 So now I leave the floor to the first lecture of today and I will wish everybody to enjoy the school. Is that okay? Yes. So I will introduce the first lecture of the school today is Celine Bum from Sydney University. She's an expert of astroparticle physics that matter early universe and she will start this cycle of lectures on astroparticle physics. Please, Celine. Thank you very much and thank you very much for this invitation. It's a great pleasure to be able to teach again remotely. Some people will understand that obviously Sydney is a far away destination and so in a sense being able to teach remotely via Zoom is an opportunity also for some other people. Okay, that doesn't work. Okay, great. So there is a disclaimer I wanted to do. There's a few things I want to say before I start. Astroparticle is obviously a very wide subject. Obviously it's astro and particle so there are many directions and I'm going to mostly focus on dark matter. However, I'll try to make a few links to gravitational wave eventually towards the end. I want to provide an holistic view of the field. So usually I start straight with dark matter. In this case I'm trying to maybe start with cosmology and show you how dark matter comes to play and why basically cosmology is so important for understanding probably the microscopic nature of dark matter. So I will start from a microscopic go down to the microscopic and then go back to the microscopic. And the first lecture is going to be very cosmology focused. So I hope I won't bore you too much probably there are many things that you know already maybe everything. But I'm going to say it in order so that we all on the same page, but also because there are a few subtleties, which I really want to raise so that later on I can make a point about the nature of dark matter. Now because I'm in Sydney Sydney and I mean Australia has tradition which is any lecture or any public event has to start with the acknowledgement that Australia was once invaded by a British. And so am I acknowledging and pay my respect to the many traditional custodian of the land upon which in this case we meet and I meet. For me actually being based in Sydney I mean the land of a Gadigal people from the Arab nation. And so I pay my respect to the elders past and present. I guess it's true for anyone in the world would be in similar situation. And before I really start the lecture I just wanted to present myself so that you know who I am and why the lectures maybe will have a certain focus. And as Giovanni mentioned, I'm across several field cosmology particle physics mostly, but then also a little bit astronomy and astrophysics. I've done a lot of work on dark matter, but also super symmetry particle physics and no structure formation and cosmic ray. Lately I've worked more on polarization have a strong obsession for polarization which I hope to to mention later on at maybe in the fifth lecture before lecture. And maybe it's worth for you knowing that even though I will only speak about dark matter I have worked and modify gravity and in fact continue to work and modify gravity. I will speak a little bit about it, but I will let the floor open for questions. So I was the head of a space mission, which was was meant to succeed today. So I know a little bit of astrometry, and you will see that it's actually relevant for that matter. My real field of expertise is dark matter interaction and structure formation. I think I'm known for like dark matter and light mediator. I've worked a lot with simplified models, which hopefully I will present, and you will see why so powerful and why so interesting. And the last thing before I start the lecture by now you know that I have a very strong French accent, and that's because I was born in France, studied there. But I've had a great honor to study or so for postdoc to work in Oxford and then Geneva. And then eventually got a position both in France in fact in the UK in Durham, which is the last picture and then right now I'm head of school at the University of Sydney. And one day when COVID will stop or we will be free to travel I hope everyone can come and see me. Right, so I'm going to start the lecture hope everyone is okay. Probably, I don't know if anyone can clap but okay. I'm sorry somehow it doesn't. It should be fun. So the first lecture as I say it's going to be more about cosmology so I want to introduce dark matter but really in a cosmological context. And then the second lecture will be more about evidence and key requirements to build coming to understand the nature of dark matter. The third lecture would be more about the particle physics aspects of the particle physics candidate. And then the fourth lecture will be mostly about signature. I think that the last lecture which will be only one hour is back to the cosmology and also we have understood all the important particle physics aspects, we can understand the context, and the implication of dark matter on the CMB and large construction. So let me start with something very basic, what is to a kind of reminder of our place in the universe. And we, we know we live in the Milky Way. For some of you you may discover that the Milky Way actually from Australia at least looks like an image of dark innocence. So this is a picture of a bird that you see on the right. And this is what aboriginal people actually realize very early on so innocence Australia is a bit of a land of the first astronomer. Now the size of the Milky Way is mega parsec. It's about 10 to 12 solar masses. It's a very big object. But it turns out that we do not live isolated. We live in a local group. I don't know if you can see the title. Is that okay. So we live with other galaxies. The most famous one perhaps is Andromeda and 31. And then we live with others such as triangle and small one and 110. And you probably all know that there is also with us we've got with a Milky Way the LMC and the small and sorry, the SMC that you see on the picture in the bottom of the image. So we're not alone and we part of a local group, but there is more to that. Which is that when you look at the map of the surroundings is full of clusters and even structure which are even bigger such as super cluster. So the Milky Way and the local group basically are sitting next to the Virgo cluster. And then they're sitting next to the Coma cluster and other clusters. And all of these in fact form a much bigger structure. So here is the structure in which we really live, which is not a bound structure. It's actually free in a sense, but it's all our companions. And it's basically the Virgo cluster and the local group. And a few of our cluster in particular you may see this picture of the center is super cluster and a few of us. So what does it mean? It means that if you're trying to understand the nature of dark matter, you need to understand the neighborhood and you need to describe it. So whatever you do as a particle physicist, if you just focus on particle physics, but you want to understand the nature of dark matter, you need to make sure that the model that you will propose is actually compatible with the observation. And that means basically understanding why those galaxies and why those super cluster are there, the way they are, and why they are together like this. Now, there is one other thing which is very surprising is that not only we are close to other clusters, but in fact, we are actually close to avoid. And avoid means that there is no structure inside. And this is a fairly big one, sorry. So it turns out we just at the border of avoid. So not only we are close to clusters, I'm super clusters, but we're also close to next to nothing, let's say. And this is another way to sit. And so you will now see the local group which is more or less in the middle of a picture. And you see on on the left side on the green basically with green image is basically the sharply attractor and you see lines going through with little arrows and those are the velocity so we are actually falling into a kind of attractor. We are not the only ones every everything is moving towards that direction. So you will see that comma, the local group and so on are going in that direction. And again, the void, which is near us. So seem to go there. So somehow, again, if we want to understand the nature of dark matter, we need to understand why the universe that we in which we live basically as these properties. But it's perhaps more fascinating. I don't know already that I found already very impressive but but I like a super cluster is actually part of the filament. And this filament is mostly dark matter, but it's also some ordinary matter. But what you see is that heavy structure in the universe is essentially connected. So it's not that we're living on our own. We have specific positions, but we actually all connected through an invisible structure substance which I will explain later on. Again, this is a very important property, and we need to understand the density of those filaments in order to fully understand the nature of that matter. So now that we know our place in the universe and you can see that we're really not in the center of the universe. The question is, how did the structure form? So how can we explain all those structures that we just presented? And that could be 10 hours of lecture on its own. So I will try to make it in a condensed version in less than basically in one hour. The beginning of a story, you know it. In fact, probably most of the story you've heard and you've already studied it. What we want to insist on is the important ingredients that we need to master in order to understand again the nature of that matter. So the first thing is, in order to understand what's going on, we need to have a space time. We need to describe basically space and at the same time, the component of time. Once we have time, we have time evolution, which we will need anyway, because we know time evolves. Then we need initial conditions and the choice of initial condition is absolutely critical to end up with the universe that we live in. Obviously, we matter, so we need matter, we need light, because every single observation in cosmology, apart from gravitational wave, is basically based on electromagnetic properties. Of course, we need gravity. We think we know it. We may have a surprise, but so far we can assume, and I will assume, Einstein gravity. And of course, we need a mechanism for growth from the initial condition to the universe that we see now. And along the way, we'll see that we probably need more ingredients. So let me go through all the ingredients one by one. So space, space time. The first thing is the first hypothesis, which already you saw is kind of wrong, is the universe is homogeneous and isotropic. Now, I'm saying it's wrong because we're already seen that we're living close to cluster and super cluster, but also close to avoid. So the universe is actually not really homogeneous. And it's not isotropic. It depends on the direction where you look at. But if you look at the big picture, it is mostly homogeneous and isotropic, and it's good enough, as you know, for a physicist to start working. And once you said that, then you want to see the kind of shape that you're dealing with for a metric. And there are many shapes you can consider, but the easiest one would be a spherical shape. You can have a subtle shape or you can have a flat space shape. Now, as I say, we kind of know whether the universe is homogeneous and isotropic, but back in 1989, for example, there was a first, I mean, that was really the beginning of cosmological observation. People didn't know if this assumption was correct. And if you don't know if it's correct, then you don't know if you have the right metric. So if you're making the right assumption to define the metric. So those observations were absolutely critical. And you can see that no one was in the first observation. There was really a validation of the isotropy and originating. However, it was indicating that the universe was actually filled and probably filled more extensively. And 15 years later, people already got a picture, which is more or less correct now, which is with a 2df, which is sorry, we already have a picture where clearly the universe is isotropic and homogeneous. So going back to now after the validation of this hypothesis and the question is how do you describe your space. And as a side you have possibly three choices you can do more complicated choices. But the three choices which are fairly easy to take because you know there would be isotropy and homogeneity would be, for example, taking a sphere. And if you do this, the metric is very simple. You need a component of time. So the first part of the metric is squared square, but then you need a component which is basically describing the sphere. This means you have a radius, the size of the sphere if you want, and then you have the angular component. What is really important is because we made this assumption of homogeneity and isotropy, we don't need to include terms which would mix to define or the radial component. So here I didn't put the radial component, I'm assuming the sphere is fixed. However, later on, one has to think about what happened if the radius is changing and this leads to a generalization, in fact, by the four gentlemen who are in the picture there. One, as you probably all know, was a priest. And eventually all of them contributed to this metric, which is now referred to as the Freedman, the Metroberson Volcker, which is written below. So as such, it probably doesn't, it's not necessarily easy to understand, but the dk square is basically representing a singularity or possibly a singularity can be actually just describing the r component. And if you want a flat space would be just the r square. fk is a component which is related to the geometry of the universe, and you must get a square is simply this component about the angular information. So, when I write it now like this, I'm using a notation which is not necessarily the one you found in the literature. In the literature you will see r of t, which actually often is a of t, and that's to denote the scale factor. Now, a of t means basically the size. If you take geometry as a sphere, this sphere which is evolving with time, so the scale factor mean the stretch of the metric, basically. And then, as I say, the fk of guy, this function will describe the geometry. Now, when you write the metric like this, you have no clue what it is. So you have a choice. And in principle, if you work well, the data should actually select the value of this function. So we see the spend the space time metric, and we need to see if it's time evolution. I'm going to refer to things that you I'm sure you all know, but just to make sure we all on the same page. If you start with a little sphere, and it evolves, it grows, then any light emitted by, for example, a star eventually, which is supposed to be received by you will have been stretched through the growth of the sphere. And so you can define basically the redshift, which would be a difference between the wavelength that you receive minus the wavelength that you was emitted. And of course, this is in relation to the wavelength, which was emitted at the beginning. So with a bit of maths, which are very trivial, you end up with a notion of redshift, which is basically one plus redshift at which it was emitted is basically the ratio of the size of the sphere at the observational time divided by the time at which it was emitted. Now, when you when you do this most, maybe most known formula is a five that then you have one plus the redshift at the time of emission equal to the scale factor. So are today, which is referred in the literature to a not divided by the scale factor at the time of emission. I see that there is a chat, but I, so I'm not opening it. Should I care about it now? Don't worry. We'll interrupt it. Okay. Thanks. So this leads to a very famous formula, which is one plus the redshift is equal to the scale factor today divided by the scale factor at the time of emission. And what is very important in this formula, I mean, it's one of the simplest formula you can think about. But what is very important is if you were able to measure the redshift. So, so basically the wavelength of light emitted by an object in the past, then you were able to tell the size of the universe at the time. That's a very strong formula. I mean, it's really remarkable, extremely simple, but it's absolutely key for going back in the past and understand the universe in the early times. Now a person who was the most, I mean, the biggest contributor, maybe at the stage was Edwin Nobel in 1929 realized, well, basically you can measure this wavelength and you can plot them in terms of a distance. So this is a plot that he obtained. This is a very famous plot, which no PhD student should repeat in such a way because you will notice that he's speaking actually about a velocity. The velocity is not expressed in the correct units. And so nothing is consistent is kilometers and then the x axis is parsec. Anyway, it's a confusing plot at first, but what is it even worse is he got some data points and draw a line out of this. I'm sure now machine learning would do worth of that. They probably get the wrong answer. It turns out that his approximation really now approximation was actually correct. What is done really is the same measure of a redshift by looking at the wavelength, but actually a redshift is an indication like the droplet effect is an indication of velocity. So once you found the redshift in fact you have an indication of a velocity. And what you obtain with this interpolation of a straight line is basically that the redshift is proportional to the distance of the objective in the past. This is proportional. So there is a constant of proportionality, which is now referred to H like a ball. And for today it's called as not as zero. So if you put things together, you have one on one hand you have a redshift with a velocity and then you have, you can decompose the velocity as a distance of the time and then you have basically this constant of proportionality with a distance. So you have a relationship which tells you that basically as not is simply the inverse of the age of the universe. In reality that's not exactly correct, but that's good enough for now. So if you can keep in mind that there is this relation between as not and the time so if you measure as not you have at least an indication of the age of the universe. There are some subtleties, but I actually won't discuss them in this lecture. Now if we think, go back to our meaning of a redshift. So the scale factor today divided by the scale factor in the past. Well eventually, if you measure, if you found an object which is extremely far away in the past, so large redshift, then the scale factor would be tiny. And if a scale factor is tiny this means that the size of the universe at the time was extremely small. So you can imagine that eventually you go back to a singular origin. And that could be the big what we call now the big thing. As I say here I'm using a sphere to illustrate the concept because it's made easier but you can do this with in principle any geometry. All right, so we have space time we have time evolutions. So I'm going to move to initial conditions. So initial conditions were actually given in a strange way. We obtained in 1964, after a discovery which was fortress and a bit weird. So the two gentlemen on this picture are Pence and Wilson, and they were basically working for Bell at the time, and we were trying to build a radio, basically a radio detector if you want. So precursor radio astronomy, and they obtain a signal, which was not disappearing. But this signal actually was spoiled by some some pigeon were lodging the detector. So they went, they went to Princeton mess you could discuss with people that you see in the box decay peabirds horse and Wilkinson people's was actually a PhD student at the time. And the story is that his advisor told him to discuss with him and see if he could help them. And I led to this paper, which is a separate paper from the discovery of what is now known the cosmic black body radiation or cosmic microwave. So there was one paper for the discovery the experimental discovery if you want one paper for a theory. And in the in the vertical interpretation, and in that paper, which is, which is shown yesterday shown here, you realize you can see basically that they realize that the trace which we're finding this in this experiment was basically the first sign of the radiation from the big bang. And you receive it today had shifted, but you receive it today. And because you receive it today you actually measure I mean it's like it's electromagnetic radiation so you can actually determine the energy of a temperature if you want. And surprisingly enough it's extremely extremely cold. I don't know that there was a big bang. This was the first, first evidence of it. If you don't know that the universe evolve, then it's also the first evidence because you have to understand why if the universe was extremely small and emitting radiation. Why in the end we end up with this massive universe where actually the radiation is a very low energy. The thing which I just wanted to show you is that in this paper so back in 1965 they really understood the notion of singularity that. So if you see the first sentence, the assumption of continuous creation, which avoid the singularity by postulating a universe expanding for all time and a continuous, a slow creation of new matter in the universe is basically what what they realize what's important condition. And the assumption that the creation of new matter is intimately related to the existence of singularity, and that the resolution of both, both paradoxes may be found in proto quantum mechanical treatment of Einstein field equation. I mean, absolutely. I mean, if you're a theoretical physicist, this is key. I mean, this is 1965. Probably when they wrote the paper they realized how important it was but maybe they didn't realize that they were actually setting cosmology forever with those two key observations. So we've done a space time time evolution initial condition we know about the black, sorry, the big bang and we know about the fact that in there was a singularity and matter of light has been related to the existence of a singularity probably produced by quantum phenomena. And now so let's discuss matter and light. And so I'm just going through this. So the thing I wanted to to mention is that first of all we said there is a metric and this metric as properties which are given basically by the Einstein equation. So it's a left side of the metric, but then the matter goes on the right side so this is very well known when you study general relativity. When you neglect the possibility to other constant. Now Einstein himself at first didn't have a constant then realize that the universe after a renewable discovery realize that probably the universe was not static. However, I didn't believe actually that the universe was expanding. And instead of admitting that is very was actually not predicting the right thing. He actually modified to make sure that I will still predict a static universe. So I think is one of the rare example where where a physician modified theory not to fit the observation but actually to do the opposite. There is a constant in this equation, which is called lambda and which we will refer to later on. It's a very important, very important constant obviously, and we will see how it's been determined. The other thing I need to mention, again, I'm hoping that you will see in the derivation of this equation, there are two free money, two free money questions. I lost the screen. So let me bring back my. Yes, not full. I'm not sure. Okay, so, so there are two equation too many questions for to describe basically the evolution of a scale factor. The first one is really directly related to the velocity in a sense, and it's just the first derivative of a scale factor with respect to the scale factor itself is related to the energy density in the universe. So that's the first term. Unfortunately, my math doesn't work, but hopefully people will recognize on the right hand side. This is the first term. Then there is a second term, which is related to the curvature of space time with K. And then, as I said, the third term is related to the cosmological constant lambda that Einstein introduced. And the second equation actually not involve the acceleration parameter, if you want, or the acceleration parameter. So there is the double derivative of a scale factor. Then it's also related to the energy density, the pressure P, and then the cosmological constant again. All right. So let me go through the first equation. First of all, so this is the first free money question. Now you have a term you have two terms in it, which you own three terms that you don't know there is a density. So this is a density of matter and radiation in principle. There is a curvature curvature of space time. And then you have geometry and then you have the cosmological constant. If the universe is flat, easiest case, K equals zero, no curvature. So the equation, and you can, I didn't say that I think, but the above right is related to a dot of a. So this is basically h square equal to a pi j row for matter and radiation divided by three plus lambda divided by three. If the universe has the form of basically of a sphere, it's like a closed universe. Then in this case, K equals one plus one. And so the free money question will take the form that is written on the left. And even universe is basically of a form of a saddle, for example, it's called open. And then in this case, the curvature K would be equal to minus one. And the free money question would be given at the bottom on the right. Okay, so a bit more maths and then I'll come down to more observations. So the first thing, which is very important to realize is what you have an equation where you have three unknowns basically K row and lambda. But if the universe was flat and there was no lambda like Einstein was considering at the beginning, then the equation would be very simple. You would say that basically the above right, so a dot of a is related only to the density in the universe. So what this means is that remember that H is telling you how the redshift evolve over the distance so is and is related to the velocity. So basically the evolution of the universe, even by H is only driven in this case by the density of matter and radiation. So what we're really saying here is that if there was no curvature and there was no cosmological constant, then you measure the density of matter for particles of radiation. And then in principle, you know the evolution of the universe, you know, basically, the right at which the universe is essentially expanding in this case. So this is giving you an equation is square equal a pi J row and a row which is critical because that's for the condition where K equals zero and I was there. And you basically can infer the value of this density for which essentially you have only the matter and radiation guiding the expansion of the universe. Now the thing you can do is saying, well, but K and lambda are not zero or we don't know. So maybe another zero. So now you can just try to divide this equation by h square. And you will recognize by doing this. So the left side of the equation is equal to one. But the right hand side, the first term would be essentially row divided by both critic. The second time, the second term is written in the middle. And then the third term is lambda divided by a pi J. So you have divided also by page. The first time is so nice. You could write an equation with all those terms. The chances that you're going to miss a few terms so it's better to start to give him names. So the first time row divided by your critic is called the first cosmological parameter associated with even matter radiation principle as such as written like this is the sum of matter and radiation. And the second term is basically a cosmological parameter associated with curvature. And the third term is a cosmological parameter associated with London. So, now if you think, well, the density is basically matter and light, then in this case you have a simple equation which is that the sum of all three cosmological parameter or four cosmological parameter if you separate the matter and radiation that is equal to one. So you may, at this stage, you may wonder why doing this. Well, the point is, if you're able to measure two of them, you get the third one. But K and lambda are actually very fundamental information about the structure of the universe as we will see. So, the other thing is exploited one equation, which was the first with my equation. If I go back to the second equation from Finland. The second equation is basically, again, as row and the pressure but if the cosmological constant was dominating, then he would just tell you an information about the rate of expansion. He would tell you if lambda is positive, that the universe is not only an expansion but actually accelerating expansion. If lambda is negative, he would tell you that the universe is actually in this writing expansion. So, measuring this quantity is absolutely fundamental to understand the fate of the universe itself. And of course, if you're not in a situation where lambda is dominating, which would be, for example, the case if, if lambda equals zero, for example. In this case, you're back to saying, well, the rate at which the universe expands only depends on the constituents which are made of matter and radiation. So it only depends on particles. So you have two choice and the question is which one is correct, which one nature choose. And the three gentlemen here are the one actually who got awarded the Nobel Prize for leading the collaboration or actually found the answer. I should say I was a PhD students at the time. And just before we had a lecture, not at the CTP, but in another school, and Joseph was showing that lambda so was either zero or one depending on time. So it was a time dependent evolution, depending on the on the decades. In the 60s was zero or something like the 70s was everywhere. Everyone thought it should be here and then back in the 80s, everyone put it to zero and so on. It was oscillating. So this was actually the first time that we had a strong answer. And this is the first answer. It was done actually with not so many supernovae so the answer was brought by looking at the redshift from the supernovae and looking basically at the distance. So on the on the y axis you have a distance between basically between supernovae and then maybe maybe I don't explain too much of this figure but because there are things I didn't really say but you can see on the right hand of y axis. Sorry, it's the redshift. Now, there were not so many. Now you have many more points but at the time, mostly all the supernovae that the group measure and different groups measure were up to a redshift one and it was really hard to get supernovae which were further away from that. But essentially the points where on this plot were corresponding to a question of whether the universe expense forever or is going to collapse. And so correspond also to a deceleration of all the acceleration. And you can see from those points that actually was very clear that the universe was not decelerating. It was not fitting. And eventually it was clear that in fact was points correspond to a universe which is actually accelerating eventually today. So it was clear from there and it was 1998. It was clear from there that actually the universe is accelerating that we knew, but actually is in accelerating expansion. And then we realized through the same occasion was lambda was not zero. And we had the first measurement of lambda. So fast forwarding a bit but essentially looking at the cosmodic parameters which fit the distance of those supernovae versus a redshift and you can see what I was saying that the maximum redshift at the time was less than one in fact. And you can see that the best fit corresponded to a curve where so take the strong straight line is a curve where actually the cosmodical parameter associated with lambda is in fact equal to 0.7. And so this was another major realization. And for me as a PhD student, this was particularly remarkable at the time because I started my PhD with a subject which was dark matter dominates the universe. And just a few months later I was actually not. It's lambda, the cosmodical constant which dominates the universe. So remember I said one equal cosmodical parameter so omega plus omega k plus omega lambda. You can see when omega lambda sorry for typo should have been capital lambda. But when omega lambda is equal to 0.7, you don't have much space for anything else, neither for the curvature nor for matter and radiation. So it already sets a very important lesson that this constant whatever it is, this constant is actually dominating the universe and driving the expansion of the universe and the right at which it expands. Another thing is this measurement tells you something about the matter and the cosmodical parameter associated with matter here is equal to almost 0.3 in this book. And that basically tells you something about the fact that you don't need curvature. It does tell you also that matter is actually 30% of the content of the universe, which is a good information because the universe could have been closed. So the sum of all the components could have been actually bigger than one, and then you needed omega k to be negative, or it could have been lower than one and you need it. So it was opposite and then you needed omega k to be positive. By now, you can see on the plot at the bottom that we're achieved. We have data with supernova data and we have data up to achieve five. Well, that's not true actually, but we're starting to have data up to a certain point which is far enough. We have lots. I mean the first few points which were measured up to achieve one where the master correct, but we start to have data far away now to be able to tell where whether, I mean, whether this is a true feature or not. And obviously, by now, we always found that indeed there is an accelerated expansion. I mean, some people try to analyze the data and have a critical look at the data, but there is a fairly good consensus on this aspect. Now on the right plot, on the right hand side of the plot, you see omega lambda versus omega matter. This is not, this is a plot from 2011. Now this has evolved, but you can see already the blue region is given by the supernovae. The green region is called organic acoustic oscillation and I'll come back in the second lecture. And the orange region is a CMB. So I didn't explain how those curves were obtained, but you can see that there is a fairly good document. I mean, they all cut at a point where actually the universe is flat. So it really says something if lambda is dominating, the universe doesn't need a curvature. It has to be flat. Once you've said that, it's a measurement for today. And then you have to look at the evolution of a cosmological parameter and you see that the cosmological parameter evolves as one over a square. So for scale factors, which were very small, so in the early universe, this term would have been extremely big. So if it's zero today, it has to be zero in the early universe. So they're very close to that. And so it basically tells you that the universe has been more or less flat for a very long time. When you may say this is not compatible with the idea, for example, of a sphere as a geometry, but there is a mechanism which explains why the universe has a size that we see today, why everything actually seems to be connected and yet may start from the singularity. And this is called inflation. I don't think I will have time to really speak about inflation in this lecture. But the two ingredients that you really need to keep in mind from now is we have a story, which is we start with a big bang. The singularity, it's basically meaning this is where the beginning of math starts for us. So this is where we can have a physical description of the universe using the math that we know. People are trying to extend what happened before a big bang, but this is not a question I will be addressing here. And then after that we have a phase of inflation, which basically delets all the dimension extremely fast. And then after that the universe is basically as it's kind of flat curvature and then can evolve and things can happen. By things can happen, I mean essentially the light and matter can start to have, can start to interact with each other. Particles can become massive and then eventually some transition will happen, which I'll describe later. All right, so now I'm going to discuss a mechanism for growth. And maybe I will slow down a little bit because this is where it becomes, it's not very known maybe. And this is where it becomes the most important for that matter. So I mentioned the cosmic microwave by Grand and I mentioned that it was discovered by Pencels and Wilson, but in particular interpreted theoretically by four people, including Peebles. Now Peebles in, so he was a young man, he was a PhD student at the time in 1965, but a few years later just in 1967, he actually post-related, so he had the initial condition and he was still wondering how you can pass from those initial conditions, where the universe is called to the universe that we see really. And he post-related that there must be some gravitational instability in the universe. And that means, read by that, there must be a region of the universe which are not extremely or basically not exactly the same in all directions. So it was in a sense questioning the notion of homogeneity and isotropic. What is interesting is that this paper is probably the most important paper in cosmology. In fact, I mean, Peebles got the Nobel Prize. But this paper has only, this is all now, but only 85 citations, like three or four years ago. Yet this is the paper which sets the whole fate for the universe. So it's interesting if your paper is not very well-cited, maybe it's just misunderstood or people are interested in other things at the time. So in this paper, what Peebles said is, it's argued that the expanding universe is unstable against the growth of gravitational perturbations. The argument is directed towards two problems, the physical conditions in the early, highly quadratic phase of the expanding universe and the formation of galaxies. So it was really trying to explain the formation of galaxies out of it. So the question is, what does it mean by gravitational perturbation? What is this? And what does it mean the growth of gravitational perturbation? So back in the 60s, it was only the fact that the universe seemed to be filled with a radiation of a temperature which was actually 2.7 K. There was no way to imagine that some regions of the universe had photons filled with radiation which was a little bit hotter than other parts because the universe was meant to be homogeneous and isotropic. But yet people postulate that the universe was not such homogeneous and isotropic and some regions would be a little bit hotter than the others. So in this map that you see here is the first discovery that Peebles was actually correct. And this was obtained by the Kobe satellite with Yerbas and another experiment that was obtained in 1992. Now this map was revolutionary because it was saying, yes, the universe is actually contained what we now know as a perturbation known as fluctuations. So the universe is almost homogeneous and isotropic but not quite. Now once you have this, then you're saying that there's an extra step you need to make which is, well, this is temperature of the universe. So basically you're measuring the photons. If the photons are related to the matter, so if the matter is basically where the photons are, then you're saying that there are pockets of matter in the universe. Some of them have a little bit more densities than others. And then you're almost there because you just need to say gravity acts on those pockets of matter. Wherever the density is a little bit higher, you will have more gravity. They would attract more. They would eventually reach a size which is critical and they would collapse and they would form galaxies and so on. So this is a critical observation in 1992. And I think Kobe was meeting a lot before being launched. I think he was meeting a lot of scepticism because people didn't think those fluctuations would exist. Nowadays, obviously, not only we've seen them, we've seen them with unprecedented precision. It's absolutely amazing. So we know that indeed the temperature of the sky everywhere in the sky is 2.7 Kelvin. But we also know that there are fluctuations and we see that the thing that you see in the middles of the red part is our galaxy. But everything else are basically the anisotropies in the sky, which relates to the pockets of matter I was mentioning which contain a bit more matter than others. And the difference of the temperature between those various places. So between the blue, for example, on the right is absolutely tiny is 10 to minus 5. So what people was actually postulating is that such a difference, which he didn't know at the time, but could have known, but not vertically, but not experimentally. That small difference is actually the creator of all the structure that we see nowadays. So when I show you galaxy, Milky Way, a cluster of galaxy, these times from such microscopic difference. So obviously now that we have this, we can go back to understand the geometry of the universe and many more things, including the type of matter that we have. So the first thing is looking at the metric as I told you, we need to know the radius, but we do the measurement today. So we don't need to know it basically because we inside the universe, so we can really measure it. So the only thing we can really measure is the geometry. And the geometry depends on you can have an information by looking at how the those fluctuations look like. If I look a bit, if I look very stretch, it looks like the universe is basically close, which means basically, you can see the curvature, there is a curvature. If the situation, so if the situation, the map of color, which you see on this on this image is actually looking like all the different places seem pretty close to each other. The universe is probably open you're more like an saddle universe. But on the other hand, if you have a distribution in the middle, you're actually corresponding to a flat universe, no curvature. And while the one that now we know is correct is a flat universe. So the CMB basically by measuring of the distribution of both fluctuation across this guy is basically giving you an important information about the geometry of the universe. So that's a major achievement because as you may remember from the supernovae. You basically compatible with the supernovae results which is the universe is flat no curvature. Okay, so maybe we can have a five minute breaks if you want, and I continue, I think a long time. Okay, thank you. So we'll have a break five minutes. Yes, there is a question from the chat. And I can read it for you. Could you please explain with a bit more of detail how the different perturbation are obtained close open and flat. So maybe I'll do that. I think I'll do, I can do that. I can do that next sorry tomorrow. But I can explain just now the details, I mean the details and I can give more details tomorrow. So the first thing is so on this map, you can see a distribution. So even if there was no anisotropy, so if there was no region of the universe with difference, everything would be the same color would be just one color so it could be red, green, whatever you want. But in reality, there is. There are some place in the universe where there's a little bit of matter more matter than others, and that induce basically an increased density. And so this is why first of all you see the difference of colors that just reflect the fact that you don't have exactly the same density. I will explain tomorrow that the densities are related to densities of matter and radiation are related together. And so if you have more matter you have basically a temperature which is a little bit higher. And so it would look a bit rather than if you have less matter which would be blue. So once you have this map with all the all the different colors you have to understand you start to see some structures happening. You see very large structures, and you see maybe you can I said knowing I don't access my mouse for whatever reason but so you have very large structure and you have very small structures. And you have to look at their distribution. And then the other thing is, when you look at their distribution you have to look at how distant they are if you want. So this is a bit of a hand wavy argument but if you see them very spread out. If you feel like the stretch, then it has to be on like a kind of sphere you have to feel the curvature of the universe. If they were actually compressed, that would be more like an open universe like a saddle. And if they, if they seem normal, like the distance doesn't seem like either stretch or a compressed, then it would look flat. Sorry, that would correspond to universe which which is flat. So there is a better way to do this analysis is not just by looking at how they stretch, which is something I will go in detail. I will give a bit more detail later and then I will give more detail tomorrow, but essentially is by looking at the distribution. So it's really how these analysis tropies are distributed across the sky. The scale. Does it answer a question. Yes, there are another couple of questions. One is by Chandana which I'm going to unmute. Hi. I have a couple of questions. First question is like, when you talk about isotropy and homogeneity. So, what about the range of, I mean, what is the range through which we can, we can observe that like isotropy and homogeneity so is there any range existing like how is it. So, if I go back to, so, if a range you mean, do you mean the magnitude to some extent. So for example, you could have seen. This is the result of an experiment right we send, we send a telescope in space if you want, which measure not a telescope but is measuring the time it's basically like a thermometer in space if you want. This is a result looking at different temperate different original sky. Every time you measure a temperature, you measure basically 2.7 K, but then you see that's very small difference. You could have got a map where it was the same temperature all across the sky and no variation at all. You could have seen something where, you know, for example, on the right would be very, very cold on the left, very, very hot, for example. What you see here is that it's more or less always the same temperature 2.7 K. But they are tiny difference and they are of the order of 10 to minus five. So the universe is pretty homogeneous and isotropic because even though they are tiny difference, they're extremely small 10 to minus five. Does it answer your question. Yes, I mean, what I'm asking is like, we cannot see the homogeneity and isotropy in our own solar system. So, so like, is there a range like beyond the solar system and then a limit. Yeah, so indeed, so you have to look at even at the galaxy scale, you will see the so some inamogenities. Also, so you need to look broader. So when when I show you to the F, which is the first big survey of galaxies and is by having lots of galaxies really looking at different region of the sky that you can see the homogeneity locally is not homogeneous or isotropic you see difference. And as I say, we are sitting at the border of avoid. So, even if we were just looking at our super cluster, we would see inamogenities and anisotropy. So it's really all about this guy by looking as far as we can by having as many galaxies as possible that you see this homogeneity. Almost homogeneity and isotropy is not perfect as you can see on this map, but it's a good approximation. Okay, one more question is, can we go to the slide where you have displayed matter and light. One is equal to omega r and so on. Before that, there was this equation one one equal to. Yes, yes here. So I actually don't understand what is this one like why we are equating these two one. Okay, so what I've done sorry I should have written it is I divided by a square the first take the first equation. Okay, I'm also divided by a pij. Okay, okay. Then like so. Okay. Next slide. Yes, here. So when you're saying lambda dominates what does that mean. It means that, for example, if you didn't have any matter, no radiation so no photons, no particles, you'd say well the energy density associated with lambda is bigger than the energy density associated with with matter and radiation. That would be the force which drives the expansion of the universe. Okay, if it's the expansion is driven by the matter in the matter and radiation. Okay, so my last question is when we say flat universe what does that actually mean. So it would mean for example, if I give you the old energy. If you think the universe as a sphere at the very beginning. And then you imagine that you blow in it like a balloon and it becomes bigger and bigger. It just means that at some stage you don't feel the curvature anymore. You can see the curvature and may still be a sphere but it's so big that you don't see, you're not going to fall for me if you want you're going to feel like it's as flat as like mean koski. So if you, if you imagine a little point, then you can see if you're working on it, you can see the cover you can feel the curvature. It's a huge ball which I have behind for example, it's deflated unfortunately but so take this one is clear there is a curvature, right. Take this one you can still see the curvature but if you're on it. Before you're not going to fall straight so for you it would be locally would be flat. So if you don't see if you don't feel the curvature you feel like the universe is flat. It may not be maybe the dimension or so big that you're not sensitive to the curvature. But what you care about is whether you feel the curvature and whether this curvature is driving the expansion of the universe. If you feel if you can measure K, this means that it plays a role in the expansion of the universe. If you can't measure it, if it's almost close to zero, zero, then it doesn't drive the expansion of the universe. That's not the main component but the main component for the universe is really the the matter of radiation and possibly the cosmological constant. So is there a way to measure K. Yes, exactly what I show you so why my computer is capricious. Okay, so maybe I'll say again there. So what you have you need to know the redshift so you're looking at objects which you're trying to find source which are far away. Because if they far away, then you can determine whether actually they felt they come closer with time or not, or they become more distant from each other. Right, so if for example you're living with a friend and at some stage where you're walking and then you can't see your friend anymore you know that you're basically your distance increase or something happened. So this is exactly what you're looking here you're looking at you're taking a bunch of supernova you're saying whether they actually go further away from each other. And what you find is the point that they obtain they could measure basically is compatible with a prediction for universe which is accelerating in expansion but accelerating expansion. And they could have found the opposite they could have found that actually they come closer and closer together. But that's not what they obtain what they obtain is that those supernova seems to go further away from each other and that goes faster and faster. So it's an it's an expansion for sure but this is an accelerated expansion. And once you have found that you basically have a measurement of the type of how do you drive this expansion so what I didn't say is lambda. If you want it's a cosmological constant constant, but the best explanation for that constant, although we don't really understand what it is but the best explanation is a force it's a kind of energy. And so, in a sense you have nine energy which is driving the expansion of the universe. And then you have also some matter because we're here so we know that this exists. The question is which one is important I mean which one is dominant. So for fitting the distance that they observe for fitting that they needed more energy than matter. So it tells you that actually lambda is dominating. It tells you that matter is important, but the sum they can measure those two components. And when you saw those two components so omega lambda plus omega m. It's almost already one. And it's already telling you that there is no need for a component like the curvature. You don't feel it that doesn't play a role in the expansion. Thank you. I try to come back on it tomorrow maybe. Yes. In the meantime, there are three or four questions maybe we can postpone them to the Q&A and continue or you want to answer them now. I can, whatever you prefer. As you prefer because then, I mean, if you want to answer all them it will take some time so. So maybe I'll finish the lecture. Yeah, maybe you'll finish and then. Okay, great. So we were here and I was showing you some fluctuations. I told you this is very tiny fluctuations tend to minus five, but this seems to have seeded all the large scale structure in the universe. I also told you that the stretch of the fluctuation would give you another information about the curvature of space. This is consistent with the supernovae, and we found that today the universe look flat. So now we can start to think about the component of the universe and already gave you the answer about dark matter. But I'm trying to go back and show you that actually we do need to have dark matter in so ignore it for now. But we know that there is already a cosmological constant which I will refer to as dark energy. So this is probably something that would answer, I mean, maybe not answering your question like this, but this would be key to answering your question. So we have those distribution of fluctuation across the sky. And if you see there is in the middle, there is a very large structure, a bit of blue and sorry, a bit of red and yellow, which goes from the middle, which is the galaxy or galaxy, which is basically shining towards the top of the view. And you have to count how many structures you have of a given size. And this is summarizing the plot that you see now. So this plot is basically giving you, in a sense, a number of structure per size. If you see very large structures, they would be on the left side. If you see very small structure, so just a little group of blue points or red points that would be on the right side. Now what you see here is that the dominant part is actually corresponding to a certain size, which, and it's the composition in spherical harmonics. The value where you have a peak is L equal to 100, doesn't mean anything to you, but it does correspond to a distance to a size if you want an angular size on the sky of one degree. So most structure on this map have a size of one degree. And then eventually you will see that as you go to the right side, you have smaller and smaller structures, but you have less and less or so. What is extraordinary is, I would say cosmology was starting, as you saw already in the 20s with Edvin Nebel and Le Maître and so on. But it became really a science of precision, I mean a precise science, probably in the 80s and 90s. And just in 20 years time, or less than that, we got already some things so well measured that by now we have the Fondamentale and Seuss, which are absolutely extraordinary. So what you see is that all the red points are the latest measure, well the first measurement by the Planck experiment. So it doesn't correspond, the map I put doesn't correspond to the distribution, but it's already there. And what is really, really critical on that is as I say, more structure are picked at L equal to 200, which correspond to a scale of one degree. And then you see a decrease because there is more structure on the right, less prominent than the one where the peak is. So there are less more structure, which means that actually we will see that later. This means that actually you have less more galaxies when you have very large structure in the universe. Now you need to analyze, so I'm going to come back here. You have this plot, you have data, another question is, can you fit the data with this analysis? And there you have several three parameters, you have a quantity of matter, you have omega lambda, so a quantity for the cosmological parameter. You have a value basically S naught, which as I said is proportional to the age of the universe. And then you have a few other parameters, which probably for now you don't need to care. So you have a number of parameters in total, really six. And those parameters help you to fit that curve. Now it turns out that you can fit this curve with the following. 69% of dark energy, sorry, lambda, the cosmological parameter, and about, let's say, the rest. So it's actually 25% of matter and 5% radiation. The point is, when you look at this map, the numbers I put this, I put 69% and I hide the rest. This is really dependent on what you assume there. So in order to, this is basically the result of a fit of the plot, which is on the corner from Planck 2013, but you can do it with Planck 2018. It's always more or less in the same book. The point is, it's a fit. So those numbers are actually a very good explanation to, I mean, or at least give you a good indication of how much the cosmological constant you have, how much matter you have, how much radiation. But you need to remember, and I'll discuss that, that would be very important later on, you need to remember that there are 10 making some assumptions. One is that the universe actually is described by the Friedman-LeMetro-Versa-Rocca metric. The other assumption there is that the component that you put, and I will discuss that, but the component that you put have simple physics that you think you can describe. That may be wrong. If you have beyond sonar model physics, that's not included in this analysis. So it could be that actually you get a good fit, but you get the wrong fit. And I want you to keep that in mind. So when you see those numbers, remember that they obtain making some strong assumptions about the theoretical model underlying your universe, which is basically the metric, the choice of metric, and then the choice of component, the matter of light and light, specific properties here for making this fit. Now, an important thing I should say, when you're a cosmologist, matter means what you call now biomes and leptomes. But for a cosmologist, matter means bionic matter means actually ordinary matter. So the only thing that cosmologists ignore leptomes is just that they call everything bionic. But in reality, it's the two components, the leptomes and the quarks, if you want. All right, so we feel that people was absolutely, and those two, I mean, I highlight them because they're kind of my heroes personally. I think what they've done is absolutely extraordinary. So people actually not only understood the origin of the radiation that pencils and wheels have obtained, they understood this was basically the release of a big bang. But you're so postulated that you needed those fluctuations, those perturbations which ground their gravity to make structures like galaxies. But then another person which is very important is Joseph Silk. So Silk, obviously people as you know is still alive and Silk and so, but Silk used to be my advisor and still a great collaborator. And he was a PhD student. So when the paper from Pibos went out and actually realized something extremely important, which someone else had realized before, but someone else had made a mistake. So basically, let me tell you the story. So Pibos came out with came with this extraordinary hypothesis that must be fluctuation in the universe. I've seen that, but that's what he postulated. And now we know he was right. But then Silk said, well, actually, if they are perturbations, so if there are regions of the universe which are made of matter, and they're so apparently connected to light, well then matter and light are interacting. So when they're interacting from, we know how they interact is the Thompson cross section basically, if they don't have too much energy. So it was starting to say, the moment you have interaction between matter and radiation, you have actually dissipation. And you realize this dissipation could be such could be so strong that you can't actually form galaxies. So what he was saying, what Silk was saying is that you may have math, you may have pockets in the universe which contains more matter than other pockets. But they will interact with with the photons. And they would have a mean free path. And instead of saying a small pocket, which is going to grow on the gravity, it may actually dissipate becoming very big pocket. But then gravity will not act enough to make a galaxy out of it. And so here is the abstract of his paper. So this is a paper which was published in nature he had to in fact. But this is basically in 67 so you see that this was more or less at the same time as people's. What he says is one of the overwhelming difficulties of realistic cosmological models in the inadequacy of Einstein's gravitational theory to explain the process of galaxy formation. A means of evading this problem has been to postulate an initial spectrum of primordial situations. So it's referring to people's. The interpretation of very simply discover three. So the 2.7 Kelvin of my great background as being of course medical origin. So it's referring to the discovery people's make implies that fluctuation may not condense out of expanding universe until an epoch when matter and radiation at the couple. So he is saying, be careful, if a steel couple matter and radiation are still couple, then the matter will fall over for tools that variation and we will not be able to form galaxies. Then the rest is basically the question he asked would fluctuation in the primordial fireball so the very early at the very beginning of the universe survive to an epoch when galaxy formation is possible. Would actually was focused on motor of matter that people's was postulating with the survive till the moment where gravity becomes strong and can make them collapse into galaxies. So, basically, what I was saying is that, and this is a modern interpretation that's not what he was saying at the time but my mind basically reading of it is, which is correct, which is fluctuation, which are made entirely of electrons cannot survive the scattering of photons so they cannot make galaxies. In other words, the fact that we see galaxies today means the universe cannot be dominated by barium, cannot be dominated by electrons, cannot be dominated by ordinary matter. So this is basically for me the strongest evidence for dark matter and I explained that again later on. But basically this paper. So people's was a genius by assuming that they were primordial fluctuations distribution of matter which was not homogeneous. But sir, realize something absolutely fundamental that if they were a couple if a matter and radiation were a couple, they would be a problem too, and you would not be able to explain the number of galaxies you see today. Now, both are right. So the question is how do, how do you reconcile the fact they both right. And it's simple. There must be something else. Something else could be, well, even Einstein isn't it wrong there's another type of you need to modify the gravity as Einstein considered you need to do something else. Obviously it works very well so it has to be at a certain scale. Well, maybe there is a new type of matter, but that type of matter should not dissipate should not feel the photons should not interact with photons. So that the pockets of matter if they feel with this new matter, but stay there but don't dissipate and then can collapse on the gravity. I'm certainly a dojo. I say as a great collaborator. This is not exactly his idea and when we pushed it and understood that what was important is biomes and photons interaction. The first one was actually miss now and it's a very sorry for sorry for miss now, because miss now understood the same thing, but he looked at neutrino photon interaction. Sorry, actually. And those are very, very small. They insignificant. So there's no dissipation from neutrinos biomes interaction. So he did the calculation. He found that anything below certain size, which was basically the size of one solar mass. So ridiculously small will not form object. But this is, this is irrelevant because we see objects at 10 to 12. So by understanding that it was bottle, sorry, and photo interaction. By doing this, he understood that actually you would have a problem to forget access. So it turns out here, I'm hoping that for PhD students here, you understand that research is also a question of looking at what people do and having a critical eye. And in this case, basically realizing if an idea seems good, but doesn't work, realizing that maybe actually even though they're famous, they may have a wrong explanation, and Joe found the right explanation. Right, so let me say it in a different way now. So I've shown you the results from plank. Now this is plank 2018. Same as before, 2013 is not much difference for at least non experts. But what I told you is that if the universe was only made of biomes, we would then form structures like galaxies. Now on this plot, you would see it already. You would see it because unfortunately, I don't have a perfect plot to show it, but this is good enough, the one on the corner on the right. If you set the cosmological parameter associated with bio and you take the biggest value that you can take. So in this case is 0.1, which corresponds to the dotted line. You see that you form a lot of various large scales at l equal to 100, lots of large scales. And then eventually you don't form small scales, they really fall straight after l equal to 100, it falls basically to very small number. But in the realistic model that we know, which is basically given by the straight line, or the straight line in this case, I think, you can see that the fit of the data is actually above for small scales or in the red region. You can see that it's actually above the dotted line. So something, even if you were not still in the sixties, you didn't know that by doing this plot by looking at the distribution of fluctuation across the sky, you would understand something is wrong here. And this something can be matched by assuming that there is a type of matter in the universe that doesn't interact with photons. And in this case, you get a perfect match to the data. You get a perfect match, providing that in addition, you had a cosmological constant. So, the fact that you see this damping of small fluctuation is called the silk damping in reference to what Joe has done in the sixties. But essentially, this is now observed extremely well with a lot of precision. This is an experiment to see it where I called act and SPT and they validated the silk damping. Now we know it's absolutely correct. So as the variance, even if we add another component such as what we call the species which doesn't interact with photon. So in a sense, if it doesn't interact with photons, it's not emitting light. So it's invisible. So it's called dark, so dark matter. And if we add some dark matter, we will see that the variance will provide some damping, some damping of fluctuation. We see less small structure than we see at the very large scales at the multiple equal to 200. So, nowadays, you could say this is the most important evidence in favor of the existence of dark matter. But as I say, this assumes some new form of matter. It could be that actually one needs instead to modify gravity. And I will show you in the second lecture, I think, I will show you that you can. It's just hard and it doesn't work so far. But people are trying and maybe one day we succeed. So nowadays, this is a picture. So utilizing those plots, you found that, as I say, with the underlying conditions, assuming the Freedman, the Metrobius and Walker metric, assuming that you have some ordinary matter, called atomic matter. You have some radiation. You also have neutrinos and photons. So plus a new form, you found that this new form of matter must be about 25% of the content of the universe in order to explain the data. So this is pretty drastic. You're saying basically at that stage that what drives the expansion of the universe, first of all, is a form, is a constant, is a cosmological constant. That doesn't make sense. And if you want to make it, I mean, if you try to think as a physicist, you would say, well, a constant must be a form, must be driven by some something like a scalar field, for example. So in reality, it's an energy, so dark energy that is driving the expansion of the universe actually making it accelerated. And the other form is actually some new form of matter, which is called dark matter. So now you have two competing mechanisms. One is a scalar field gravity tends to collapse. And then energy obviously tends to dissipate and to bring things to accelerate the expansion. So you have on one hand, the universe wants to expand. And then on the other hand, you have a matter of tries to collapse. And that is the way basically, you can already start to see if the dark energy was always dominating, you would have never formed the galaxies that you see nowadays because the universe would be just expanding and they would not be enough matter to collapse. So the matter and the dark matter in particular must have dominated the expansion of the universe at some stage. And then the question is when. Again, tomorrow I'll come back on that. I think I'm close to the end. So I just want to say a few, few things as a spoiler for the next lecture. So we have initial conditions that the black body, the big bang and the black body spectrum as a result. And then what you need to say is, well, you have all those components, dark energy and some form of dark matter, the dark matter feels a gravity. And if you neglect for a moment, dark energy and explain why tomorrow, if you if you neglect it, then eventually you just say well you have basically universe which you can take like a box if you want and you can distribute particles in the box. And then you let the gravity act on it. And as you know, the box was not homogeneous, you had some pockets of matter in some places. So you need to increase the density in some regions, then gravity is acting on it and eventually you start to find structure when it becomes on linear. And you can see this result right in front of you, this is a result of a simulation. So simulating the gravity acting on those pockets of matter. And what you see is what the theory is predicting. And it's basically you don't have general activity here. It's just Newton Newton. What you see here is basically already some filaments, which is good because I told you we are connected to feel and we all connected for filaments. And then if you zoom in one of those filaments, you may find a cluster. And then when you found, for example, the big red thing in the middle is a cluster. And then if you zoom in, you may find a galaxy. Obviously those simulations are made so that we understand the test, the nature of dark matter. So what you want is to find the galaxy which looks like ours, like the Milky Way, so that you can fully understand the dark matter and the dark energy. Now just initially I started telling you where our place in the universe was the Milky Way, which you can see here. And then some galaxies like the Large Magellanic Cloud and the Solar Magellanic Cloud. You can see them here actually on this picture. They're visible in fact if you like taking photos of the Milky Way. But what is incredible is that those are little galaxies and they're living with us in our galaxies. They are companions. And we know now that actually our galaxy has a credit of our galaxies and they penetrate it through the disturb ours and they eventually merge with it. So, sorry. Looking at the simulation and comparing to what we see, it looks like a perfect fit. And I will show you that it's not. And the reason why I'm speaking so much about cosmology is that dark matter is an essential part of cosmology of the universe. And we need to understand if you don't discover dark matter in a lab, then you really need to get the data that you obtain from cosmology and understand them to get clues of what could the dark matter be. So this is not something I will discuss now, but there are spoilers about we have more and more results of the surveys. I mentioned 2DF, there's a new one which is this, delivering results. And there are small differences. We don't know yet if they're important, but there are small differences. I mentioned the age of the universe. You can make a measurement of the age of the universe by looking at the distribution of a fluctuation in the universe through the cosmological microwave background from the map I show you. And you can make a measurement of the age of the universe today with objects like Cepheid. It turns out it's not compatible. So there's something to understand maybe it's related to dark matter. And then there are things in a simulation like this, which are not quite correct. So it looks like quite good, but the agreement is not perfect. And maybe it's a question of bionic physics here. Maybe it's the ordinary matter which is plain, but maybe not. So in the next lecture, I'll bring everything together more on the particle physics side. And I'll show you eventually the last lecture will be really showing you how the particle physics properties can influence all this cosmological picture. And it's really, we could speaking about astral particle, but it's really cosmoparticle in a sense is the whole, the two fields merging together for giving you an answer, which is probably the most fundamental. I will lead to the most fundamental discovery really in probably in this century or next, hopefully. All right, so I think this is the end of my lecture for today. Thank you very much, Celine. Okay, so we can move directly to the Q&A session. We already collected several questions from the chat. Priority to those that raise hands, maybe. So if everybody wrote on a question on the chat want to raise their hand and ask that it would be better. Otherwise, when this, the other question finish, I will read those that have been unanswered. Okay. So I see already one, one end up.