 Okay, we can start with the course about Dark Matter, we have Francesco Deramo from the University of Padua. Good morning everybody. I would like to start by thanking the organizers for inviting me. It's a great pleasure to be here giving four lectures on Dark Matter. That's the topic of my four lectures and as you have already seen this morning it will be a big player in this school. We already heard about Dark Matter in the first lecture on CMB. What I will be giving is more a perspective from the particle physics point of view because it's more connected with my research. So as I said it's a great pleasure to be here. It's actually the first time I got invited to a summer school. Hopefully not the last. We'll see how it goes. And in this same room it was also my first time as a student at a summer school a few years ago. And I have a very good memory of that school. It was two fantastic weeks where I was just beginning doing research and I learned a lot of useful things that they were useful for the rest of my days until today. So I hope this school I'm sure this school will be as useful as it was for me for you. And I will do my best to give my contribution for this school to be useful for you. So I need your collaboration. Your collaboration is simple. Whenever I say something that is not clear you interrupt me and I try again. So as the first lecture Professor Komatsu said this morning don't be shy. I may explain things not in a clear way. I may say wrong things. If you think I say something wrong stop me and we'll discuss about that. And this is true in this room but it's true also outside of this room. I will actually be here. I will be teaching only the first week but I will be here both weeks. And so if you see me and you are curious about something I discussed in the lectures or something I do for research just stop me anytime and talk to me. I will be very happy. So I think we are done with the introduction so we start. And to put this lecture series in a broad context I would like to start from a question. So this is the question that we try to answer every day in our research. So that's what we want to know. We want to know what the university is made of. And by the way is this size big enough for everybody? People in the back can read otherwise I can magnify. So that's what we want to know and I'm not the first one asking this question. We have evidence that more than 2000 years ago people in Greece were asking the very same question and they actually came to an answer that it was very close to be right. Namely the atomic theory of democritus. Very close to be right because we actually learned that atoms are not indivisible despite their name that in Greek atomos means something you cannot split. But what was amazing is that they never bothered to test their theoretical ideas. So they had this atomic theory. Say this is my theory. It makes sense. It's beautiful. I'm happy. But that's not the way we do physics today. So the experimental validation by performing the experiment and checking if this theory is right or wrong is at the basis of the scientific method today. And so many centuries passed by until the development of scientific method. But actually the atomic theory was validated experimentally only two centuries ago more or less. Right. So the question is very old but we started to come to quantitative answers only in the last 200 years more or less. And then what we learned in the last century or so is that atoms... So okay, there are atoms. But then we learned with the discovery of, this was 1897 by J.J. Thompson that the atoms, they actually have a structure despite the name as I said because atomos in Greek means something you cannot split but you can split the atom. That's what Thompson did. Later on we also learned about quarks and this is very recent. This is very recent and by reason I mean roughly 50 years ago. So 50 years ago more or less we learned that we experimentally verified that the nuclei are made of nucleons which are protons and neutrons. Protons and neutrons have a structure. They're made of three quarks. They're a bound state of three quarks. And that's what our resolution stops today. So as far as we know quarks do not have a structure but it's only an experimental limitation. So in some sense we succeeded in answering the question by the Mocritus because we know now what the building blocks are of the universe. I emphasize here that what we know are the building blocks of the visible universe. So it doesn't come as a surprise. We already heard this morning that most of the universe is invisible. But let's stick to the visible universe. Now we have a very compact understanding of the visible universe. Everything we can see from this chair to this table to us, this building, the planets, the stars including the sun, the galaxy, the luminous part of the galaxy. They are made of the same building blocks. And these blocks are quarks and leptons. So quarks are, there are actually six quarks in nature and the two lightest ones are the ones that bind together to form neutron and protons. Leptons, it's another class of particles like the electron, like the neutrinos, and heavier cosings of the electron, like the muons and the tauts. So as scientists we would not be satisfied with just this answer. So what is the building block and then you give me a list of building blocks. It's not really what the answer, the question was about. We didn't want a list. So I wanted to understand the principles according to which these building blocks interact with each other. And so this is very nicely summarized by the standard model of particle physics. So in the rest of my lectures, sometimes I will refer to the standard model, SM stands for the standard model. And the standard model explains in a very compact way the interactions among these building blocks. The gluons. No, I mean even the photons and the z, but this is matter and the interactions are coming here. Oh, okay, okay, okay. The valence quarks, I didn't mind valence quarks. Yeah, but gluons are what kept the proton bound together, but the quarks bound inside the proton. So we know these are matter fields. We know the way they interact. There are strong interactions and electro-weak interactions. So strong interactions are precisely what was just pointed out that in the protons and the neutrons quarks are bound by gluons that are the mediators of the strong force. Electro-weak interactions are what we see today as two separate things. Electro-weak interactions responsible for beta decays and electromagnetic interactions, which is why you can see me with lights. And now we know that they are just a low energy manifestation of the same theory, the electro-weak theory. And this is, by the way, why Abdul Salam with Weinberg and Glashov got the Nobel Prize for developing the electro-weak unified theory. There is, of course, also gravity. We also know that this particle interacts gravitationally in a way described by general relativity, GR. And I'm missing one particle here, which I'm sure you have heard, which is the X boson. So the X boson is, I'm sure you heard in the news six years ago by now, it was the last missing piece of the standard model. Missing piece experimentally. We knew it had to, well, no, we didn't know that. But the theory was developed with the X boson. But as I said before, it's very important to experimentally test our theoretical ideas. And finally, the X boson was found. So the standard model now is a complete description of the visible universe. It tells us what are the building blocks, how they interact with each other. So these are fermions, these are mediator particles are bosons. The X boson is also boson. And it's a very elegant and compact description. So if you go to the GIF store, I saw this morning, they sell t-shirts with everything you need to know about the standard model. So from everything is in that t-shirt, you can compute probability amplitudes for these fundamental degrees of freedom to interact with each other. So it's a very elegant description of the visible universe. And it's also very robust and working very well because we have been testing the standard model at colliders in the last 40 years, at least if not 50 by now. And we found at collider no deviation from the standard model. So we are happy but not completely happy for the reasons I'm about to say. So we are happy because we have a very good understanding of the visible universe. We know how to describe interactions between these models. But there are convincing reasons to think that the standard model is not the final theory of nature, it's not the fundamental theory of nature. And the reason is that there are many phenomenon, and I will describe some of them, or many conceptual points that we don't quite understand well or we cannot reproduce well. We need the standard model alone. When I say BSM, I mean physics beyond the standard model. So as I said, there is more than one motivation. For example, there is the hierarchy problem, there is the strong CP problem, why strong interaction do not violate CP to a very good accuracy. There is a problem of biogenesis. How do we end up today with just variance and not anti-variance? There is a problem of neutrino masses. Why neutrino masses are what they are? The standard model alone predicts zero neutrino masses, at least at their normalizable level. And there is dark energy that you will see a lot in the school, and I will not be talking about dark energy, but a very robust, and it's not the only reason to be convinced that there must be physics beyond this, it's not the only one. But a very robust evidence for physics beyond the standard model is the observed abundance of dark matter. So I say it's very robust because this is not about explaining small numbers like you could be for the strong CP problem or for the hierarchy problem. This is something we know has to be there, but the standard model fails at providing a viable candidate. So this is a big open question in the field of fundamental physics. It's the center of a lot of activity, both theoretical and experimental, because as I say, the two activities must go together. I'm a theorist, so I'm more on the proposing ideas part, but of course then every idea we propose has to be tested and has to be validated from the experiment. So it's a very active field, there are big open questions to answer, and it's a chapter of the book of fundamental physics that has to be entirely written. So at the moment we do not know the origin and composition of dark matter from a particle physics point of view. We know it's there, but we don't know what it's made of. So it's something we'll to work on. Let me remind you some numbers that we already saw in the first lecture this morning. So in cosmology it's what we usually do, we give mass energy densities in terms of dimensionless ratios. So we define the energy density of one species i as the ratio between its energy density and the critical one. And the critical density is defined this way. So H0 is the Hubble parameter that we saw this morning, 68 km per second per megaparsec. G is the Newton constant that everybody should know from classical mechanics and gravity, Newton and gravity. And so if you plug the numbers and you express energy in Gv, this is a very common unit in particle physics. So express energy and masses, they are the same because of equal mc2. You can express masses in Gv as well. So the critical density is 10 to the minus 6 Gv per centimeter cube. So an energy corresponding to the energy density, to just give you an idea, if you take a cubic centimeter in this room, then there is 10 to the minus 6 Gv. For comparison a proton has a mass of one Gv. It's a very small density, so you have one millionth of a proton per centimeter cube. So let me give you some numbers. So we saw this morning that for baryons, and when I talk about baryons, I really mean everything that is in this blackboard. So most of the mass density today left over from the sun model is accounted for by baryons. So the energy density of baryons is 5%. So this morning I think we saw like 4.7. For comparison, the one for dark matter is 27%. And the one for dark energy is 68%. So you see from this blackboard, one of the reasons why we cannot be satisfied with the sun model alone. The reason is that we only understand 5% of the universe, of the energy content of the universe, we only understand 5%. The rest is unknown. We know it has to be divided between 27% dark matter, 68% dark energy, but it's something we don't know. We don't know the origin and composition of 95% of the energy density of the universe. So if you sum this number you get one or 100%. So the total energy density of the universe is very close to the critical one, so omega total is one, but the contribution from stuff we know is only 5%. So that's what the big open problem is about. And so the goal of this first lecture, and then as I said, I come more from a particle physics perspective, so the next lectures I will discuss about theoretical ideas and how to test them. But since I'm assuming that there is, at least on average, no previous exposure to the field, is to go through a review of evidences for dark matter, how we became convinced that actually there is 25% of matter that doesn't shine and it cannot be belonging to this black one. So that's the plan. And let's start from one example that has nothing to do with dark matter, but it gives you the idea of the techniques that are used to probe this type of physics. So here we are on a very small length scale. We are on the length scale of the solar system, a very small part compared to the universe. So in the 1840s the planet Neptune was discovered, but I put this with that language because it was not really seen, Neptune. So what astronomers did was they carefully studied the motion of Uranus. So Uranus is the planet going from the sun outside of the solar system to the one before Neptune. So it's closer to us, so it was easier for us to observe that. And they found mismatch, a mismatch between the theoretical prediction of the orbit of Uranus and the observation what they actually saw in the sky. So a few words about the theoretical prediction. Well, we should know very well, this was in the 1840s, so all you need to describe the motion of a planet, all you need is this two equations, f equal mA, vectors, and then the force between two massive objects. So the way the theoretical prediction was performed was to exactly compute f, the total f acting on the planet based on all the forces that were acting on the planet, assuming that the only bodies attracting the planet were the ones we could see. So from the mismatch between this theoretical prediction and observation, they concluded that they could infer the presence of some other celestial body that was dark at the time. So in the 1840s, Neptune was some form of dark matter, in quotes, because it was something that we knew it was there by studying the motion of visible objects, but we didn't see it. Then later on, of course, our astronomers got better, they could observe Neptune, and now we know that Neptune belongs to this blackboard. It's made of stuff we know. But the techniques is very similar, so you see something that moves. You know that it moves under the influence of gravity. You make a prediction for the motion you expect. You compare with observations. If you find that it doesn't correspond to the observation, then there must be something else pulling that object. Okay? Okay, so now this was one example that had nothing to do with dark matter, but it was a good illustration of the basic idea. Okay? The first time that some invisible mass was pointed out was by Zwicky, so almost 100 years ago, so not even 100 years ago. And Zwicky was this Wiss astronomer that observed the Coma cluster. It was a system that was a bound state of galaxies, gravitationally bound among each other. And by the way, if you sit in a dark matter talk, it's very, maybe more for colloquium, physical colloquium, it's very common that the speaker starts the discussion with a funny picture of Zwicky doing the okay sign on a very strange face. So that's why, because he was the first person that pointed out some missing mass, some missing invisible mass in the universe. So, okay, and this is more important historically, okay? So it was not a conclusive evidence, it was not taken seriously for many decades, but since we're doing a review, let's just go through history and there is still some useful lesson to learn from this. Okay, so Coma cluster. So as I said, a cluster of galaxies, many of them, like hundreds, thousands of galaxies, gravitationally bound among each other. So what did he do? He measured the speed, the velocity of these galaxies moving within the cluster and he found that the galaxies, they were moving too fast. Okay? So you look at these galaxies, he measured the velocity, they were moving very fast, too fast. But too fast, what does he mean too fast? So too fast with respect to what? So again here, the story is about the comparison between a theoretical prediction and an astronomical observation, okay? So how did he predict the typical velocity of the clusters, of the galaxies within the cluster? So for a system like the Coma cluster, there is a result known as the virial theorem and the virial theorem connects the average kinetic energy, k, and the average potential energy, v, of the system, total energy of the system. So this is not only valid for gravitational forces, it's valid for every force that goes like one over r squared, like the one I wrote there. And it's also valid for other forces, there are different coefficients, but let's focus on gravitational forces, okay? Q times the kinetic energy plus the potential energy is zero, okay? So all we have to do now is to compute the kinetic energy, the potential energy, compare them and see if the virial theorem agrees with the observations. So the kinetic energy, the kinetic energy is compute as the sum of the individual kinetic energy of each galaxy. So it's just one half sum over i mi vi squared, okay? So the index i runs over the galaxies. So I said there are like hundreds or thousands of them. And for each one, we have a mass and we have a velocity. Now, we want to go through a qualitative argument, okay? Without going into too many details. So let's assume that actually vi less the typical, these are average quantities. The virial theorem holds for average quantities, okay? So let's assume which is actually a very good approximation that the average velocity of each galaxy is the same, okay? So this vi doesn't depend on i. I can take it out of the sum. I'm still left with the sum over the mass, but this is just the total mass of the cluster, okay? So the kinetic energy of the cluster is approximately given by one half the mass times the typical velocity square of each galaxy. So the way we compute the potential energy of the mind without the square. So you sum over all the different pairs of galaxies. That's why there is i less than j to avoid double counting. And then you sum over the potential energy of each pair of galaxies. So there is, let me check the number, five over three, yes. So if these galaxies are distributed uniformly on a sphere, then this is something you can check. Gravitational potential energy is five over three. It's negative, of course, because it's a bound system. It's minus five over three mass square of the cluster over the radius of the sphere, okay? So this is just the potential energy of a uniform sphere. Okay, so now all we have to do is to compare and use the virial theorem. So 2k plus v is m comma v square plus three, no, minus because I have a plus here but v is negative. So I need to put a minus. Minus five over three and this is zero, okay? Virial theorem. So now we solve for v square. I mean these are just approximate results but they give us a feeling of the order of magnitude. This is the final answer, okay? So what you can do and what actually it's v he did was to measure v. You can see how fast the galaxies are moving and then you can also measure m. How do you measure m? You assume that all mass comes from the stuff you can see, okay? So you can see these galaxies. You detect some given luminosity. You use some mass to luminosity ratio. And then you compare. You compare and ask yourself, do they satisfy the virial theorem? And what Zliki found is that this was bigger than this, okay? So the result Zliki found was v square was too large with respect to the expectation from the virial theorem, okay? So he concluded that there must be some form of in v. Actually it was the one that invented the name dark matter. It was v he. It was in German. I don't know how to say that in German but the translation is dark matter. And for the first time there was some serious evidence that there was some form of invisible mass in the universe. Now this was not taking, we are now in the 30s, okay? We are in the 30s. This was not taken very seriously, okay? And so I mean, of course I wasn't there. I don't know why it was not taken seriously. But I can tell you when the evidence for dark matter was actually taken seriously. And that was in the 70s. 1970s. This is, yes, yes, ask questions please. So this is a, it's just an approximation. Now if you have a uniform sphere with constant density of mass, you can compute just by using classical mechanics. I think it's 3 by 5. Oh, 3 by, oh, it may be, it may be. Okay, I can check this because I have the, 3 by 5. Yes, yes, thanks, thanks, thanks. 3 by 5, so here it becomes 3 by 5. Yeah, so as you just saw, I make mistakes. Interrupting. Okay, other mistakes? So I think if I remember correctly, I can tell you the number, like, how much extra mass you needed, okay? So, which is how large was compared to, okay? So I think it was between 10 and 100. The mass, if I remember the number correctly. Yeah, yeah, yeah, no. Without changing the potential, without changing Newtonian gravity. Or you are saying if you modify gravity. So I wasn't born in the 30s, so I don't know. But it was just a single evidence and the observations were not so accurate. As accurate as the one I'm about to say. So I think it was, it was tough to convince people. But I wasn't around, so I don't know. Okay, so 3 over 5, very good. Now, let's go to the 70s. Yes, so this is, yes, yes. So the question is how do we know if the coma cluster is viralized? Okay, so we can roughly measure the, and I'm not an astronomer, so I take my answer with a grain of salt, okay? It's enough long-lived that there was time to, so when you prove the virial theorem, you take the average of the kinetic energy of V and then there is some quantity. So this is non-zero in general. But when you take the average over a long amount of time, it goes to zero. Okay, so the answer is that you had enough time to realize and we can compute that. Oh, yeah, okay, yeah. So the answer is there only when gas gets shock-heated to very high temperature, this is only possible after the war. We can also estimate temperature from extra gas. We can estimate mass for weak-lensing. Yeah, yeah. I will get to that too, to the gas and to the lens. But, okay. So yeah, probably they didn't know in the 30s. I think it's fair to... Okay, other questions? Yes? This one? So I don't even think this was the way that Viki did the estimate. I'm just doing a sketch to give you a feeling of what are the relevant physical quantities involved here, okay? So this is not the case in the actual cluster. So if you look at Viki's paper probably this is not the way it did. It's just to say that the typical kinetic energy must scale as the total mass and the typical velocity, okay? But the actual calculation is more involved. Yes? Yes, there is also the gas and I will get to that in the modern days. So in 10 minutes I will discuss also about the dark matter evidence we have from clusters today. So I will get to that. The velocity I think is from the Doppler shift. So you detect photons and then you see how the spectra are shifted with respect to the ones we know and we measure in the labs and that tells you about the velocity along the direction of observation. So from Doppler effect you can know how fast things are moving. Other questions? Good. We are doing very well. Okay, so rotation course. So this progress was linked to a development in the radio astronomy. There was a significant improvement in the 70s and we could measure so now I will sketch again our galaxy. Actually we know now also the rotation curve of our galaxy but imagine you look at some spiral galaxy in the sky spiral as our galaxy. Okay, and what you want to do here is to measure so let me get to the quantity we want to measure. V of r, the velocity of stars in the galaxy as a function of r where r is the distance from the center. Okay, so that's a well-defined question. I want to make a plot V of r as a function of r and again here there is a theoretical prediction something I expect from my knowledge of physics and then there is reality, what we observe and in this case it's different in a very convincing way as we will see. Okay, so I prepare the plot without revealing the surprise r V of r and so what we expect is based on the calculation again, without knowing too much fancy physics f equal ma and f equal the Newton's law okay, Newton's law so f is g this is the force so if I look at a star here, okay this is a star in the galaxy which is at a distance r from the center the force that the star feels is proportional to g proportional to the mass of the star lower case m is proportional to the distance and is proportional to the roughly, so this will be true actually only for a spherical distribution our galaxy is a disc so we have to do the calculation again this is just a qualitative sketch but it gives you the feeling, okay then if you want to do things properly you have to take the distribution of a disc and compute the force you got the cell function it's not something that you can easily do on a blackboard but the scaling is the same so this is the force and the force must be equal to m m is again m and a v square of r over r okay so now you see immediately that m goes away the mass as it should okay we know it goes away now you do some simplification for example you simplify the r here you remove the square and then you you solve for v you solve v equal to something and let's see if I get this right g m of r over r okay I just solved for v now what is my theoretical expectation so our galaxies galaxies like ours they shine up to 10 kilo parsec so we can see the luminous stuff up to 5 to 10 by the way the solar system is 8 kilo parsec away from the center so we are really at the edge of the luminous part of our galaxy but with these radio techniques we can look at the very rare stars on the outskirts of the galaxy and we can get a rotation curve up to 200 kilo parsec okay so these numbers are important because now I want to give you a rough theoretical prediction so of course to make a proper theoretical prediction we have to solve the equation of motion with this distribution do things properly but with few simplifications we can get at least a qualitative behavior so inside the galaxy so and really I much smaller than some critical radius that I take roughly of the order of 5 kilo parsec which is where the galaxy shines so we are here and we can assume that the matter is distributed with the uniform density inside the galaxy so if it's distributed with uniform density the mass is like r cube it goes like the volume so r cube over r is r square I take the square root I get r so actually here let me just put a proportional to I don't care about pre-factors but I expect that if I measure the rotation curve very close to the center I see a linear rise okay if I go far away so then the critical radius then you see that basically the all mass becomes a constant okay most of matter is concentrated within the first 10 kilo parsec so this m is a constant if this m is a constant then you expect and this is crucial at large radii v of r dropping down as the square root of the inverse radius so this is also known as K-plier and decrease because it's in agreement with the third law of Kepler and I'm putting so much emphasis on the second result because that's where the trouble comes so let me draw the theoretical prediction I use a dash line because I want to compare with the observation so this is and I emphasize again this is just a sketch of the derivation you can provide the theoretical prediction rigorously by solving the equation of motion with all the details but roughly speaking you expect a linear rise and then decrease with the inverse square root of the radius now what about observations? Observations show that you actually get it right here but then the rotation curve is flat it's flat, out flat well it's pretty flat as far as we can make measurements so it stays flat all the way to let's say 200 kPa at some point we run out of stars we cannot provide this rotation curve anymore so in the 70s this was the first time I think the community got really excited about dark matter because it was not just one case many galaxies were subject to this type of comparison between the observations and theoretical predictions and they were all consistent actually were all inconsistent and so again here is an evidence of the fact that if you want to reproduce this flat behavior then well I would say at that point the most conservative options was this, nowadays I think it's the only option and I'll come to that, is to assume that within the galaxy and our current understanding now is that the sparred galaxies are embedded in a spherical halo of dark matter which provides another source for them we don't see but we can infer it's there because of this behavior now before anybody asks I will answer the question so one alternative option is to say well maybe the laws of gravity are the ones given by the Newton's law as far as we can test here but maybe once you go all the way to the outskirts of galaxy you are measuring the Newton's law you are probing gravity at very large distance and maybe the laws of gravity are different so these are known as MOND Modified Newtonian Dynamics so I think it's fair to say that for the galactic rotation curves it's an option you may like it or not but it may be a viable option to fit this curve okay I don't know much about how theoretical compelling is but but I think it's fair to say it can be an option so I will it's already noon so I cannot go through all the evidence I wanted to show but there are evidences the one I'm going to talk about that makes life for MOND really tough if not impossible so adding one extra particle, massive particle at this point it's the most conservative option and I also think it's the only one that can account for all the observations in the 1970s now we are 2018 we've been collecting evidence for dark matter not only on galactic scales but also on scales of clusters and on cosmological scales as we are this morning okay and everything comes together beautifully to a consistent picture with adding a new form of non relativistic matter massive new form of massive particles explains all the observations at different scales okay so let's see let's go to clusters and then I will be brief on cosmological evidence because we have other lectures on large-scale structure and CMB like this morning where we will also see why we need dark matter to explain those observations clusters so almost a century after Zviki we went back and look at clusters and now we have more convincing evidence that dark matter also populates this this type of environment so going back to the previous picture of a cluster as was already mentioning mentioned before inside the cluster there are galaxies and there is also gas gravitationally bound to stay within the system and this gas emits X-ray so it's typically ionized so it emits photons through Bremstrahlung and this X-ray emission scale is like the number density square so by detecting this X-rays we can measure the density of the gas as a function of the radius and we can also measure the temperature of the gas from this spectra, thermal spectra of X-ray now another way to convince that there is some form of mass that we don't see within this environment is to study the hydrostatic equilibrium for this gas hydrostatic equilibrium so this is a P if yes so I use row here ok so there are two competing effects on the gas pressure that wants the gas to expand and go away and then there is gravity gravity tends to bring the gas back together and the system is in equilibrium so these two effects must compensate each other and that's what's written in this equation this is just f equal mA written in other form so I say that we measure row and T but we don't measure the pressure but that's just an extra step because we can use the equation of state for a perfect gas and actually the number density here I'm making one approximation I'm assuming that all the gas is made of protons so it's really also considered multi component gas there is no problem now if you plug this expression here you've got an equation relating energy density and the mass within a given radius ok so I say that we measure T we measure row from x-ray emissions and we measure m through lensing as was mentioned before again here we found a mismatch between what we see and what we actually expect from this this relation ok and well sorry what I meant is that actually the total mass we measure through lensing is consistent with this equation I meant that the mass we see cannot be the whole mass and so we infer the presence of extra mass ok so since time is going very fast let me mention a couple of other things so we have evidence of dark matter on the galactic scale we observe many galaxies like ours we have dark matter evidence on the scale of cluster of galaxies and now we also have we also have dark matter evidence on cosmological scales so this is what we heard this morning about CMB so here I can go fast because there are people more expert than me giving lectures in this school so I will let them tell you why why we think and we are convinced that also on cosmological scale there must be this form of dark matter so CMB is something we already heard this morning but on Wednesday I think we will see how the spectrum the power spectrum we saw this morning depends on the cosmological parameter the density of the baryon the density of the total matter and we see that from CMB what we derive is omega baryon omega matter and these two are different omega matter is 6 times bigger than the one in baryons which means that there must be something else that cannot be baryons to explain CMB observation same story for this quantity that I call p of k so p of k is the matter power spectrum and I am sure this will be discussed we have two lecture series one this week one this week on large scale structure so LSS large scale structure we will hear also why in order to reproduce the observation of this quantity with the theoretical prediction we need something beyond just baryons the prediction of the universe populated by only baryons is completely different last thing I want to say something very important which is another very convincing evidence for the existence of dark matter and evidence where theories like modified gravity really troubles to account for the observation so let me put it in dark matter is why we are here so without dark matter we will not be here why? there is a very simple estimate to come to this conclusion than in justice blackboard so we heard this morning and we know that the universe back in the days back at very early times was very homogeneous because we measure fluctuations in the CMB as we heard this morning really really tiny fluctuations 10 to the minus 5 so as we will hear next week we think now that this the seed for this fluctuation was inflation again that's something for next week but all I want to say now is that we know that at some point even for the energy density of total matter this was more as we heard this morning it's reasonable to take this number up to order one factor to be really small so this is the initial condition for the evolution of structure formation and our universe the way we observe it now is very nonlinear so what I'm saying this is that here in our galaxy so let me say Milky Way delta rho over rho is 10 to the 5 so our galaxy compared to the entire universe is a very dense region the average is 10 to the 5 denser than the average so how did we get from here to here okay how did we get from a universe that was very homogeneous up to 10 to the minus 5 to a universe today where we are very non-linear means that this ratio is not small 10 to the 5 so we change the sign here and the way we believe that what happened is that these fluctuations that were seated by inflations evolved through gravitational under the influence of gravity giving rise to the structures we observe today but there is a problem if you don't put dark matter the problem is the following is that delta rho over rho if you solve the equation for the evolution of perturbation it scales like the scale factor so the universe expands it gets bigger with time A is the same scale factor we saw this morning and the growth of the perturbation is linear in the scale factor we also know that the last scattering surface the one we saw this morning corresponds to scattering surface over as we saw today the actual value of the scale factor is not something physical but we can talk about the ratios of scale factor so universe was smaller at the last scattering surface when CMB formed and the scale factor was 10 to the minus 3 more or less the one of today the universe was it's a thousand times bigger today than at the time of last scattering surface so if if there are only variance variance perturbations in the variance as we will hear I'm sure in great details in the school but let me just tell you the conclusion in a variant photon fluid perturbation in variance so delta rho B over rho B they cannot grow until the last scattering surface okay this is why because before the last scattering surface the universe was ionized and the electrons were tightly coupled to photons through just Compton scattering and the perturbation just could not grow okay so if we assume that there is only variant the best we can do for delta rho over rho today is delta rho over rho at the last scattering surface the ratio of the scale factors between these two moments and this factor this ratio is a thousand so in a universe with only variance we barely get to 10 to the minus 2 in the relative fluctuations okay so this is a problem because this will not explain why we have no linear structures today okay so this is one of the most striking at least in my opinion evidence for the need of something else if you only have variance you never go no linear okay one more thing that is actually not very connected to dark matter but it fits nicely within this picture is so Big Bang Nucleosynthesis or BBN so this is unlike what I told you so far is the great success of standard cosmology so we can predict the abundance of some of the lightest elements that were synthesized synthesized in the early universe and compare them with observations and we find an amazing agreement and all of these abundance all of these abundances more than one they only depend on one number the energy density in variance okay and BBN system with CMB observations okay so this fits within the picture in a nice way because it's an independent measurement of the energy density of variance and so we are very sure that the variance are at most 5% of the total energy density and we know that the the other energy matter is 32% so we need something else the reason why I want to mention this is also because of what I will tell you about tomorrow so BBN when the temperature of the universe is roughly 1 MeV and just for completeness the age of the universe is one second then it continues for the first three minutes which describes how you form these like elements and the reason why I want to mention this value is because our success to extrapolate the history of the universe all the way to one MeV and getting these abundances right make us confident that we know the thermal history of the universe up to this value because as we are this morning a temperature higher than the last scattering surface that 0.3V so a temperature about 0.3V there was no way for us to have direct access to the universe at higher temperature than this because of what we saw this morning the photons were scattering a lot and they don't come to us they only come from the last scattering surface so to be 100% conservative we can say we have a photograph of the universe only up to the last scattering surface but our success with reproducing these light element abundances made us confident that we actually know the history of the universe so this is important for what I'm going to talk about tomorrow because we will move back in time to the early universe and I will tell you how the most popular dark matter models get a successful production in the early universe and there is always the assumption that we know what the universe looked like at very high temperatures and that we know the energy content but to be very honest I think we can say with confidence that we know the history only up to this number I will repeat this tomorrow just as a preview we don't know about the energy budget of the universe we have no direct way not even indirect way to know about the energy budget of the universe above 1MEP so in the last 8 minutes so is there any questions so I hope I convinced you that dark matter exists it could be it could be so tomorrow we will have a discussion about possible ways of producing dark matter one, possibilities through the case of the inflatone that's a way to populate the universe with dark matter I don't know if we will discuss that tomorrow but that's definitely the possibility yes so I was about to do that today because now in the last 7 minutes I will tell you what we definitely know about dark matter and clusters are important because they give us a feeling of the self-interaction so I will get there I will try, yes for the gas so the question of state for the gas so the way it's done it's in a proper way so there are other elements in the community you sum over all the, you have people have models of the gas also with different temperatures so the estimate is done in them this was just a sketch of what the basic idea is but then yes, yes, yes, yes is the evidence is still there questions ok so in the last 5 minutes I will tell you what we ok so I hope I convinced you that there must be some form of dark matter so now this is a good news because we have something to work on well, they are all good news the other good news is that we have no idea what it is ok so when you try the model or you build an experiment do you guide yourself ok if you really have no idea about the properties of this particle so here I have a list of things that we know and whenever you build a model to explain dark matter then you can test the experiments you have to make sure that you respect these constraints if you want so this is something we learn by looking at the sky and these observations not only tell us that there must be dark matter but they tell us something more they tell us something about the properties of dark matter so I want to conclude this first lecture with the list of these properties and then tomorrow we discuss about more concrete models ok so density go fast whenever you build a model you want to make sure that you have omega dark matter 0.27 ok there is a precise number so when you actually write the paper you are careful about these numbers but that's a ballpark number then what else do you want you want to build a model where the particle is very stable ok very stable what does it mean very stable very stable means that it has to be stable enough to be around today because we observe it today in the universe so at minimum we want the so if the particle is stable period then it's also very stable because it's stable but if you have some form of decay in dark matter you have to make sure that it's enough long lived that we still have it today so the next you can ask is that the lifetime is longer than the age of the universe this is the Hubble time it's 14 giga years and it's also if you convert to seconds let's see if I get the number right yes 10 to 17 seconds more or less so this is the simplest thing you can say longer so this is not the real limit the real limit depends on the decay channel so if the dark matter decays visibly visibly I mean to electron photons then it's going to mess up the CMB ok so the actual lifetime the limit is more severe so the bound is actually much bigger than the Hubble lifetime by 13 orders of magnitude so it's a very strong limit of course if you assume that the decay products of dark matter are invisible so nothing that is going to affect the CMB then the bounds is more relaxed but still it's longer than the Hubble lifetime it's 200 giga years and the Hubble lifetime the Hubble time was 14 so it's in one order of magnitude bigger than the than the one from Hubble ok what else so I don't have time I will focus on the main properties this is very important it has to be called ok sometimes you see acronyms like CDM called dark matter we try to understand what cold means before we before we go for lunch so this means that when you have a dark matter model that you produce in some way in the early universe there are multiple options but you want to make sure that when the temperature of the universe is 1 kV so remember in Tokyo really about low temperature it's between BB and CMB formation the dark matter particle must be cold so what does it mean cold must be that the equation of state for the dark matter particle has to be pressure equal 0 to a very high degree of accuracy cold dark matter is identically 0 why so this is a limit that comes from structure formation and the 1 kV is the it corresponds so 1 kV, why this magic number is the size of the horizon the moving size of the horizon of the smaller structure we observe ok so if dark matter particles were hot at 1 kV so if they were moving very fast there isn't a fat called free streaming that would wash away perturbation on these scales and then we would not observe what we observe ok so whenever we build a model we want to make sure that 1 kV dark matter particles are not free streaming by the way small parenthesis this is one of the reason now not only reason this is why neutrino of the standard model cannot be dark matter they are hot at 1 kV they move very fast so they would wash structures out ok so somebody mentioned clusters there is no colliding cluster sorry if you want to know more about that come talk to me I will just give you this number and then I will conclude these are very important because they give us no sigma so centimeter square over gram so by observing colliding cluster not only we have evidence of dark matter you may know this picture famous picture of the bullet cluster but we also get the bound cross-section for self-interaction of dark matter by looking at what we look and comparing with other dynamical simulations so this is the bound you get so whenever you build a dark matter model you want to make sure that the cross-section for self-interaction by self-interaction I mean elastic processes where two different particles just collide ok so you want to make sure you respect this bound and tomorrow morning we will see a few examples of thermal history how to produce a dark matter in the universe keeping in mind these bounds whenever we build a model we want to make sure we don't get into contradictions with this thanks