 If you're not a lecturer, please do not sit on the two-side column. If you're not a lecturer, if you want a lecture, please feel free to sit over there. There's a reason for it because we will have active learning questions and answers forming in groups and stuff like that. So the biggest challenge is move yourself over to the center of two columns here because otherwise you won't belong into any groups, or group with the lecturers, which might be harder than not. Organizers can stay over there. Okay, start moving. This is the hardest part of the lecture. And also you might need to talk to someone, which is also sometimes very hard. So see this, it's called fun time. You try to sit in the center of two columns. Thank you. Oh, I don't have to, oh good, perfect. I don't have to yell at them then I guess. If for personal or religious reason you really don't want to sit with a group, you might be, but you might still need to join a group to talk to them. Then the next reason is why you will need to sit in the center of two columns because you will form groups. Here is the blackboard, where the blackboard is you can tell. So the group one will start from here, the first two row. And then there will be four groups as you count backwards. One, two. I just realized there are more seats. Okay, so I just realized there are nine rows in each column, which means we can have the first three row being in group one, okay? Then the rest it goes down as it should be. You can scoot a little bit, everyone. You can move in a little bit. There's also seats here. You can move in a little bit, yeah. Now in the center two column, it's hard to fall into a group. So those who just came in late. So just to be clear, the first three rows are group four, okay? You start the group five. Okay, group five, group six, and group, what, sorry? Five, six, seven, eight, sorry, wrong one. So eight, the seven, sorry, miscounted one. Six, and group five, okay? And so you guys will have to join across when the, you know, when the discussion is happening, because I know there are not enough seats, and there might be other reasons you don't want to sit with them because they're smelly. Okay, I know this is the hardest part of lecture, to sit with everyone so close to each other. Okay, let me just introduce myself quickly. When we talk about the larger structure, I'm Shirley Hill from Carnegie Mellon. I will be moving very soon to different parts of the world, but you can talk to me afterwards about this. I have a lot of materials borrowed from modern white for the larger structure series for summer school. And if you have any questions, feel free to ask me, but you'll have a lot of questions you will have to answer as part of the groups. That's why you need to start thinking. The first three rows will form group one, and the first three rows form group five. Then the rest is every two rows, okay? If you don't know which group you are in, let me know, okay? Everyone knows which group are they in? Okay, good. The lecturers and organizers, please do not help them with the questions, because that will be unfair. Are you group five? No, no. Okay, thank you. The lecture series outline are here, so this is the first lecture. It's probably the easiest, but I'll ask the hardest questions. You'll see why that's the case. We have the basic, quote-unquote, larger structure introduction, which includes two terms that I know it makes no sense right now, but it's bare and acoustic oscillation, the BAO, or the RSD, the Racial Space Distortions. And then the second lecture will be clean props by combining and joining things between larger structure and CMB, the Cosmetic Curve Background, which actually you learn already, but I will tell you a little bit more about what you can do with combining the two. And then what else can you do with the larger structure? Lecture three, that's not the first two lectures, but it's not covered. There's a little bit more fans and things that you probably haven't thought of before. And the last one is the new props of larger structure. It could be things like filaments and voice and clusters that you might have heard of before. And you've never heard of them, that's okay too. Okay, so we did that, the fun time part. We'll actually do the questions first to make people warm up to your own group. So hopefully you'll come back to see in similar group numbers the next lecture, so if you like the people, if you don't, you can move. But that sends a very strong message to your group member, okay? You have eight groups, you know where you are right now. So group one to four, group five to eight. The first three rows forms the first group one or group five, okay? Sorry, I miscounted one group, one row basically. So now one question, I need one. Find two pieces of paper within your group. Write down the hardest, stupid question and your group can come up within larger structure. The reason is I want you to know what is the question you think you should know but you don't. But within your group, you cannot come up with the answer. And write down in two pieces of paper the same info, your group number and the question. And you will know why I want two pieces of paper because one will go to me, the other one pass to I plus one, your group number plus one group. And it's periodic boundary conditions, so group A pass to group one, okay? Pass the other piece to me when you're finished. And you have to answer the question, of course. I'm so five minutes from now and so that I can get to lecture. All right, start. And please, if you move next door to talk to the people here. To the people here, does that make sense? So this is group two, you both, not group six, sorry. So you have to talk to the people across. I know you don't want to sit with them, you need to talk to them. Same thing here, thank you. Okay, we have one more minute. Start writing it down. If your group has finished, you can pass one of the two pieces of paper to me because I want to see the question too. All right, we have a winner. Group six. We have one question from group six. 20 seconds. All right, start bringing down the question. So only bring me one piece of that two pieces of paper you've written this on, right? They're the same question and the group number, okay? I want one of those two. Yes, exactly. So when you bring me that piece of paper, bring the other piece of paper to group number plus one, periodic boundary conditions, which means eight brings down back to one. Thank you. Start working on the question you get. You have five minutes to answer the question. The next group just brought you as a challenge. Thank you. I know you might hate your classmate, but if at this point you haven't passed the question to the next group, they have very little time to come up with the answer, okay? Where's group two, three, seven, and eight? Thank you. Write down your group number on it, okay? I'm still missing group two, seven, and eight. You have three minutes to answer the question. One more minute, guys. And yes, you're allowed to use the internet to help you answer the question. That's part of research. It should have the answers written somewhere on the piece of paper now. Just 10 more seconds, otherwise I don't need to lecture, which could be good sometimes. You don't want to bring down the answers? Actually, you might not need to bring down the answer. I actually need them to read out your answers, but you might need to come down at some point. Okay. Okay, we have a few struggling groups. Everyone's waiting for you guys. Peer pressure. So this is one lecture for you guys, is that deadlines sometimes cannot move for you. Especially grant application deadlines. We're still having a few people have an actual, a few groups haven't submitted the answers. Okay, actually I might just start reading the answers and the questions for the people, even if they haven't finished passing this down, okay? So the group one has a very interesting question. What is large scale? And surprisingly group eight also had the same question. So given the periodic boundary conditions, they actually cannot answer the group eight's question because it's the same question as theirs. Group two's answer to this is hundreds of megaparsec, where cosmological principle holds in the region where density perturbations are small enough for consistent perturbation treatment. Sounds reasonable to I think to all the lecturers. So you guys are actually really good. Okay, group two, what the question is, how can one tell the difference between gas and halo bias from a theoretical point of view, but haven't got the answer yet? No answers yet? Do you want to just come say it? You don't have to write down. Just stand up and say it, or you can use my mic. That's what happened when you're turning late to get to speak your own answer. So their question is how can one tell the difference between halo and galaxy bias from a theoretical point of view? So for the bias, we said as a submission of galaxy plus halo with their coefficients and for man body simulation, we can compute the halo bias and make some predictions for galaxy bias and trying to look them for an observation point of view. So the thing is the difference may be explained in terms of the smaller number of halos because smaller halos are no galaxies. So that can be one reason for that. So there are many ways to answer this question. What is the difference between galaxy and halo bias, right? From a theoretical point of view, I think Rafi actually is the right person to answer that question. But I wonder if galaxy bias with infinite orders, all the orders included, would that necessarily describe everything about a galaxy? So you're asking if I had all the endpoint correlation functions, would that completely specify the point process? And yes, it would. There are some density fields for which it wouldn't, but I think point process is it does. But we are rarely so lucky to be able to measure all of them. So usually halo bias is just, usually people just take like first order, maybe even second order for halo bias. So that doesn't include all the high order terms, but if you include all infinite high order, I guess, in principle, yes. Third group. This is the group I cannot read the question properly. Do you guys want to say what the question is? Paolo, do you mind helping them? The question is so hard to read by itself. It's a challenge. Yeah, it was a question about massive neutrinos. And the question was, because they free stream, and they surprised the matter power spectrum. But they would expect that if, and we say that if they are more massive, they suppress more the matter power spectrum. But I thought that if they are more massive, they would start free streaming later, and then suppress less the matter power spectrum. So yeah, maybe just very naive, and yeah, maybe even wrong. I don't know. That was the question. Does group 4 want to answer that question? We're not completely sure. We got the question right, but what we answered is that neutrinos themselves are massive, but they have really, really tiny mass. So for all practical purposes, even at our time, we still think they behave like radiation. So they just suppress the structure formation because of the radiative pressure. But I'm not sure if that's what the question asks or not. But that's a very good, very good guess, I would say. It still suppresses the structure formation. I'm actually going to show an animation at some point, maybe not this lecture, how different masses and neutrinos affect the correlation function and the power spectrum. So you'll see exactly what it does, which is a good way to officialize it. Good, perfect. All right, group 4. This is a very hard question. I don't think it's a larger structure question, so I'm not going to try to answer it. Does QFT quantum fluctuations hold up to pre-inflation energy density? Group 5, that's a hard question. I don't know the answer. You guys want to try to answer that? Thank you, Paolo. One second. Right here, right here. How we tried to answer this was trying to think of all the possible direct observations of QFT at different energy scales. We couldn't think of any direct test, any experiment that would reach the energy scales that theory predicts are at pre-inflation. So we said we don't have any proof to disprove or prove that QFT is valid. Good. Sounds like a good question. How about the other people? How about the lecturers? Do you guys feel that's the right answer? I mean, I don't actually know the answer. I didn't understand the question. Please. No, I didn't understand the question. Does QFT hold up at pre-inflation energy density? Pre-inflation energy density. Well, I would say that it is valid, quantum theory meaning GR as a quantum theory is valid up to energy scales over the M plank to the fourth. So it is much higher than inflation, which occurs at the much lower energy scales. Of course, at a certain point, you will exit the regime of value of effective theory. And now there is a... I totally agree. At what scales does the universe become isotropic and why? Group 6, do you want to answer that question? So our answer is above 100 megaparsec or of order 100 megaparsec. And for the why part, it's because both it's an empirical fact from observations and because the correlation functions for galaxies drop significantly at those scales. Very, very nice. Okay, Group 6. How does dark matter affect logical structure? That's a long answer. The answer is one full page, so... So we said in the early universe you have gravitational potential wells which formed due to quantum fluctuations or thermal fluctuations, and essentially your dark matter falls into the gravitational potential wells which kind of deepens them or stabilizes them. And then because now you have this deep gravitational potential well, your photons and barions can also kind of clump in the well. And then that... Because those are couple that creates your barion acoustic oscillations and blah, blah, blah. So now you've got this cold dark matter which is sitting in the well. If it's completely cold, then it just sits there and it can't move. And so now you've kind of got this stable well. If it was warm or it had some velocity then it would be able to stream out of the well and like a massive neutrino it could wash out the structure below some scale. Very good answer. I feel I don't have to teach anymore. Okay. The next question. Group 7 had that question. We have different structures in a larger structure like filaments, voids, or cosmology can different structures constrain other than bias. Group 8, are you ready to answer that question? Okay. Well, we think that first of all, it depends on the preservation of probes you are considering. So it depends on two-point angular correction function or cosmic shear or galaxy-galax lensing so you can constrain all the cosmological parameters with this. So it's not only a matter of the structures you're considering. So voids or filaments or clusters but also on the observational probes and then you can also constrain modified gravity theories and so the answer is a mixture of it depends on the observational probe and the structure you're considering. Very good answer. So you guys all did really great. I feel I don't have to lecture but given that Powell invited me here I have to do a little bit but let's give a round of applause for people who spoke and of course the people came up with the answers and the questions. Okay, so I realized this is a way to survey how well or how high the level is in the class here. So the next lecture will be a little tiny bit easier but I think you guys will benefit from just learning all the equations a little bit and then the next lecture will be a lot hotter just because I think you guys actually higher level than I expected, okay? So stop me at any point but I think today is a little easier than you guys would actually need. Alright, larger structure, the lecture one. This is a movie. Oh, you guys can't see it because of the light. Do you think we can turn off the light for like 30 seconds? Thank you, Powell. He's exercising a lot. Alright. So this is the larger structure of the universe from real data. If you're going out from the center of Earth, well, from Earth, every single galaxy is actually observed by Sloan Digital Sky Survey. All these images are real. These are actual galaxies. That's actual real. And what you're seeing when the red dots here is these red luminous galaxies that are basically red and dead old galaxies that's forming, the structure is start to see this cosmic web, this larger structure, these voids and this web-like structure which are filaments that you probably heard of before. For those who are wondering why is there only a certain area of the sky that's mapped with this structure, the big structure with all this fan-out structure. Do you guys have a guess why we only have certain parts of the universe mapped out like this? Louder? The Milky Way is one thing. There are more than one reasons, but that's a good reason. Observation time. Time? Yes, different parts. You can see different parts of the universe. And now you actually see the C and B cosmic background as you go out to the universe. This is proportional to the physical scale. And the little blue dots here are the quasars. These are basically supermassive black holes that are creating things and they're actually emitting quite strongly. So you can see what we've learned is the stuff... I'm going to concentrate on stuff in this center which actually maps to half the distances and you have already learned quite a bit about C and B. Okay? The lights on, please. Thank you. So this is the larger structure we'll be talking about today. All right? And as you say, it's very large scales, hundreds of megaparsecs. I hope you see everything else. So our lights for today's structure is quickly talking about dark energy standard rulers because I'm going to tell you one standard ruler in particular, which is the cosmic sound bearing acoustic oscillations, the theoretical issues, the modeling issues, and the prospects and conclusions. So this is based strongly on a modern wise lecture in, I believe, one of these conferences. I forgot which one, but I think it's Santa Fe Cosmology Summer School. We've probed dark energy field cosmology. This thing, you probably have seen this before. We basically see dark energy theories effect on the expansion of the universe because of that particular equation. H of C is basically as a function of rho of C for all of the different components. So if you don't know anything, you should know that the expansion universe is affected by the components inside because of basic physics, you know. And there are three different approaches, standard candles, standard rulers, and growth fluctuations. So I know you've heard from Barbara's talk about luminosity distances. Standard candles tells you about luminosity distances, which is an integral of H inverse 1. Standard rulers measure the angular diameter distance, which is also an integral of the extra minus 1 and extra C. You have growth fluctuations, which is crucial to test extra components versus modified gravity. So earlier people mentioned about modified gravity can be tested by foils and filaments. Do you guys want to mention how you might do that? I guess this grows back to group 7 or 8. I forgot which one. No? Yes? Okay, if you don't want to answer, it's okay. So foils basically are supposedly in regions. Galaxies in foils supposedly might behave differently in different density. So if it's in foils versus in cluster, the galaxy would experience different kind of force. That's one type of modified gravity theory. So you can, in principle, use things like foils or filaments to test modified gravity. In principle. I think they still work on-going, that type of situation. Okay? So that's one thing to look at growth structure, to test normal gravity versus modified gravity. All right. Standard rulers. So what is a standard ruler? That's actually really trivial. They just literally have a ruler that knows exactly what the size is. So by measuring the angle is subtended from U, like the theta, delta theta angle, they actually can tell how far that ruler is from you as a function of rest shifts. So if you can measure distance and rest shift, then you're actually in a process to be able to tell, using this follow equation, to tell the Hubble expansion of the universe. So that's basic idea of standard ruler. And I'll only talk about one particular standard ruler today. So ideal properties of standard ruler, you'll be start thinking, so what standard ruler would you like to have? You want to have competitive constraints of dark energy if you think that's important, but think about mapping the expansion of the universe. It could be for dark energy. It could be for other things. And if you want to map the expansion of the universe at about 1% level, then we'll actually get to equation of state about 10% level. You need to be able to calibrate the ruler accurately over a huge range of age of the universe, huge volume of the universe, and you want to make extra precise measurements of the ruler. And you're like, so what is the standard ruler? Where do we find this ruler, right? Individual cosmological objects might be never uniform enough. Using statistics of larger structure of matter and radiation might be something to do, because if we stick with early times and large scales, perturbative treatment, the stuff you've been doing of the universe will still be valid, and the calculations, analytical calculations will be under control, and that's why people would like to do large scales and things that are deal-willing with early times. And prefer length scales arise from physics of early universe is good and is imprinted on distribution of matter and radiation because you want to see them. So all these things together, so these are the references that if you're interested in going to the calculation, that's what you should look at. I'm not going to go through all the calculations because this is going to be very interesting and very hard to do it all in one lecture. So what is this standard ruler? I'm going to tell you one, I'm hoping that you might be able to come up with other ones. So this is the baryoncosic oscillations. It's the fluctuations from the cosmological background that you can see in one part in 10 to the 5, when the universe is 300,000 years old, that evolved to today is an order-unity fluctuations. You can see this large scale structure that we saw in the movie before, which is actual observations. This sound wave can be used as a standard ruler because dark energy changes is a parent size. Well, because it changes what it looks the subtender angle from you. Okay, so this is a very simple animation, but what it does is to tell you that if you have an initial fluctuation at the very beginning, so the universe is much hotter at that point, the pressure is coming out from the radiation pressure, the photons and electrons interacting with each other with inverse quantum scattering, and it drags everything along. So the photons push us out, radiation pressure pushes us out, it drags the electrons along, electrons drags the protons along because the electromagnetic attraction of each other, and so you can see that it goes out, but then at some point, the temperature of the universe has dropped enough that you do not see these photons electrons coupling anymore. These interactions between photons and electrons depend on the temperature. So once the temperature is cold enough, you actually would have the photons free stream away, becomes a CMB that you study that Raphael has hidden, I don't know where he is now, and you will have this ring around the initial perturbation, because all the electrons and the protons still there, the photons gone, so what do you do? You have this proton's electrons ring, and it imprints on the early universe, early universe matter distribution, and it evolves forward. This is all at, you know, 300,000 years old of the universe, and it evolves forward to something we can observe today. So I mean we do this again, but this is a picture of all the different fluctuations, so it's not just one particular perturbation, all of the fluctuations. So when I talk about statistics of larger structure, we're not talking about one galaxy, we're talking about millions of galaxies, and each galaxy will have a tiny bit extra probability of finding another galaxy at about 150 megaparsec away. That is a standard ruler. I'll repeat this in a different way very soon with more equations, so, this is the first time, this is the cartoon version. Okay, so BAO, the bangles of oscillation, possibly this is the cleanest probe of dark energy. Well, you say, well, C and B is also really clean, but actually it's the same physics, right? So it's actually really clean. BAO is possibly the cleanest probe of dark energy because it measures at low redshift. So at the very low redshift, you want to be able to probe the distances and versus redshift because dark energy is in principle kicks in somewhat at low redshift. We're working on eight large scales so we can possibly over all the messy nonlinear physics because nonlinearity stuff is hard. Its physics are determined at early, early times when the C and B is done and the perturbative treatment is valid and under control at that time. Okay, because everything is small perturbation. I think one of the question was like, you know, when is it okay to call something, call the universe as so tropic and homogenous? That's because the perturbation is so small at that time. Okay, great question again. You guys are like ready for a group discussion quickly. It's only for five minutes. Can you come up with other types of standard candles? Nobody's answering a question right away. We can have your group start working again. Write down your group number and answer on a piece of paper and pass a piece of paper. I'll have a hard deadline of five minutes because we won't be able to talk very much otherwise. Okay, other types of standard candle other than supernova because I know you know that one. So this is actually a hard research question. Unless you've read the paper, you might not know what I'm talking about. But there are two possibilities I know of. Five minutes, hard deadline, okay? At 12, I need the answers down here. You're allowed to use archive. Or randomly select a group to present the answer and I haven't figured out what the random method is yet. All right, I might randomly pick a group to decide to present the answers. Get ready, okay? So what I'm going to do is to count up the number of people on this column at mod 8 and see which one is the group number. Okay, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17. 17 mod 8. What's the number? I think it's group 1. Do you guys want to present your answer? You don't have to write it down. Just say it. Are you guys ready? All right, guys. R is listen to the group 1 answers. You can disagree. Okay, cool. We figured that Cephites, Quasars and Pulsars would also be standard candles. It's one of the answers. And applause to the group who just figured this out on their own. Any other suggestions? Pulsars, Cephites are there. And galaxy relations like Cormandy, Faber-Jackson, we can use that. Relations like Cormandy relation, for Cormandy relation for elliptical galaxies and Faber-Jackson relation for elliptical galaxy or elliptical plane sort of thing we can use to get the parameters in parameter space. So that's great. Applause again for also doing this. So the point is that you need a standard brightness, basically. So however you want to do it, there's other new ways to do this and even these ways that you suggest that people haven't really used it so much, like the Quasars who just talked about this, basically. Okay, so that's great. You have one more suggestion. That's another new paper that people just wrote about using. Actually not new. The gravity wave as a standard candle was written, I think, a few years ago, like five years ago. But that's a great suggestion. That's a paper-worthy suggestion. That's great. You guys are really good. Okay, good. So I can continue with the simpler cartoon after such a hard question, okay? You guys have seen this cartoon before. So I'm going to describe this a little bit with a little bit more equations. At early times, the universe was hot, dense, and ionized. Photons that mattered tightly couple of years were Thomson scattering. If you do not know Thomson scattering, we have to go back to textbook back in the days. Short mean-free path allows fluid approximation. So that's easy, because once you use fluid, everything is a little bit more understood because it's quite traditional. Initial fluctuations in density and gravitational potential drives acoustic wave in the fluid. So here's the fluid that I'm talking about. The M-effective is basically a combination between the baryons and the radiation and the matter. And then you have F as a function of potential. So that's basically driving this acoustic wave. It shows up as the C and B, actually, which you could solve the first equation. So if you were an undergrad, I would have asked you to solve the first equation to give the second answer, basically, because it's a harmonic wave that you can probably solve from the first equation. But all of you probably have seen this before. A simple SXM, basically. Simple harmonic oscillator. So you can solve this pretty easily, but this is a cartoon picture, okay? Granted, you should do the C and B for exploration properly. But that gives us most of the idea. The first compression, this is a C and B map. C and B, and I saw Tropic Power. This is a CL that you probably have seen in Raphael's lectures. The first one, compression is at... So CS is a sound suite. That's the last horizon. And then you can see a density maximum, and the velocity is now at the first compression. And then you have the velocity maximum when it's actually at the dip right there. And you can actually all write this all out because of the simple harmonic wave function that you actually just solved. The acoustic scale is set by the sound horizon at the last gathering. So that is the S equals to CS times TLS. It's the last gathering surface time times the sound speed at that point. That's the sound horizon. People keep telling you this is a sound horizon, and you're like, what is that? And the sound horizon more carefully is basically this particular integral that goes...it depends on the apocryan and I say recombination. So it integrates to the recombination time. It depends on the expansion of the universe because you can tell that it has as a function of 1 over h of c on the first equation. And it also cares about the barrier to photon ratio through the sound speed. So there are actually quite a lot of stuff in that particular integral. And this sound horizon actually would dictate something very important for the bearing acoustic oscillations, which will come up soon. So not coincidentally, the sound horizon is extremely well determined by the structure of the acoustic peak of the CMB. Planck basically has nailed this now. This number originally was third year WMF third year data, and right now Planck has it completely nicely nailed that. And I'm sure the future generations of CMB experiments will make it even even more precise. And once you have that, the bearing oscillations are pretty well calibrated to the level that we need. Since bearings only contribute 15% of the total matter density, what you're looking at is that the total gravitational potential is affected by the acoustic oscillations with scales set by S that we just talked about. And at least a small oscillation is the matter power spectrum, the P of K. So you've seen this before with the correlation function that you guys have seen many times with the early universe. This is a late universe matter power spectrum. But this is suppressed by the bearing on the total matter ratio, which is just 15% we're talking about. That's why everything is a lot damped. And you see it from here. This is the root mean square fluctuations. On top is radiation, below is the matter. And they both acoustic oscillations. The one on top is the CMB. The one below is the matter at late time, which is what we see right now. So you can see this little wiggly form. And you're like, okay, what does that really mean? Because we don't really see the matter. What you see is the galaxies or anything that's bright that emits something that you actually have to receive electromagnetic radiation from. So we usually talk about galaxy bias that people actually mentioned in question before. You observe the galaxy power spectrum, which will be some kind of function of the matter power spectrum depending on the prescription of the bias that you're thinking about. Depending on how you say map, even 21 cm that you might have heard of to the matter power spectrum, question. Very good. So this is actually the next question. You'll see it first, and there's a question for this. A damped almost harmonic sequence of the wiggles in the power spectrum of the mass perturbation amplitude about 10%. If you divide out the gross trend. And that's the question I wanted people to think about. The matter and the radiation oscillations are not in phase. Why is that? And the phase shift depends on K. So homework, why is that? We will talk about it in the next lecture, but I suspect you guys will figure it out before then. Let me just flip back that slide. You see the shifts and how it depends on K. So that's something that I would like to have you think about it a little bit more. Why is there a shift and why is that shift depends on the frequency? So that's the homework. And there's a subtle shift in the oscillations with K due to the fact the universe is expanding. So that part is easy, but how does it work? And become more matter dominated. Once the universe expand and more matter domination, there's a subtle shift. And the duration of the coupling means the photon can diffuse out also of the overdensities smaller than a certain scale leading to a damping and oscillation at small scales. So you can see why it dims out at the small scales. Back to that plot. Okay, regardless the spectrum is calculable and S can be inferred from the data. And these features are frozen into the mass power spectrum providing a length scale that can be measured as a function of C. Because you will see this nice oscillation and you can see exactly what those scales should be by very early universe physics simple perturbative treatment. All right, this is quite fast, but the homework is hard. Dark energy or early universe field awareness. So key to computing as this town horizon is the ability to model the C and B anisotropy. And that's not easy. We want to be sure we don't mistake our error in modeling basically early universe physics for property of dark energy. So what could go wrong with early universe physics, right? Do we understand recombination properly? Do people know what recombination is? I hope you have reached that in the C and B lecture, yeah. Misestimating CS, the sound speed, or the barion to photon ratio. Misestimating the Hubble expansion at very, very early universe. Maybe you miss the radiation components or maybe you miss some neutrino mass. Strange thermal history, decaying stuff. Isocurvature perturbations that you just heard about. So all that stuff could in principle affect what we know of S, okay? And it seems like the future measurements of C and B anisotropies like C and B S4, I don't know if you guys talked about the stage four experiment of C and B a little bit, not so much. But basically it's the next stage two stages from Planck. So we have like act and SPT, there's a fans act and SPT S4, SPT something. SPT 3G, that's the next stage. And then there will be C and B S4, that's something people are planning on right now to happen in the time span that you will become faculty at that point. And this will constrain S so well that even all these different things that we don't know about would not be a problem. So that's why I think it's really cool to learn about larger structure, because C and B will be so good at determining sand horizon that will calibrate the standard ruler so so so well, it will be very useful to use it to determine the expansion of the universe. Okay, B here in configuration space, do you guys know what configuration space is? Yes, no, kind of? Yes? Okay. If you don't talk to those people, they'd be not in hands. Okay. Configuration space, basically sort of instead of 4A space, you do it like in real space, but why don't you use the word real space, because what you include is something like Russia space distortion is actually measured in Russia space, something that we observe, not something that is in real space that is the God's view of there's God. The configuration space picture offers some very important insights here, and that's what I'm going to talk about a little bit. And you'll offer something that will need to understand nonlinearities and bias. People measure bias before, we're talking about nonlinearities, but you're like, okay, but I thought BAO is very clean, we don't need to worry about this. Yes, but there's always a little bit we need to worry about. A harmonic, so in configuration space, what does the BAO look like? Well, I kind of gave it out here, because basically if you have a harmonic sequence in 4A space, you have a delta function in real space, right? For those who have been doing this FFT in the head for free, okay? Well, but this is very similar, we have a harmonic sequence, and we actually now will have something basically peaky, but it's not entirely a delta function. The shift in frequency and the diffusion actually dims out and broadens the feature. This is the acoustic feature in configuration space, plotting 10 to the 2 times the correlation function, versus the distances on the x-axis. The acoustic feature is at about 100 MPH with a width of about 10 MPH. It's a silk scale. Okay, so this is a little bit cartoon picture again. We have started with the baryons and the photons and the mass profile. And you start with single perturbation, the plasma is totally uniform with excess of matter in the origin. High pressure drives the gas plus the photon fluid towards very, very, very high speed. I never actually understood it was so high, the speed of light more or less. That's a really fast gas plasma. It drives it out. Initially both photons and baryons move outward together, the one that we just talked about because of the Thomson scattering. The radius of the shell move at over half the speed of light. That's something I myself didn't understand until I did the calculation that it's actually really fast. And then this expansion continues for 10 to 5 years. That's a very long time, actually at such a high speed. And then after 10 to 5 years, the universe has cooled enough that the protons capture the electron to form neutral hydrogen. This decouples the photons from the baryons because they cannot interact with the electrons anymore. The former quickly free streamed away, leaving the baryon peak stalled. As you can see there, the photons is going further. You'll see in the next part. The photons continue to stream away while the baryons having lost the mode of pressure remain in place. That's the acoustic wave you're talking about. You can see how the matter and the photons behave very differently at the 2D level. That's basically the plasma wave that we're talking about. You have questions? We can plot the dark matter fairly easily. It actually kind of follows where the protons and electrons, but it kind of lacks a little bit. Exactly. I have, don't forget, what I'm showing here, I did not show the central peak. There's a central peak I deliberately did not show because it gets a little confusing, but then you also have the central peak, which is where the dark matter and all this stuff is, and then you have a little bit of blip outside. That's the blip I'm showing. Cool. Features of baryon oscillations. We have firm predictions with models that have some baryons. You need to have baryons to have baryon acoustic oscillation. That's something you need to know. Positions once the physical matter and baryon densities are known and calibrated fairly well by the C and B oscillations are very sharp, and that's why it's useful because other features with power spectrum are very smooth, so it's very hard to fit things. An internal cross-track can be done. That's something you should think about. Why is there internal cross-track? The angular diameter distance should also be integral of H inverse of C. Why do you have both of them? How do you measure both of them? Let's write it down for a second homework question. Why do you get both D of A and H of C from BAO? Unless someone has the answer? Nope. That's a homework question. Since we have D of C, which is the distances for several rush shifts, you can check for easy things like spatial flatness. You can also tie the low C distance indicators, like the supernova to high C ones, which is the C and B, all together. That's pretty cool stuff. What are we waiting for? What can we do? Say that again. What is the dispersion relation between... That's a good question. I don't know the answer off the top of my head, but I can calculate it for you. What are we waiting for? We need to find A, a trace of mass density view, and compute the two-point correlation function. Do we want to locate the feature, which is this little bump in the integration space, and we want to measure delta theta, which is the subtended angle, and delta C, subtended by the sound horizon, a variety of rush shifts. We want to compare this value to the high rush shift ones, at basically a thousand, to get D of A, which is the angular diameter distance and the Hubble parameter. You can do all these other cool stuff like cosmology, and you're like, okay, this is hard. I've heard about all the physics. What are the possible problems you can come up with? Give yourself five minutes. I think you have the answers, at least some of the answers, with possible problems of bain-cousin oscillations. Because to tell you all the good things, what are the bad things? Talk to your group member, five minutes. Okay, so you actually all have really great problems for the BAO, some of them like rush of space distortions, which is the peculiar philosophies that a lot of people, you guys and some of them talked about the volume of the universe is finite. Well, finite as we can observe, actually. So we don't have that many BAOs you can fit in, so the signal to noise could be low. The other problems that were mentioned, for example, the zoom cosmology to compute the distances before you calculate the correlation function. Also, you have the zoom cosmology before you can calculate the BAO. All great ones. I still miss a few, and the foreground effects from stars and stuff like that. So you guys did great, and I'll quickly go through a few problems in the last couple of minutes that you probably have talked about. Listened and come up already. So just quickly go through them. Survey too small so people actually mentioned this earlier. Finally, technically possible is pretty recent. One of my major contribution is actually doing it for BOSS. Another prediction verified. This is 2005, and we weren't even planning to do BAO. This is not my work. This is Daniel Einstein doing the first detection using low-reshift galaxies. This little red galaxies that red dots you saw early on in the video. He used those little tiny red dots, basically to do the first bearing because it oscillates. It's a tiny, tiny peak right there. And the different lines basically shows different variants to radiation ratio. So different curves right up there. And you're like, wow, this is a very tiny blip that we're trying to measure. And those pesky details, we measure nonlinear galaxy power spectrum. Could be not galaxy. Could be quasars. Could be 21 centimeter in ratio space. So the peculiar velocity comes in. And we don't have a turnkey method to go from measure galaxy positions or whatever position that is to sound horizon constraints because it's hard to propagate systematics, how to do tradeoff studies, how to investigate sample selection effects, like the foreground stuff that we mentioned. So BIO service also always in sample variance dominated limits and can afford to take a large hit due to theoretical systematics and uncertainties. So there are a bunch of them. I'm not going to go through all of them, but people have used numerical simulations and people have done this a while back. Even in 1999, they actually simulated the dark matter BAO back then with tiny number of particles back then. And then now we have a very large number of particles but our understanding of galaxy formation actually has also dramatically increased but we still don't know how to paint the galaxies on top of the dark matter. Exactly 100%. So numbers versus insights we try to learn from the simulations what range of behaviors do we see what kind of galaxy prescription works best how do we parameterize this effect. Can we gain an analytical understanding of these issues or the shortcuts to describe all these things, right? Complexities. There is Lagrangian displacement distribution for those who are interested go to read Eisenstein's story in white 2007 and can we push product into non-linear region. People mentioned reconstruction earlier one of these problems is to try to remove the non-linearities. So let me just leave you a couple interesting questions. This is the non-linearities how it smears the peak. We have analytical model here with a linear theory with N body. And you can see that the N body simulations matches quite well with analytical model but then when what I'm going to talk about something about reconstruction is a very simple idea. This is a correlation function at Russia 49. It's a very sharp peak but at Russia 0.3 it becomes really really not sharp, right? Much much more smoothed out. So sort of this is homework question you don't have time here. What are the ways you imagine doing reconstruction? So I know there's one way to do it that everyone's doing it right now. If you can come up with other improvements to it, that would be greatest part of the homework. The other question is how the fun homework problem today. This is the actual big one. This is really big. So don't do everything. Calculate the correlation function of gas in the universe. What is to guess how to do it? A. How would you calculate it? The final hard part is similarly 100 gas. It's not more than that because if you're too many I think you crash your laptop with the right matter power spectrum how do you do that? And calculate the correlation function from it. So that would be the hardest homework problem I think at least for tomorrow. If you are able to in your group, if you are able to come up with all the answers for different problems within a group, I think that's fine. Fine for me. And I will just draw on you know random people tomorrow to tell us what they done. Okay? Thank you very much.