutrinos have a mass and then what would be the mass to feed those observations? And in this paper, they were saying there should be a limit which is 80 EV. At some stage it was 17 EV. So it's always of a range of a few EV, let's say. So fairly small mass and that would be enough for explaining the whole dark matter. And the reason is that there are plenty of neutrinos because they never disappear. It's like the photons never disappear, always there. So the worst thing which can happen to them is basically becoming non-rightivistic, but otherwise you can treat them as photons. 1977, an important limit came out which is saying which is not really the case for neutrinos, but which is saying that if there is new particles, if they annihilate and you would see that there are plenty of other hypotheses, then the mass of a dark matter has to be bigger than a proton, essentially. So with those paper in mind, people started to realize that the neutrinos have to be very light. The question is, I mean, they can be around a few EV and explain the dark matter, but then maybe you can also think about a new type of candidate which will be heavier than a proton and that would actually fit the observation, not the CMB, but just everything else that you observe, mostly the rotation curve of that actually. So what about the neutrinos per sec? So the neutrinos, if you have ATV, the neutrinos have a following story. It's always a bit technical. It's probably, maybe it's not very wise to finish, I have a few more slides, but maybe I'll come back again on this later on, but I just wanted to show you the following. If you have neutrinos, you know that, so the mass would be small, a few EVs, and you know that they don't interact much. We know that they interact through their weak force and most of the time their interaction cross-section is less with electrons, for example, is about 10 to minus 40 centimeters square at 1M EV which is considerably lower than the Tonson cross-section and it could be smaller than that. So basically what it tells you is that they spend a lot of time basically not interacting with anything. I mean, their mean free path is very large and so they tend to diffuse. And if you remember, I told you in order to explain the galaxies, the Syriac argument was there should be no dissipation because you don't want something to diffuse basically. So the neutrinos tend, you cannot cluster them in a small region of the universe. They would immediately tend to what we call free stream because they don't have interaction which allow them to stay coupled to the balance, for example. So they spend most of their life on their own freely propagating in the universe. And as they do that, they basically they never stay in a small fluctuation. And so what neutrino can do is create very large fluctuations, very large structure. So they will be able to create cluster but you will not be able to create galaxies. You cannot explain the formation of galaxies very easily with neutrinos. And so because of that, so I will come back on this side I give you much more explanation and further lecture, because of that it was very clear that it's not going to work. They're not going to be good candidates. But the final straw was actually given in the 80s and people started to simulate what would happen, what the universe would look like with neutrinos. And what they found is called hot dark matter because most of the time, if you want because they, what dominates because they don't have a mass, it's just the velocity. So that's why it's called mostly relativistic. So that's what they call hot. But if you do the simulation, you can see that they don't fit, actually everything will produce the data. So these papers from the 80s and basically the 1983 was a clear no to neutrinos. It's like it can't be the dark matter. So I put three in fact, you can see the one in the bottom which was telling you, well, the dark matter has to be heavy. Otherwise you cannot explain what we see. The last paper that you see is starting to think already new particles, so not just neutrinos, but beyond the stonar model. And they start to mention supersymmetry because supersymmetry was actually developed in the 70s, starting in the 70s. And by 1980, supersymmetry was already developed. So they could actually start to look at specific coordinates. I think all this is more technical and it's probably late and you're tired. So I'll skip that and I'll come back to it. I just wanted to show you this briefly. So the evolution of the field is really starting in the 1920s really to some extent, but the key point was 1966 with pebbles and then with silk in 67. And then in the 70s with the rotation curls of a galaxy. But there you could indeed think that neutrinos were a possible dark matter candidate. And by 1982 that was over. And from there, this is what I call the, really the birth of cold dark matter in the sense where people saying, well, we need a massive candidate and the interaction shouldn't be too large to avoid dissipation. So it has to be something and I explain why it's called cold, but it has to be something which is fairly collision-less. Then the major step we will see later was in the 90s, so 85 basically people started to think about techniques. So mid-1980s techniques to detect those particles, direct techniques and indirect techniques. And then as I say, then the CMB was measured. And I think basically the last rule was in the 2000, after 2001, then that was really clear that whatever it is, it needs to be there basically from the early set up for the universe to nowadays. So what we're looking for is as I said, possibly modification of gravity, but really hard to achieve to explain the CMB or a particle, a particle that is there formed basically early on with the CMB to nowadays. And this means basically needs a lifetime which is essentially the same as the universe. So it's a long lasting particle, it doesn't decay. And that will inform the type of particle we can think about. More details if you want here, more reference. And maybe I'll finish on that slide probably. So just to remind you all the evidence. So when I told you, well, the CMB provides evidence for the dark matter, it's not just the CMB, it's also the fact that we see some galaxies with halo, we see some lensing, we see some filaments. All of this is extremely hard to explain with other things than new particles. So there may be a big surprise and it might be that we need to modify gravity, but it is absolutely understanding that with new particles and I'll explain why with new particles you can explain all those observations but providing that you had a substance which is a dark energy. Thank you, I think I'll finish here. All right, perfect, many thanks. So I think I will proceed to take the group picture and then we can continue with the Q and A for the human minutes. Oh, is it possible to, I need to leave at eight? Yes, okay. So I guess you can take them tomorrow for the question though. You prefer that? Okay. No, no, no, I'm saying if you leave at, yes, we can finish sharply at eight, that's fine, yeah. Yeah, okay, all right. But first let's take the group picture. I need to...