So now we are going to start the first lecture on CMB by Blake Sherby from Cambridge. Alright, great. So thanks very much for the opportunity to speak here. So I'm really excited to be back. I was sitting in the audience for one of these cosmology schools. I don't know when it was 40 years ago or whenever I was a student. And I really enjoyed it, so I'm really excited to be back. No, I'm kidding. Not that old. But it took a disturbingly long amount of time for people to realize that that's magic. Right, so I'm going to start this off by talking about the cosmic microwave background. And let me start by giving just a brief motivation for why you should pay attention during these lectures and why you should want to learn about the physics of the cosmic microwave background. So there's a huge list of regions why it's important to know about the CMB and I'll maybe just sketch some of those. So in short, the CMB is our most powerful arguably and certainly our most robust probe of really interesting cosmology and really interesting physics. So the CMB is a beautiful probe of the history of the universe. It really shows you effectively the baby picture of the fluctuations in density and potential as they were early on and you know from these sorts of fluctuations all of the structure that we see around us today grew. So if you want to understand the history of the universe, the CMB is crucial. It's an image of the way the universe looked very, very early on, right at the beginning. The CMB is also arguably the best way of figuring out what the universe is made of. So I'm sure you all know that 25% of the universe is dark matter, 70% is dark energy and 5% is baryonic matter and these high precision numbers to a large extent come from the CMB. So it's an amazing tool for figuring out what the universe is made of. It's also almost certainly currently our most powerful tool for understanding the physics of the very early universe and testing models such as inflation. And finally, the CMB is not just a great tool, a robust tool to understand cosmology, but it's also just a very, it's an amazing probe of fundamental physics. We've already talked about how it can probe the early universe and as we'll talk about when we discuss B-modes, you can access scales that would be impossible to probe with terrestrial experiments, probing inflationary scales that are a trillion times higher than the LHC or particles that are so weakly interacting that you could never see them on a realistic experiment on Earth. So in short, the CMB is an amazing and robust probe of both cosmology and fundamental physics and you should all learn how it works. So I will try to just start this topic in these few lectures that I have here. So given that the audience is quite mixed, I should apologize to those of you who are real experts in the field of CMB because I'm not going to assume that you've taken a course on CMB before and especially the first few lectures will be very introductory. Especially this first one. But hopefully even if you do work on CMB towards the end we'll cover some more advanced topics such as gravitational lensing of the CMB and CMB polarization so hopefully those will also be interesting. And I should note please feel free to just interrupt and ask questions. I might not be able to answer them all but it's more fun that way. Alright, so what are we going to discuss in this course? Today I'll talk just about the very basics. What is the background CMB? Why is it amazing evidence that the hot big bang happened and how do CMB photons propagate in our universe? And then in later lectures I'll talk about the CMB power spectrum, what it means, how we can use it to learn about cosmology and later on I'll discuss some more advanced topics. And I've drawn from a very nice list of references that I've noted here and hopefully I'll make these slides available to you and if you want to know more you can look at Wayne Hu's amazing website, Anthony Chaliner's lecture notes if you want to know a huge amount of detail and Daniel Baumann's new book has a nice summary of CMB physics as well. Alright, let's get started today with the very basics. What is the CMB and why is it a clear and unavoidable prediction that sort of proved that the hot big bang is indeed the beginning of our universe. So I'm sure you all know basic cosmology, you all know that we've observed an enormous number of galaxies and you all know also that Hubble discovered that these galaxies are all running away from us and the further away these galaxies are the faster they seem to be moving away from us. And that's not because we're unusually repulsive hopefully but is instead interpreted today as the fact that space itself is expanding the more space that we have between two objects the more it expands and then the faster they seem to move away. Now, quantitatively we can describe this observation as explained fully by assuming that the universe has the most general homogeneous and isotropic metric, the FLRW metric that I'm sure you're all familiar with here. And the distances here in this FLRW metric are rescaled by this scale factor A of t as I'm sure you all know and I will often be using conformal time eta because then I can draw nice space time diagrams where light rays travel at 45 degrees, right? So dt is AD eta, that's the definition of the conformal time. Okay, now just reminding you further of some basic cosmology I'm sure you all know this, you can plug this metric into the Einstein equations and connect the geometry of the universe with the matter and energy content of the universe and that gives you this connection between the scale factor A and what's in the universe. The density parameter is omega lambda, omega matter, and omega radiation. Okay, and so that's a differential equation that tells you how quickly the universe is expanding as a function of what's in it, right? And so if you're just to remind you, the scale factor is growing as t to the one-half during radiation domination, t to the two-thirds during matter domination, and later exponentially. And as I said, we'll often use conformal time and I'll, when I don't say anything, I'm going to be assuming flat lambda CDM and I'm going to set, I use natural units for c equals 1. In any case, what we see is that the scale factor grows with time, all distances grow with time. It's a clear prediction of the standard hot big bang model with an FLRW metric that at early times, if we run that picture in reverse, the scale factor has to have been very small and every, you know, all distances were really small and everything must have been really close together. The universe must be extremely dense at early times. Now, you can easily show, and we will actually show this later, that the temperature of a photon is proportional to the energy to a photon is proportional to one over the scale factor. So at early times, when the scale factor was really small, therefore the temperature was huge. So the early universe was incredibly dense and incredibly hot and that's crucial for the emission of the CMB. So just the standard hot big bang picture predicts clearly a extremely hot and extremely dense universe and in fact, if I go to early enough times, the universe has to be made up of a plasma, an incredibly dense and hot plasma. So at the beginning of the universe, that's what you have in this standard hot big bang picture. What do I mean by that? Let's go into a little bit more details.  So the electrons and protons are not bound and everything is just flying around. Now the photons rapidly scatter and they rapidly scatter in particular off of the electrons. Does anyone know why they mainly scatter off the electrons and not the protons? That's right. So if you look at the Thompson cross-section, it was a factor of 1 over mass squared and so the scattering with protons will be suppressed quite heavily. So the photons mainly scatter off of the electrons but the protons obviously are affected by this as well because through sort of Coulomb interactions they scatter with the electrons in turn. So that state persists for some time. Early universe is this glowing hot plasma of photons, electrons and protons. I'm neglecting some helium, which is a small number of... But then what happens is the universe, of course, expands and it cools off and eventually a terribly named process called recombination happens which is that the universe becomes so cool that electrons and protons can come together and form hydrogen. Now, because the photons were scattering so rapidly off the free electrons in the early universe, the early universe was basically opaque. You couldn't see through it, the mean free path was really short. But now after recombination, I said it's a terrible name because this is the first time protons and electrons combine to form hydrogen. After recombination, the universe is neutral, the scattering is much, much, much weaker, maybe you have a tiny bit of Rayleigh scattering but you can neglect that. And the photons will just free stream through the universe all the way until they reach our telescopes. Okay? So that's sort of the basic picture. Again, to summarize this, hydrogen forms very quickly at a temperature of around 0.3 electron volts from free electrons and protons and before recombination, you have lots of Tonson scattering, the mean free path is short, and then the universe is neutral, photons free stream to us. All right? Just to show you a really terrible illustration of this process, you can see these photons in blue bouncing off the electrons in green and the protons are doing very little. But then the universe cools, neutral, the hydrogen forms, and then the photons travel through the whole picture where we can fly along with the photons. So you all know that you cannot do this, right? But the photons then travel through the universe to us. So I like how, you know, when people try to make PR images, they sort of tell you as many wrong things as correct things. Okay, are there any questions about the very basic picture? And then we'll get a little bit more quantitative. Yeah? I think it's made by the sort of Planck PR team, so you should just look at, like, Planck PR videos or something. I've cut out some other funny things that the photon does in the middle, which are also not correct. Yeah. Okay, so let's now get a little bit more quantitative in terms of when recombination happens and when the photons get released and stream through the universe, okay? So you can do a pretty good job by just assuming that this process of electrons and protons forming a neutral hydrogen is in thermal equilibrium. That's not going to give you an exact answer to get an exact answer, so you have to use the Boltzmann equation for this process and, you know, consider the details where you have a three-level atom and it's actually quite complicated to get this exactly right. But you get a good answer if you just assume everything is in equilibrium and you probably know that in equilibrium, in thermal equilibrium, the equilibrium number densities of the electrons, the protons, and the hydrogen. Okay? And so I will have you do this as an exercise, but if you write down those expressions for the number density and equilibrium, those just depend on a sort of Boltzmann factor which contains the mass and the chemical potential over the temperature. And if you want to know how ionized the universe is, in other words, how many free electrons there are versus electrons that are bound into neutral hydrogen, you can write down the free electron fraction N e over N b, or N e over N p plus N h. Okay? So when that free electron fraction is one, everything is a plasma. Everything is fully ionized and when it's zero, then all the electrons are in hydrogen and the universe is neutral. Okay? So as you will show, you can sort of plug in these expressions for assuming thermal equilibrium and you can rearrange to get a nice equation for the free electron fraction. So you know how ionized and how versus how neutral the universe is as a function of a very small number of quantities. That's the amazing thing about thermodynamics when things are in thermal equilibrium, everything just pops out from nothing. The first one is the temperature and the binding energy, mass of the electron, and this factor eta, which is the barion-to-photon ratio. How many barions do you have per photon? Okay, and then what you can do is you can solve this. You can say, when does the universe recombine? When does this ionization fraction become really low? Okay? The binding energy of hydrogen is 13.6EV. You know everything else. We know the barion-to-photon ratio is 10 to the minus 9. And we can just plug in and solve and naively you would think, okay, the binding energy is 13.6EV. Recombination has to happen roughly at a temperature of 13.6EV. But instead it gives the temperature of 0.3EV. So does anyone know why? It's so much lower than the naive answer. Exactly. So there's so many photons that even those rare photons that are way in the tail of the Planck distribution, rare rare exceptionally high energy photons are enough to ionize hydrogen and keep it ionized until the number density drops way way way below 13.6EV. So all these photons push that reaction to the left. Now that's just when, that was a calculation of when the universe becomes neutral and you've seen that we've done the SAHA equation calculation in the dotted line, but a proper calculation agrees pretty well, at least for the onset of recombination with this very approximate thermal equilibrium expression. Now what we're interested though is when the photons get released because that's sort of the cosmic microwave background as we'll talk about in a second that happens when the Thompson scattering of these photons off the free electrons becomes inefficient. And as you probably know you can compute when a process when a sort of scattering process becomes inefficient and when this particle freezes out by setting the rate of interaction to be equal to the Hubble rate. Because when that rate falls below the Hubble rate then I don't even have one interaction per Hubble time this process has basically stopped. So if we write that down for the photons scattering off electrons what we find is that because of this exponential cutoff basically decoupling happens right after recombination. So the electron density drops so quickly recombination happens so fast that decoupling happens very soon afterwards. And that occurs and if you'd like I can walk you through the calculation at redshift 1100. So that is basically when these C and B photons no longer scatter because all the electrons are bound into hydrogen and the photons can escape. One key point I want to emphasize is that this process is set by the local temperature this is all just effectively a thermodynamic argument we get 0.3EV just from the binding energy of hydrogen and some sort of basic quantities like this. So at a fixed temperature of 0.3EV recombination happens and then photons are released. So as an exercise if you haven't done this already and I suspect many of you will have please just go through and derive the SAHA equation it's worth your while. And then I have a quick question for those of you who thought a little bit about C and B so you always hear that C and B temperature anisotropies we measure in the sky they probe the fluctuations and the radiation density that were there primordially. How can I square this with the fact that photons are emitted at a fixed local C and B temperature independent of the radiation density. So it's always emitted at 0.3EV. So how can I see the radiation density how can I see the fluctuations in the radiation density in the C and B. Does anyone know? That could be the answer but it's not. There's some physics there also, yeah? Yeah, so you're right that there is and we will talk about this there is an effect where it climbs out of the potential and that changes the that changes the the temperature but that's not the only effect something else. So even if the potentials were 0 you would see the variations in radiation density even though the local temperature of emission is the same which is a very good approximation. Alright, we'll think about it and we'll come back to that later. Alright, I'm glad. Okay, so in any case the key point is there's a clear prediction of the hot big bang model and this is extremely, maybe not of importance now but historically this was a huge debate, right? Is the hot big bang cosmology correct or do you have some steady state model and this is the proof. If you have the hot big bang model you have a clear prediction that the afterglow radiation from this primordial plasma should be released and should travel through the universe to our telescopes, okay? So we should see this radiation every time we look out in the night sky we should go out and we should look in the sky at a burning sea of fire because that's radiation from the sort of big bang plasma. Okay, so if I look in the sky I should see the glow of the primordial plasma because the light has to be released. So this is an obvious question but why, hopefully when you go out at night you don't see a burning sea of fire in the sky, why do I not see that? Obvious question. That's right. So we talked about how the energy of the photon is proportional to 1 over A. The wavelength stretches from redshift 1100 to today by a factor of a thousand and when the CME is emitted it looked very much like the surface of the sun, right? That was a similar kind of temperature and similar black body spectrum but that gets now redshifted that gets redshifted to microwave frequencies. Okay, so you need to build specialized microwave telescopes with lots of effort to be able to see this cosmic microwave background or you can just get lucky like these people did. That's completely unfair. They did an amazing job. I'm sure you've all heard these stories of Penzias and Wilson, how they built this telescope to do astronomy and test communication equipment and you've all heard the story of how just by being really careful experimenters they, you know, they trapped this down. They found an excess signal that eventually they concluded has to be real, right? And then the Princeton group helped them to interpret this as the cosmic microwave background, the prediction of the hot Big Bang. So I'm sure you've all heard these stories where they tried everything they could possibly try and at some point they even climbed in and removed the pigeon droppings from their experiment because they couldn't explain this mysterious, you know, thermal radiation and that didn't get rid of it and eventually they were convinced this is real. So I always heard the story but at some point I came across what I think is kind of a dark side to this story and it probably shows just how upset they were getting if their telescope not working which is they didn't just clean the pigeon droppings one of them went out and shot all the pigeons which I think is just kind of illustrates just how frustrated they must have been getting if their telescope not working. In any case, this was the proof that indeed the hot Big Bang happened. We can see its radiation. We can see its afterglow and that killed these steady-state models almost entirely. So that is, well, I should say though that obviously it's not enough to just say oh I found some radiation you need to prove it is cosmic microwave background radiation and one really good way of doing this is showing that it is a black body a nearly perfect black body because that's what you'd expect from a glowing plasma. So if you measure this that is then the definitive proof that this is radiation coming from the hot Big Bang and I'm sure you're all familiar with the Kobe fire ass measurement one of the most amazing experiments in cosmology where the error bar has to be magnified by a factor of around 200 so that you can even see them on this plot.  Now if people know something else you can feel free to correct me on that and you know you can ask how can they measure it the most perfect black body so it's kind of an interesting experimental question but unless people are interested I won't go into that. In any case that was the confirmation that this is the CMB we found this background radiation. Are there any questions about what the CMB is and the sort of background properties of the CMB before I move on to the fluctuations? So our universe today is not perfectly uniform but the CMB is not almost perfectly uniform. And for some time experimenters struggled to find variations in the CMB. In fact they had already ruled out the levels that we find today due to some errors. So you can increase the contrast by a factor of a thousand maybe you see a dipole but basically you cannot find fluctuations in the CMB temperature until you increase this contrast but then you see them. Then you see these beautiful measurements made by the COBE DMR experiment and this is sort of the first image of the almost primordial fluctuations that we can see in the CMB. And this is again showing the full sky unfurled into this lozzinge. This is a map as a function of direction of the sky so some directions the CMB is a little bit brighter has a higher temperature and some directions it's a little less bright has a lower temperature. And so this is a really really amazing observation and very much it's one of the better noble prizes I think. Okay it is, isn't it? I don't know. There's some other ones that are not so cool. Okay but of course luckily we didn't stop at COBE. There is a question in the chat. Okay. So it's asking if the universe were still not expanding would we expect to have received a different picture of the CMB? Well, right. So if it weren't expanding follow and if the universe keeps expanding in larger scale times will we have different picture of the CMB? Yeah. So if the universe was not expanding in other words if the scale factor wasn't increasing with time there's no reason let's say it was static then there's no reason to think the past was dramatically different from today. You wouldn't expect it to be at a temperature of many thousands of degrees Kelvin when it's at a temperature of 2.7 Kelvin today. So indeed you would not expect this. You only expect that if the universe is evolving and has a very hot early phase because it's so dense and small. And then the other question was is the CMB evolving? And the answer is yes. So it's as the scale factor continues to increase the CMB temperature will continue to fall and in fact we're kind of lucky because if we lived I don't know how many hundreds of billions of years in the future dark energy will have blown up the universe a lot and the energy density will be a lot lower so it would be harder to observe have a much lower temperature and the CMB patterns will also change with time but on time scales of billions of years that depends on scales. Anyway someone made a video how the CMB will evolve if you want to see that and try to dig that out. In any case, okay so after this Koby discovery we didn't stop fortunately but we built a successive series of better and better experiments going from Koby to WMAP to Planck. Okay and the current state of the art along with ground based CMB experiments that I work on that I won't talk about quite as much this is our current best image of the Cosmic Microwave background fluctuations the variations in the brightness or the temperature across the sky which I'll call theta the fractional difference in the CMB temperature is a function of where I looked and obviously orange is showing you regions that are a little bit higher in temperature and blue regions directions in which the CMB is a little bit colder and you know this is I think an amazing amazing image of the universe as it looked 400,000 years after the Big Bang okay so I'm going to start discussing a little bit what exactly it is we're looking at and I'll finish that at the end of this lecture okay so what are we looking at exactly right so just in terms of the background now you probably are familiar with the concept of optical depth which is an integral over any sigma t it sort of tells you the probability of scattering and in particular e to the minus tau is the probability that a photon has not scattered from a time eta to today okay so if e to the minus tau is the probability of a photon not scattering we can also use that to derive the probability of a photon last scattering at a certain time and with a little bit of thought you can convince yourself that that's basically the derivative of e to the minus tau and therefore is given by this quantity minus tau dot e to the minus tau which is called the visibility function that's the probability that a photon last scattered at a time eta now here on the bottom is a plot of the visibility function versus time or versus temperature and you can see on the bottom is the visibility function what's the probability of a photon last scattering at a certain time or redshift and on the top you can see the ionization fraction that we talked about with the sa-ha equation and you see there's a big step right a big step here and that corresponds to recombination and decoupling and so there's a big derivative in tau there and that explains why I have this spike in the visibility function so from thinking about a little bit you conclude that the most of the last scattering happens in a very narrow range of redshifts and times so basically photons last scatter right after recombination, right near decoupling okay there's a big spike and usually we assume that to be approximate treatment of the CMB you can assume this is basically a delta function right it's a very sharp peak in the visibility function so it's called the visibility function because generally where photons last scatter that's sort of how far you can see into a medium you can see maybe one optical depth okay so what that means is that the when we're looking at the CMB we're effectively seeing a surface right we're seeing a surface in both time and space 14 billion years in the past and I think it's worth just trying to visualize this properly because it'll come in handy later when we're talking about CMB fluctuation okay so just make sure you have a picture of what exactly it is we're seeing so here's sort of a space time diagram but I've suppressed one spatial dimension instead I'm plotting time okay so these are equal time slices through the universe and I'm using conformal time so photons travel at 45 degrees so this is early on the universe is in opaque plasma photons are rapidly scattering and then the universe cools and cools and cools and at one time at one temperature redshift around 1100 suddenly from everywhere these photons can stream free stream okay so they're released all at the same time in every direction but the photons we see define a surface right so we only see photons that were released from you know 14 billion years ago basically 14 billion light years away right so the ones that are gonna end up exactly at our point in space time when we're observing today uh yeah that is actually gonna be the answer so we'll come back to that okay so this is the picture you should have effectively we are uh you should have this picture that we're sort of seeing a surface when the C and B photons were released that's very far away but it's also of course 14 billion years in the past right so you're seeing back along the light cone and uh what you're seeing is sort of the intersection of that constant time or constant temperature surface with that light cone okay does that make sense it's a little confusing in cosmology always to think about uh you know to think about us visualizing things along the light cone but we're seeing things far away therefore we have to be seeing them far into the past this is what we're seeing when we're looking at the C and B it's a shell around us 14 billion years in the past okay yep yep yep yep mm-hmm yeah it does right so in fact as you're saying there's some yep can you repeat the question oh sorry yeah of course uh so the question is I talked about the visibility function being strongly peaked but it's not exactly a delta function it has some width does that do anything and indeed it will do things to the observables that we're measuring so probably the most prominent of fact of the fact that this kind of this surface is not exactly flat it has some width is the fact that very small fluctuations kind of get blurred out okay so if I have a very small fluctuation that gets blurred out and that's one of the reasons the C and B power spectrum is cut off the other one which is diffusion but that's the contribute similar amounts roughly so you know it's hard to see tiny fluctuations because I'm sort of integrating over a finite width what's that uh so at some point maybe it's not seeing the C and B yeah I think that that is effectively true right it'll be increasingly difficult just the energy will fall so low and yeah so that is certainly true in fact if you have W less than minus one that will happen in a finite time you won't be able to anything will be thrown apart so the question was okay yep as long as I can go over a little bit I probably take some questions can you repeat this oh sorry the question is if I have dark energy do I see sort of well will it be increasingly hard to see the C and B that was sort of the question um yeah I think that's right so the sort of co-moving horizon will sort of shrink right and so we won't be able to see as uh yeah as far just like inflation right you're sort of zooming into the patch yeah so sorry say that again I didn't click yeah so you have to be careful about distinguishing then between the sort of the particle horizon versus the the co-moving Hubble radius and those will give you a different answer so if you think about the co-moving Hubble radius it does look like it's shrinking but of course actually we have information you know we don't lose information that we had in the past and so we can actually proceed so there's some subtleties there I have to think about this yeah okay uh good alright let's move on but let's look at this now from the top I'm going to stop plotting uh this time coordinate I'm always just going to plot sort of x y and you should remember that this surface is 14 billion years in the past and we are in the middle looking at this today okay so there's a shell around us and it's looking far away but it's also looking far into the past okay now I want to try to describe quantitatively what uh we are seeing and then I want us to be able to understand and derive the CMB power spectrum but before we can make things quantitative we need to introduce the relevant machinery that I'm sure you're all familiar with but I'll just remind you about the machinery used to compute a power spectrum what is the power spectrum etc so let's quantify the information in this CMB anisotropy field so again we have a pattern of hot and cold spots and currently our theories and there's good reasons for this do not predict the exact realization they don't predict the exact distribution of hot and cold spots you could say that's due to symmetries or because our theories are quantum mechanical but instead what we need to do to quantitatively describe this CMB anisotropy pattern is describe it statistically in terms of variances and correlation functions and things like this okay and that's what our theories can robustly predict now before I talk about spherical harmonics I want to just consider a small cut out a small two dimensional cut out of the CMB because then I can assume what's called the flat sky approximation a small cut out of the CMB last scattering surface I can just use Fourier transforms and then everything is really simple so let's start by looking at this small 2D cut out of the CMB and assume this is flat and then I can describe this field using the point correlation function psi which is the average of the temperature at a point x multiplied by the temperature at a point x prime averaged over realizations of the universe okay now one thing that we have to assume just due to homogeneity and anisotropy for our correlators our two point correlator for example is that there's no difference between the correlator in this direction or another direction so basically there's a translation in variance in this statistical quantity the CMB should be the same statistically in that direction and in this other direction and so what that means is that two point correlator has to have a translation in variance they have to be able to move it by an arbitrary vector a and still get the same answer now what does that mean for the Fourier modes of this field so I'm going to take this temperature map theta of x or theta as a function of where I'm looking and I'm going to Fourier transform it and I'm just going to write that as theta of l I'm not going to write any tildes on it whenever there's a Fourier index you should just be clear this is the Fourier mode so I'm going to Fourier transform that and ask what does this translation in variance imply for the Fourier coefficients one second so what I can do is I can take that correlation function write it in terms of these Fourier modes using the two Fourier transforms and then I can say I want this to be unchanged by translating by a vector a so how do I translate by a vector a I add a to x and x prime now in general that's going to change the answer for general theta of l, theta of l prime that's going to change the answer the only way that translation is not going to introduce an additional phase factor is if I impose that l prime is equal to minus l in other words the only way I can have this symmetry is if these two Fourier modes are proportional to this delta function so translation in variance requires this delta function and the pre-factor is the C and B power factor so effectively it tells you the variance as a function of l as a function of which Fourier mode you're looking at so there is a question no so I guess it works sort of both ways we sort of assume one of the foundational assumptions in building up quantitative cosmology is that we're not special there's no special point in no special direction so we assume a cosmological principle of homogeneity and isotropy and we just sort of assume that has to hold for correlators that we can write down obviously though for isotropy at least this is something we can test extremely well and so far all tests with a few asterisks have passed extremely well so we have tested this and it does work sorry I should repeat the question there was a question about why can we assume this translation in variance to some extent it's a foundational question you heard my answer good let's move on this is the power spectrum it's basically just the square of a Fourier mode but now Fourier modes are not good to describe a sphere they're good to describe a flat surface but if we want to describe the full sphere we need to use better basis functions we can't use Fourier modes but the ideas are exactly the same just like I can expand a field in terms of Fourier coefficients I can expand a field theta in terms of spherical harmonics and instead of Fourier modes I have spherical multiple coefficients ALM and I can use the fact that these spherical harmonics which hopefully are familiar with for example quantum mechanics are orthonormal over the sphere to figure out what all of the spherical multiple coefficients are just by multiplying by a spherical harmonic and integrating over all directions I do what's called a spherical harmonic transform and again just like in flat sky this sort of translation or rotation in variance imposes these delta functions just like I had for translation in variance on the flat sky this is the definition then of the power spectrum effectively it's just the square of a mode or the variance as a function of which multiple I'm looking at now unfortunately we don't have access to an infinite ensemble of universes that we can run over and over and over again in average ALM and A star LM instead we have one universe and we can compute an estimate of the power spectrum by just taking the ALMs that we have assuming that due to rotational in variance all the M modes are statistically the same and averaging over all of these M modes so this is an estimator for the power spectrum and that's the best we can do because we just have one universe but it's an estimate of a variance with a finite number of samples there's some error I just can't get around so that's what's called the cosmic variance error alright let me give you a little bit more intuition about the power spectrum like if I show you a power spectrum you should be able to have some feeling for what it means and basically the power spectrum is telling you how strong the fluctuations are as a function of the angular scale that I'm considering so the standard C and B power spectrum again it plots how strong the fluctuations are as a function of multiple or what scale I'm considering the scale in the left at low L and small scales on the right at high L and as I'm sure you know the standard C and B power spectrum has a peak and that peak reflects the fact that in the map there's a characteristic size of the spots these spots are around a degree typically and that's the peak of this power spectrum but if I had a map with a lot smaller structures in it then that power spectrum would have a peak at higher L on smaller scales and if I have a map with huge blobs in it very large scale features then that power spectrum will peak at low L which corresponds to larger scales ok so does that intuition make sense I'm quantifying how strong the fluctuations are as a function of scale and that's how I can describe this map and because the C and B is very close to Gaussian it remains nearly all of the information any questions about that ok hopefully you've seen this all before and what happens if you go out and measure it you get this beautiful plot that will be our goal to explain this is one of the current best measurements of the C and B power spectrum with the Planck experiment and it's amazing again just how good these measurements are you can't even see the error bars for these these band powers of the C and B power spectrum so first of all this is amazing number one because the measurements are fantastic but the other reason this is an amazing plot is because of this red line and what this red line is basically our current theoretical model for what the C and B power spectrum should look like and it contains only a small number of free parameters this isn't a function huge number of parameters that we can fit it only contains the matter it contains basically a few density parameters and a few initial conditions six parameters and you're able to fit thousands of degrees of freedom at sub-sub precision accuracy so this is a real triumph for theoretical cosmology as well as experiment and so our goal will be to explain and at least give you a reasonable understanding of why this red line and why this power spectrum looks the way it does okay so there are several steps that we need to go through in order to understand this C and B power spectrum first we're going to try to understand how photons propagate in a perturbed universe then we're going to talk about the initial conditions and finally we'll talk about the evolution of these initial conditions forward in this primordial plasma to give us the perturbations in the density of radiation and potential etc that we see in the causing microwave background so let's start we're going to start today by discussing how photons propagate in the C and B to us okay there are any questions about this plan propagation, initial conditions, evolution that's what we need to understand and then we should completely know why the C and B looks the way it does alright any questions? alright let's talk about C and B photon propagation and the basics of the anisotropy there is a question so the question is why the measurements do not explain so well the predictions in the power spectrum at large is good yeah that's a really good question so the question is I think basically about this dip here right and the answer is we don't know statistically this is a totally acceptable fit you know you get a very good chi-squared to lambda-cdm and so you know it's tempting to just wait to just say well this is a posteriori statistics there's some fluctuation and you're looking by eye for features that look weird but when you have so many data points there's going to be a few things that look strange so you know overall this is a very good fit and you know this is not this is maybe not too surprising but I kind of agree it does look intriguing so it might be worth thinking about more I think there have been some proposals for interesting phenomenology that could explain this the issue with these low L-modes is we can't get we only have a small number of low L-modes the number of modes the number of M-modes is basically the numbers of samples of that variance that we have in our universe and we only have a small number of samples for these low multiples so there's not much better we can't measure these much better than we can today potentially there's some room for you know improving measurements with large scale structure but that's very hard so yeah it's a good question how you could test theories that just modify the low L's yeah so that's a good question I talked earlier about oh sorry why do the air bars depend so strongly on L so I think there are a few factors here one of them is we're trying to estimate the true variance from a finite number of samples and the number of samples I have is the number of M-modes per L so naturally at higher L I have more samples and so I get a smaller cosmic variance error that's one reason and that's actually the main reason here that the air bars shrink so I just have more modes for each L and that's I have more samples I get a better estimate of the variance now there are also other effects for example here you see they get bigger again that is because the plonk noise in the plonk detectors and there's a finite beam and those sort of together cause the error bars to increase again at higher L so if I went to even higher L just the experiment limitation would give me a blow up in error bars okay there is another question in the chat asking about the relation between L and scales why do we say low L corresponds to larger scales right so I mean if you're familiar with Fourier transforms sorry the question you read the question sorry I have to think about all these technology so yeah basically you're familiar with Fourier transforms how there's an inverse relationship between sort of wave number and wavelength right it's like 2 pi over lambda and it's exactly the same in the correspondence between multiple like wave number and angle which is like wavelength okay so there's a sort of a Fourier inverse relationship if you will that's one way to imagine you could say why don't we do this correlation function in real space the translation variance has a nice property that means that these different measurements are independent that delta function means different L's are independent and I don't have to have a measurement where all the data points are correlated in some funny way that's very hard to understand okay so again we want to understand this power spectrum why does it look the way it does we'll talk today about photon propagation and really this is a nice calculation and it's worth paying attention to this because it tells you what exactly we're seeing in the cmp when you look at that cmp picture what exactly are you looking at so how can we compute the propagation of the photons from the last scattering surface to today well we need to relate the cmp to the conditions on the last scattering surface and the conditions on the way and so how we do this is the following we first start off by writing down the metric in a perturbed universe so the differences in density in the perturbed universe cause changes to the space time distances and you can see the metric is then modified if I choose a Newtonian gauge of perturbation and I assume that anisotropic stress is negligible I can describe these perturbations to the metric by just a Newtonian perturbation phi okay that affects both the spatial and the time part of this metric okay so that's how I'm going to describe using perturbation theory in my perturbed universe which is clumpy what is the trajectory of a photon to first order perturbations through that perturbed universe okay so just to remind you of how we do this you want to describe your trajectory in terms of a parameter lambda the way this is done in general relativity is that for a massive particle the particle path is determined such that the proper space time distance is minimized and this gives you the geodesic equation I'm sure you're all familiar with this with these Christoffel symbols that make everything coordinate and variant and for photons it's convenient to rewrite this in terms of momenta and this is the geodesic equation that we can then apply to momenta there's obviously much more vigorous ways of deriving this okay so if we want to compute the photons path in GR we need to evaluate the geodesic equation that describes the photons trajectory now this is written in terms of momentum components but we would like to relate this to sort of physical quantities that we can actually measure like the energy that we measure using our detectors and in special relativity I can I note that the energy is given by p new u new where u new is the four velocity that's an invariant and I can just carry that invariant over to general relativity except now my velocity is not given by just one zero zero zero but instead that derivative of the the zero component with respect to proper time is given by this slightly modified expression and so you know you don't need to know the details but basically the energy is given by the zero component of the four momentum and there's a slight complication due to the perturbation okay so if we want to know how the energy of the photon evolves which is what's relevant for determining the temperature we just need to evaluate this geodesic equation for the zero component of the four momentum okay now I'm not going to walk you through this if you want to go through this I can sort of show you how to do it and I'll point you to some hints etc so if you really like calculations and you really like evaluating the crystals and symbols let me know you're welcome to do that I'm just going to not crunch through this this calculation I will just give you the answer once you plug in all the crystals and symbols etc you get this differential equation that describes how the energy evolves along the photons path so time derivative this is a total derivative of the log of AE with respect to conformal time is given by the total derivative of the potential perturbation with respect to conformal time plus two times the partial derivative of phi with respect to conformal time okay so now what I'm going to do is I'm going to integrate along the photons path the photon is emitted and it travels to us so I integrate from emission to us and what I get just doing this integral from emission to us is this expression I can then tailor expand this exponential because these perturbations are small and I get this expression relating the energy of the photon today to the energy of the photon when it's emitted and the scale factor of the photon when it's emitted and these perturbations I'm just going to add by hand but it's easy to justify this the fact that I've assumed that everything is emitted at rest if the last scattering surface is moving towards us energy is affected by a factor by this additional term minus if it's traveling towards me it gets a boost in energy and if it's traveling away it gets a decrement in energy okay I told you earlier we discussed earlier that the energy of a photon and the temperature evolve in the same way and so I can just take a ratio of the energy today divided by the energy at emission and that's just given by the temperature I observe divided by the temperature at emission so now I know almost everything I know how the temperature I observe depends on the temperature at emission which is always fixed it's always 0.3 electron volts and it's all written in terms of things I can I know what they are I know what the potentials at emission are I know what the potential today is I know what the velocity means and I'll talk about this term in a second the one thing I don't know in this expression is what the scale factor is when the C and B photon is emitted so we said it's emitted at a fixed temperature but what scale factor does that correspond to what is the scale factor what is the redshift when this photon is emitted and it's not enough to take the average one well we said earlier this was the quiz question that I asked so it's emitted at the same local temperature of 0.3 electron volts but if I have an over density then the universe has to cool a little bit longer to reach that 0.3 electron volts and so it's emitted at a slightly bigger scale factor okay so the time when it's emitted has to be a little bit different if I have more radiation in that in a certain region so that's kind of the physical reason why it can be emitted at the same local temperature but I'm still sensitive to the radiation perturbation it's because if I have a lot of radiation it has to, the universe has to expand for longer to cool to the right temperature and it's emitted later okay so let's make this quantitative what you can show is that if I have a radiation density perturbation delta r delta rho r over rho r bar then the scale factor of emission is not the sort of average one but it's a bit bigger it's emitted a bit later because the universe has to cool just a little bit extra now you can work out exactly why that's the case so basically what you do is you assume that the temperature at emission is the same and that has to be given by the perturbed radiation density in time just as much as it's given by the unperturbed radiation density in time so the radiation density always and the temperature has to be the same at emission and so these perturbations to the time of emission and the radiation density of emission have to cancel because it has to be emitted at the same local temperature given just by this nice recombination and decoupling business alright and if I do a Taylor expansion of this these perturbations have to cancel I can do some rearrangement to figure out the time delay this causes and plug that in to a Taylor expansion of the the scale factor with time and then I get this expression but again to emphasize the physics here if I have more radiation if I have a perturbation in radiation density the universe has to cool for longer it's emitted at a larger scale factor and therefore it experiences less red shifting along its path to us ok so where we have a higher density the CMB is emitted later with a larger scale factor giving us less red shift and that's why we see a temperature fluctuation that's the physics ok let's put this all together putting this all together this is an important expression this tells us what we're seeing in the CMB and it relates it to quantities on the last scattering surface and along the path of the photon so if you haven't you lost the plot how's the time to pay attention again ok so the CMB temperature anisotropy theta as a function of direction depends on the radiation density perturbation evaluated on the last scattering surface in the direction I'm looking so if I'm looking in that direction depends on the radiation density perturbation at that point on the last scattering surface and at the time that corresponds to emission and similarly it depends on we just explain why that is it depends on the these terms which I'll walk you through so we just talked about the fact that the density perturbation causes you to get less red shifting and the temperature increase now that second term I think makes a lot of sense if the photon is emitted on the last scattering surface from a region where there's a potential perturbation let's say there's a potential well that photon has to lose energy to climb out of the potential well and therefore it's red shifted and I have a negative temperature fluctuation on the other hand if it's emitted from maximum of the potential it actually gains energy and I see a higher temperature that makes complete sense finally second are you talking about this diagram this might not be the most ideal diagram you could just draw and then it's falling down the hill is that what you mean or did I misunderstand it's emitted from inside the potential well at a fixed energy so that's it hasn't fallen in it's emitted from the bottom of the potential or from the top so it's because it comes from the potential well it's not because it traverses it although the question was why doesn't it cancel out when it falls in it's because it's emitted from in the potential well although we will come back to your question in a second it's a very interesting point this third term is called the Doppler term and I think it makes complete sense if the last scattering surface is moving towards us then I get a sort of Doppler boost to the energies of the photons and I see a positive temperature fluctuation the last term is a little bit more subtle and it's actually related to the question the point that was just made so normally if I have a potential well along the photons path that won't do anything because the photon will fall into the potential well and it will gain some energy but then it will crawl right back out and it will lose that energy again so the blue shifting falling in is completely canceled by the redshift crawling up the only way that cannot be the case is if while the photon is traveling through the potential well that potential well changes in amplitude so it decays or increases in other words that partial time derivative of the potential is non-zero so then I can actually change the photon's energy for example if a photon falls into this potential well gains a lot of energy gets blue shifted and then the potential well decays although it has to give up less energy than it gained and so that can introduce a net boost or decrement to the C and B temperature in the direction of these decaying potentials now that's a pretty small effect usually has normally during matter domination the potentials are constant but there are some regimes where this is important and the first one is dark energy dark energy domination at late times dark energy it's a non-clustering component it causes the potential to decay and so this late ISW or integrated sex wolf effect is one way that we have of testing dark energy as we can sort of check whether the potentials decay the way dark energy says they should there's also another there's also an early ISW effect though because the C and B during matter domination but not long after radiation is stopped being important so it's not long after matter radiation equality and so there's still a little bit of radiation around and so there's also an early integrated sex wolf effect from the radiation causing the potentials to decay okay but that basically summarizes the meaning of all these terms when I look at a C and B temperature fluctuation the sum of density perturbations that cause more or less redshifting due to the delays of emission potential minima or maxima that cause me to lose or gain energy Doppler term which causes a Doppler booster to the energy if the last scattering surface is moving and this integrated sex wolf effect that we talked about so hopefully you now understand what the C and B is and what exactly it is in terms of these perturbations you're seeing when we look at these beautiful images of the cosmic microwave background and so in the next lecture we will connect these perturbations here with the initial conditions and then go all the way from the initial conditions to a prediction of the C and B power spectrum and that's all I have for today happy to take more questions though so we'll have a discussion session in half an hour so perhaps we can keep questions for them thank you and see you in half an hour bye


around what's happening there today are the sponsors of this show the people and the partners that enable this and make this possible for all of you to be here, so I want to give a big round of applause to all of our sponsors and everyone and a special thank you to our diamond sponsors, the ones that participated in all the keynotes thank you gave you a good view of how this ecosystem is coming together you know why we as Horton work spend so much time with many of these companies and why they are so focused on what's happening at Duke and how they go build an integrated solution for all of you so with that I want to close down the keynotes say thank you to all of you for joining us on this we'll see you back here next year in San Jose thanks everybody, bye bye


What's going on, everyone? Sam here at late sports guards. We've been 23, putting in a prison baseball hobby, six box break, number four. Pick a team style, read off lists for names in our teams. We've got A to D with the Giants Athletics, Alexandros, Royals Cardinals, Andrew S. Angels, Brian H. Blue Jays, Brian M. Phillies, Brian J. Rockies, Christopher F. Nationals, Dean W. with the White Sox Guardians, Diana D. with the Red Sox and Reds, Edward P. Yankees Astros, Eric N. Twins, Ferhan A. Rangers, Flavio N. Pirates, Francis H. Diamondbacks, Braves, Padres, Marlins, Jacob R. Orioles, Keith J., Tigers, Michael T. with the Mets, Noah H. Cubs, Patrick M. Mariners, Ronnie K. Dodgers, Roy M. Brewers, and Ryan B. Reyes. Got these copied over, or copied over, I don't have to get these copied over anywhere because this is not a random team.  All right, anyway, let's keep it going. Back these up. I'm just gonna dust this really quick. Good ol' prism dust. Prism dust is whack. Some of Bob Lemon, Kid and Wallace, Ruby Wave, Zack Neto, and for our giraffe skin as well. Red is Andrew Jones to 199, Carson Whizzenhunt, Ice, Ice is hobby exclusive in this, which is cool. Silver, Kamenara, Ruby Wave, Bobby with Junior Rookies. I was thinking about that in my drive-in this morning. I'm like, I wonder if Bobby Whitz can pin this as a rookie, like the only rookie. So, 149, Mick Able, nice one there. Really? Paul Molliter, Melvin Gordon signed with the Ravens? What? Is that for real? That's weird. Just another guy on the washed up, running back to Carousel, that goes through Baltimore, joining Latavius Murray, Mark Ingram, Devonta Freeman, Kenyon Drake, now Melvin Gordon, Brooks Lee, Potty Gold, Silver, Evan Carter, pre-shipping valid on eBay, I never do pre-ships, I live in Europe, and I never do card check. I don't know if it's, are you part of the, did you sign up for the Global Shipping Program, Ali? Ever since Pereira, Silver Rookie, or Prospect Signatures, Yankees, Trevor Jones, look into the Global Shipping Program, Ali, that eBay offers. I don't know if it helps from the buyer's side. Jack Leiter, Silver, Luke Gold for the Tigers to 99, a Gabriel Gonzalez, Hyper, Pete Rose, Silver, Wadi Herzog, there's Jackson Ferris, nice one there too, 199, Mark McGuire, Hyper, Juan Gone, Jose Salas, going to the Twins, nice one there, Minnesota, Jose Salas. Kevin with the Guardians and Six, thank you, Kevin. Marcy with the Suns in a, either select or revolution, see the, I think it was, select. Going to the next one, Auto, Harry Ford, nice one there for the Mariners. His bowman stuff is red hot right now still, dude. He has a stud, nice one there for the Mariners, Peter up, pot of gold, Pete Rose, what's that, Pete of gold? Pete of gold, Pot Rose. There's a red Michael Bush for the Dodgers to 199, cool Papa Belle, so that'll be part of, we'll do a non MLB card random at the end, every single non MLB card, base, insert, numbered card, we'll go to one spot to make it easier. Mojo is Gavin Williams for the Guardians, one of last teams taken to 25, congrats, Cleveland, 12 of 25, that is Colton Couser and base. Easier to hit too, we've hit one in every half case so far Shane.  Blue, Rhino, Ryan Sandberg to 149, Mark Grace, ice. So hoping there's some really cool, I hope Beezio has a manga dude, that would be so sick. Red is Chase Delotter to 199, ice Tyler Soderstrom, Pete Rose, reprismed baseball, I wanna see if the manga check, let me see really quick product checklist, baseball prism, manga. Yeah, it's still too awkward to use right now, it's weird dude, the checklist on Panini stinks. They'd be more rare. Yeah, they're kind of similar to like the prism draft picks. Kind of similar to the prism draft picks in that sense. Yeah, they're a little bit easier to hit but they still look cool, luckily. Silva, Griffey, second to none, Griffey fireworks. See what we got, that is Tyler Soderstrom for the ace, potential penmanship. Nice one there, Oakland. I can tell if Kyle was trolling me about the, Silver or Feller, Mark Grace to 199, Hyper Graceffo, that's kind of too like, Yankee, I know Ravens did sign Melvin Gordon, wow. I'm a Yankees fan, unfortunately, Diana, I am a Yankees fan, from Boston, oh no. Can't really say anything, because the Yankees blow this year, Silver Vecara, what'd you say? I said I'm with Diana, I don't know. The say hey kid, Willie Mays, nice one there too, 50. Javi Lopez, Tipper Jones, unfortunately, you crazy. I don't know what that means. That doesn't look like a real person to me. Bobby Miller for the Dodgers, nice one there. Battle for the bottom is right, oh my God. Oh my God. Chill dude, Gordon Graceffo, Hyper Auto, going to the Cardinals, yeah, both those teams, not good. Orioles and Reyes dude, even the Blue Jays are doing better, that stinks. Rafael Palmera, oh, I'm also on, yeah, fair dude. To 99, Palmera, Averson Ortega, not that bad. Nah, the Yankees, they kind of stink this year, man. Yeah, prison baseball's been pretty solid, Ryan. So yeah, my dad basically said, when I was younger, if I want to live in this house, you have to be Yankees man, so that's how I became a Yankees fan. The 99 Javi Lopez for the Braves, Luis Apparaccio. Some of Jackson Job, Cooper Ajerpie. Yeah, I think we have him at like 160. Al Bridwell, Johnny Pesky, and base. Same with my dad in the Reds, oh yeah. Yeah, my dad is like, oops, sorry, my bad, is baseball's like his favorite sport, so he's, oh wow, thank you, baseball facts sent in a fire. Here we go. Sent in a 32, 36, 40, 43, 47, 50. Good Lord, dude. Appreciate it. That is a Red Brandon Barrera, man, up to 65, 66. That is Hyper Jackson Sharia. My husband's shaking his head right now. Oh, Jake is definitely upset. Oh, Jake's pissed, dude. Yeah, sure. Jake came in like crying. There's Vladimir Guerrero, senior. Randy Johnson. I could pick another team, who would I pick? If you asked me 10 years ago, it'd be the Houston Astros. Yuan Rojas, Randy Johnson. That was always my like second team when I was a kid.  I kind of, ever since they won the World Series last year, I kind of just forgave them for all the cheating stuff. That's Brandon Barrera. There's Justin Crawford, a 75, nice one there. JR Richie, the O-Cards. No, I would not pick the Mets. I think I would, in a Mets Red Sox World Series, I'd root for the Red Sox.  I hate the Mets so much. Angel Martinez, nice one there for the Guardians. Solid one there. I know, they just hit like a slump, to be honest, Futo. Since the Killer B's played, yeah, I love the Killer B's, Jose. Yeah, B shows my guy. Nice, James Wood, potential penmanship for the Nationals, nice one there, Washington. Yeah, I love Berkman, I love Bagwell. Vijo, Vijo I would still say is my favorite player of all time. Yeah, Lance Berkman's the man. Michael Bush, to go into the Dodgers. Like nothing against the Mets, just I went to school in Western New York and everybody was like from Long Island, they're all super obnoxious Mets fans. There's a Lou Brock to 149, nice one there. That's Paul Conerco and Bobby Witt. And like my issue with like, it was every year, they're like, yup dude, this is the Mets year. Like I had one buddy who would make like playoff brackets at the beginning of every season, Mets all four years had him winning the World Series. And I'm like, dude, just at least be realistic. And then they missed the playoffs all four years. Tyler Locklear to 149, Goose Goslin, Buster Posey. I don't know, Shane, I don't, cause we don't have a lot left. Like most of it we're ripping today, all but like five cases. So we probably might honestly, Owen White to 149, Pedro, J.C. Young. So I don't know what the, what Richard's plan with the rest of the cases are. I don't know, maybe we'll get more, who knows. Archie Vaughn, that's your boy right there, Archie Vaughn. There's Brooks Lee, Red Wave and base. And then Hiney. And then Hiney Grow. That Hiney Grow is your boy for sure. It's a go right there. Silver, Buster Posey, Hiney Grow. Speaking of, there's Dylan's boy, Hiney Grow. And Babe Ruth. I'm hoping there's some more prism random breaks. This is actually, I mean, it's a good product for the price man. Like I have, there is nothing wrong with this whatsoever. This has been pretty solid. What we got, number five is next. I think we need, no, number six has spots or five has spots. No, five is sold out, six has spots. I believe there's eight to go. One, two, three, four. No, seven to go. Seven to go on number six. Honestly, it's all rich in lane and forest are the ones that schedule the breaks. That would be, that's really their call to be honest. It's a lot of it has to do with inventory. A lot of it has to do with like, you know, different, like what we have, what we can get in, what sells the best, all that kind of stuff. That is early win to 1.99, Grant McCrae and Kyle Harrison. I mean, honestly, I mean, there's still golds, there's black golds, there's case hits, there's gold, we pulled the gold vinyl one-on-one already, Sam Crawford, Chief Myers. I actually have, Nicholas, I've opened one blaster of 23 Bowman and it was actually pretty good. Yes, Ellie is on the checklist, Ryan. At least to my knowledge. Yeah, we pulled them in inserts and stuff. There's a Bruce Souter, nice one there too, 25 on the Mojo. That's on that one, Ice Noel Di Marte. Silva Kirby, there's Jordan Lawler. Silver A-Rod fireworks and A-Rod base fireworks. Robbie Snelling to 1.99, Ice Luis Aparachio or Aparicio. Gotta say that exactly. That is a Silva JR Richie, Purple Jared Schuster to 2.99. Hyper Bobby Hit rookie.  I think that's still gonna be funny no matter what. Otto Jacob Barry to 50, Orange Wave. There you go, Marlon, congrats Miami. Miami, nice Juan there, there's Evan Carter. And guys, if you buy into Breaks with us, I would check out the national promo, the top prize in the national promo. 2009 Mike Trout, Bowman, Refractor, 9.5 Auto, valued at about last sold for 15,000. And the second prize is a PSA-8 Jordan 86 Fleer. There's Kaden Wallace, nice one there for the Royals. That's on that KC and Ricky Tiedemann. Well, Jordan last sold at auction for 7,600, so pretty good. Just in the first two prizes, there's like over $20,000. Ralph Kiner, there's George Brett, blue to 149. Bobby Miller and Brooks Lee. There's gonna be, I think, I think Rich said either two or 600 winners. I don't remember how many winners it was. We're giving away break credit, we're giving away boxes, giving away a lot of cool stuff. That is two, 149, Eddie Matthews, Pulsar, McGinny Cappy, Evan Carter. You gotta buy into national base. Yeah, so starting Tuesday, Diana, we have the breaks that say national promo and whatever the product is, random team, PYT, blah, blah, blah. Every spot you buy gets you one entry into a random. Once the national breaks are over, we do the random and then that's where you see the prizes. So basically, all you have to do is buy into a break that says national promo. Certain ones give you more spots depending on the price. Like I think Flawless gives you two. I think, I don't know off the top of my head, I can go look really quick because that's on Tuesday. Saturday, Sunday, Monday. Like for Flawless, that gives you four spots basically. There's nice, Jackson Holiday. Grats on that one, Orioles. First holiday of the day. Happy holidays, baby. George Brett. So yeah, that's how that one works. Lot of national breaks. I don't know how long it's gonna go on for. Off the top of my head, I know it went on for a decent amount last time. But it will definitely be from when the national starts and when it ends. I don't know how much further it's gonna go. But yeah, like I said, the top prize, 2009 Bowman first Mike Trout Refractor Auto, numbered to 500. BGS95 valued at about $15,000 for that one card. And you will get it. That'll be your card. Someone is gonna get that card. Maybe it'll be me. I'm gonna be buying into those breaks. Can't buy into my own breaks, unfortunately. Ricky Tiedemann, Red Wave. So I'll probably be buying into Kyler Math Breaks. Sold a raw Super Wave out of 50 for $2,300. Nice preacher. What year is that from? Silver, Luis Gonzalez. There's a Paul Moller. Talk about Trout or, I'd say Tom Siebert. Nice one there, $2.75. Ice, Hans Lobert. Point's not right. I'm wood, I guess. Blue, Dick Williams. Two, $149. Ice, Cal Ripken and James Wood. So those are gonna be a good time. National breaks always stuff that I know a lot of you guys look forward to every year.  One team will receive all of the Cool Papa Bells and Tomayuki Sugano's. That is a Curtis Mead to 99, the Mead for Mead on the Purple Auto. Nice one there. Grats on that Tampa Bay and Nolan Ryan. Whoa, whoa, whoa, whoa, mackin' cards over. Okay. I'm gonna give you a yellow. You will, you'll get one before the end of the day. Mariano, Blue, Reggie Crawford to $149. Hyper Orlando Sepeda, base. Soba Alchimeras for the Matz A-Rod. Edgar Martinez for the Mariners to $199. Hyper Gabriel Gonzalez, Mariners as well, and Bobby Miller. That is a Kyle Manzardo going to the race. Nice one there. There's a little ink stain on the back. Probably from when they were stacked them. So we'll send you an empty box and wrap for their race. Thanks for all the follows on TikTok. TikTok, we're out live over on YouTube and Twitch as well. YouTube and Twitch, we stay live. We don't stop live over there unless OBS crashes. Auto, Yuri Perez, nice for the Marlins. He, this is one of his first like autographs. Yuri Perez, not, not the first, but one of his like early autographs, which is nice. Cause he does not have a first bullman, surprisingly. So nice one there for the Marlins. Yuri Perez, not an easy auto to find out there. Another guy who's gotten called up, well in the majors, Red, Whitey Ford to 1.99. There's Jace Young and Griffey. Yeah, what's up Ollie? You can ask questions for sure. Absolutely. Nice, Ellie De La Cruz to 75. Let's go, Diana, congrats on that, my friend. That's awesome. Nice, Ellie coming your way. 11 of 75. Omar Biscale and Juan Marascha. I could throw that in the recap. That's a little Ellie action there. Chris with the Yankees and a national break, tops Chrome, get all the tops Chrome baseball will all be eligible for national breaks since they, since it comes out next week. One, two, three, four, five, six, seven to go. Seven to go on number six, everybody.  My thoughts on Jackson Cherry.  He, I mean, he's hit, he's had three games this year with three extra base hits. He's got like 19 home runs in double A and he's 20 or 19.  He's so good. So good. I think he's, what, number two now? I think holiday's won. In the entire MLB. What, Cheerio is rightfully number two. Silver, Cheerio prismatic speaking of, holiday prismatic. I'm a good Yankee fan now. Oh man, thank God, thank God. There's Otto, at least, Luis Angel Acunha going to the rangers to 50 on the orange wave. And Tink Hentz. Yeah, I think he's gonna be a stud in the majors, Jason. I am a big fan of Jackson, Cheerio. Silva, Jim Gilliam. Bobby Whit, red to 1.99. Andre Dawson, nice hawk there. Yeah, of course, Jason. Yeah, he's a good player, man. Lefty Williams. Mason Wynn to 1.49. Hyper, Johnny Pesky and Cheerio again. So we got a green scope coming up here. That is gonna be Emerson Hancock to 75 for the Mariners. Nice one there on the green scope, Otto. Grats, Seattle. Nice one there, Vladimir Guerrero Jr. Heir's points, knew we weren't gonna get away without him. It is 600 though, so not bad. Do two randoms at the end to determine points and not MLB cards. Purple, Ivan Melendez, the Hispanic Titanic for the Diamondbacks to 99. Devisan De Los Santos, big unit, Randy Johnson. Hot of gold. That is green scope, Jordan Lawler to 75 for the D-Backs. Mario Soto, we'll just cruise through the base. Silver, Juan Marichal, Joey Weimer, Red Wave or Ruby Wave, Rupru. I'm just another guy I think we got called up this year. He was like the top guy in Bowman Chrome without an auto. Connor Prilip, that is Red Wave of Luis Gonzalez, Lugan, Jacob Berry as well, Mr. Trashcan. Brett picking up a Breakers Delight spot. Again, Breakers Delight is a new top Chrome skew that came out this year. Similar to like Bowman Chrome Choice, only 10 cards, all refractors, parallels or autos. So very auto and parallel focused. Luis Apparazzo to 149, Kyle Manzardo and Ellie. Prismatic. Guy picking up a couple spots tonight, thank you Guy. That is gonna be Devisandelo Santos to 149, Larry Doby and McAbel. All right guys, we're gonna do a quick random here. We've got 600 points and we're also gonna do a random for the non MLB cards that we pulled, AKA Cool Papa Belle and Tomoyuki Sugano. So we've got non MLB and points, points. All right guys, so we'll start with the non MLB. Got four times on that. This team will receive all the non MLB once it goes through sorting and chipping. One, two, three and four. Gonna go to the brewers. Brewer's gonna get the non MLB cards. And then 600 points. One team will get 600, 10 times. One, two, three, four, five, six, seven, eight, nine and 10, gonna go to the Tigers. Gonna get the points. Do a quick recap here guys. We have the LA De La Cruz, 275, Bruce Souter and Gavin Williams Mojos, the 25, Angel Martinez, James Wood, Michael Bush, Kyle Manzardo, Yuri Perez, nice one there. Jackson Holliday, nice one there as well. Tyler Soderstrom, Bobby Miller, Harry Ford, Jose Salas, Everson Pereira, Gordon Graceffo, that is a kid in Wallace, Curtis Mead, the 99, Everson Hancock, the 75, Jacob Berry and Luis on Helicunia, the 50. That's gonna do it for the break guys. Thanks again for getting that filled up. Coming up next is number five.


Welcome to the second meeting in 2016 of the SPPA Committee. Good morning to all the members of the committee. Our first item on the agenda today is a decision on taking business in private, which is consideration of the mandatory committees in standing order, all changes, and do members agree to move into private session to discuss these. That would be done at the next meeting of the private session. Our second item today is for business to consider the rules and membership of cross-party groups. Section 6.4.1 of the code of conduct requires that each CPG has at least one MSP member from each of the parties or groups represented on the parliamentary bureau. In private session, a number of CPGs seeking to re-register experienced difficulties in securing full cross-party representation, and it's anticipated that this situation may reoccur in this session. Members have been invited to consider whether they agree to general modification of section 6.4.1 of the code of conduct to allow CPGs that have at least one MSP member from the majority of parties represented on the parliamentary bureau to register. I would invite any comments from the members regarding this. It's a very sensible proposal, and it continues to require members to demonstrate a breadth of political interest in establishing new groups. I think that it will be welcome going forward with Mr Scott. Yes, I would support that proposal. It's very sensible one, too. I adore what Patrick said. I invite members to approve the general modification to section 6.4.1 of the code. Thank you very much. Agenda item 3 is mandatory committees remits. It's the final item today, and members to consider the remit changes for mandatory committees. This is a result of the decision by the parliamentary bureau and the passage of the Legislation of the Scotland Act. I invite members to make general comments about the paper that has been proposed by the clerks. I am broadly content with that. I think that there has been a reasonable degree of discussion between the political parties before reaching some consensus about the remits that should be allocated to the newly established committees. I wouldn't have a problem agreeing this as it stands. I think that my only comment would be to acknowledge the representations that we have received from external groups regarding equal opportunities and equalities and maybe suggest to the committee concerned that they might want to look at the recommendations of the frequency of their meeting so that they feel that they can deal with their remit adequately and deal with the concerns that have been raised in that representation. I know that the same representation has been made to the members of what is currently the Equal Opportunities Committee. Expanding the remit of that committee is not an onerous task for either the convener or the people who are on the committee. I am sure that the introduction of human rights to the committee is such an important issue that I am sure that it will take a nice sense of what has been said, but I will be able to mitigate the concerns that have been raised. I understand where the concerns are coming from. It is worth noting that a number of significant equalities organisations have expressed that, but many others who have not expressed those concerns. It might be perfectly reasonable to ask if the clerks or the convener would be able to meet the organisations who have been in touch to discuss their concerns, but comparing the remit of the Equalities and Human Rights Committee as it would be if that is what is agreed, I think that it compares favourably with the remits of other committees, for example justice, which is where human rights issues have traditionally sat. That has been limiting in the sense of framing human rights arguments always in terms of justice and specifically the criminal justice system. There is a long-standing view among the human rights advocates and organisations in Scotland that it needs a broader understanding in terms of its position in the parliamentary committee system. I think that that is the appropriate way to do it. Would you like the convener of the Equalities and Human Rights Committee as it stands to meet the organisations? I think that they choose to. I think that we should certainly offer the option to meet the committee if that is possible. I am happy to do that, if the clerks could organise that for us next term. I completely concur. I think that that is exactly what is required, so that we ensure that everyone is being accepted and that their views are being expressed. If there are any concerns, they are being tabled and they are being said to the right people so that everyone understands where we are going. We all move forward in that new structure that they are looking to achieve. It would be beneficial for us all. Thank you very much, Mr Stewart. I will just reserve my judgment until I see the working paper that is brought forward. I think that Patrick Harvie raised elsewhere and suggested that there might be more to do for the finance committee than might be reasonable. I am not sure if that is the case. I am never having served in the finance committee. I do not know what the burden of work on that committee is, but I would like to withhold my view until such time as we see the working document that is brought forward. I would like to echo what Mr Scott was saying, that I would like to see the document in the autumn and then express it to you. The suggestion would be that we do not approve the draft report to the Parliament setting and standing order rules and changes after summer recess and not make a formal approval of the suggestions today. I will ask the clerks to take back their concerns about capacity for the new powers and that the new powers should be normal in terms of the ordinary working and scrutiny of the committee. I will also ask them to consider whether, although we are in a very fluid situation and things are very difficult at the moment to make any firm plans about how they should go forward, but to look at where existing remits of the ministers could be reflected in the committees that would normally scrutinise that kind of work. We will look forward to that paper in the summer, as everyone agreed on that. That is the last agenda item. I wish everyone, hopefully, a recess of some kind over this summer. We will see you all again whenever, as we do not know if Parliament might be called, but a very happy summer to everyone. We will see you soon. Thank you.


The US Secretary of State there, Rex Tillerson. Joining me from Washington is Andrew Wilder from the Asia Center at the US Institute of Peace. He's been in charge of the Institute's Afghanistan program. It's good to see you. Thanks very much indeed for joining us. I'm really interested in this focus that there seems to be on India and what India can do to try and help America deal with the Afghanistan question. How much of a change do you believe this is from past administrations in bringing India into the fold in this area? Well, I think there is continuity in terms of what the overall objective is in Afghanistan in terms of wanting to prevent it from becoming a safe haven for transnational terrorist groups again. So I think that's constant. But we have seen some changes in emphasis in the new Trump policy, in particular by not stating the timeframe to withdrawal troops or focusing so much on troop numbers, which I think is also positive because in the past I think we focused so much on troop numbers that that sort of became the strategy rather than the tactic to support the overall objectives. But the other area which is different, as you noted, is I think more focus on having a regional approach to resolving the conflict. And I think that's positive. But I am personally puzzled a little bit by the emphasis on India. So on the one hand, we want Pakistan to be more cooperative. And yet the number one reason why Pakistan is interfering in Afghanistan and providing safe havens to the Taliban and the Hakani network is because they want to ensure that that's an asset to guard their interests in Afghanistan against what they perceive to be Indian interference. So if you're basically asking India to do more in Afghanistan, if anything, you risk further fueling the concerns in Pakistan that Indian influence in their western border and the neighbor to the west is going to grow and further threaten Pakistan interests in Afghanistan. So again, trying to ask India to do more, I actually think can be counterproductive. But as you say, you point to one more of a regional holistic approach, I suppose you could say, getting regional players more involved. And that obviously includes India. But if you get India and Pakistan around the table, which it seems to be what Rex Tillerson and President Trump want to do in trying to sort out what's going on in Afghanistan, then perhaps Washington can say to to Delhi, well, you stop meddling and Pakistan stop meddling and everyone will be better off. Well, yeah, and I think that we should be having more focus on Indo-Pac conflict because ultimately the Indo-Pac tension I think is fueling a lot of the conflicts in the region and including in Afghanistan. But I think that's that's where there's been some, you know, difference, certainly an emphasis between President Trump's speech, which focused lots more on the military angle.  And I think it was, you know, very helpful for Secretary Tillerson to emphasize that no, we need a more of a diplomatic and a political approach as well. Because I think if there's one lesson from Afghanistan as well as Iraq is that sort of simply killing bad guys, you know, it doesn't win the war. And, you know, where I think that the real opportunity lies in Afghanistan is, you know, I'm actually encouraged that we're sending a modest increase in terms of military support. But clearly that's not going to be sufficient to defeat the Taliban. But it could be part of a stick to try to incentivize the Taliban to come to the negotiating table. But then we need to have a much more robust political strategy, including this regional piece, to incentivize the Taliban to come to the table and get Afghanistan's neighbors to play ball with that. And I think in particular, if we can be clear to Afghanistan's neighbors, not just Pakistan, that the U.S. is actually really interested in bringing peace and stability to Afghanistan so that we can then withdraw our troops, I think we might get more cooperation in the region. Yeah, I mean, Lyndon Johnson focused on the body count in Vietnam, George W. Bush focused on the body count in Iraq. And we know what happened there. But given that there seems to be a little bit of conflict between what Rex Tillerson is saying and what President Trump is saying, Freudian slip there, who do we believe? Well, at this point, I'd like to think that they're complementary. I think for the speech that President Trump needed to give yesterday, including appealing to his base already as your feature before this mentioned, there's a bit of a U-turn from what he campaigned on to what he gave in his speech. And so first, I'm certainly someone here who's very happy. He didn't follow his gut instincts of simply precipitously withdrawing from Afghanistan, because then we know that the result of that would probably be state collapse and a return to anarchy, which would be bad for Afghanistan as well as the region, as well as the U.S. And so I'm glad he actually listened to his advisors and changed his policy on that. But then again, I'm hoping he will follow the advice of Secretary Tillerson and give a lot more attention to the need, attention to the need for a diplomatic and a political strategy to complement what I think will also be an important military strategy. I mean, are there really elements within the Taliban who can be spoken to, negotiated with, as Rex Tillerson and by extension the president seem to suggest? I think there are, but I also think that's a proposition to be tested. Up until now, I don't think, frankly, in the last 16 years, the U.S. has ever seriously suggested that we're interested in a peace deal, politically negotiated under the conflict. Sometimes we've paid lip service to it, but it's our military policy that's always dominated. Also, when your policy as it was under the Obama administration was, is we want to withdraw by 2016, if you're the Taliban, why negotiate if your adversary is about to withdraw pretty much all foreign troops from Afghanistan, wait until they're withdrawn and then try to win on the battlefield? The fact that the Trump administration is now signaling that we're not going to withdraw, and I think along with our NATO allies are going to remain engaged, that combined with a more robust regional strategy and I think some incentives for those Taliban who want to negotiate to come to the negotiating table, I wouldn't rule it out as an impossibility. I mean, I think some of the Taliban themselves are tired of fighting after so many years and as much as the Afghan national security forces and are taking out the Taliban as well. So I do think that there's elements that would be interested in a politically negotiated end to the conflict. Andrew Wilder from the Asia Center at the U.S. Institute of Peace. Thanks for joining us, Andrew. Thank you.


Human intestinal organoids, HIOs, can be used as a source of intestine for regenerative therapies. However, HIOs require a suitable environment to grow and thrive. We found that HIOs seeded onto acelular porcine matrices did not thrive in vivo, but HIOs seeded onto PGA-PLLA scaffolds did. This suggests that PGA-PLLA scaffolds may provide a more suitable environment for growing HIOs and could potentially be used to create a functioning human intestine. Further research is required to explore this possibility. This article was authored by Stacey R. Finkbiner, Jennifer J. Freeman, Minna M. Week, and others.


When the child was interviewed them by the police and by other people involved, of course the first question is where did you get the marijuana? And the child said that the marijuana had been given to her by Timothy Coleman or sold to her by Timothy Coleman. So based upon that information as well as other information, the state police got a search warrant, went to the home of Timothy Coleman and his wife, Verlia Coleman and and executed the search warrant, found different kinds of drugs there including marijuana and prescription medications. They also found things like scales to process and weigh out and sell marijuana and other drugs. I deal a lot with drug dealers that sell drugs to adults and that's bad, but it's especially bad when drug dealers are selling drugs to children and we intend to make sure that Timothy Coleman realizes and is punished for what he has done involving these children. So these are very serious charges and he's looking at some pretty serious prison time and again knowing that at least one of the victims in the case is a minor that was buying these drugs, we intend to see that he gets a little special attention.