 Okay, we can start. So we have a 15 minutes later, and try to sit in those two columns, okay? Hello everyone, welcome back to the second lecture of the larger structure. Thank you for those who actually already move to the center two columns. So if you're a student, please do that because then we'll actually have to make you talk to each other, which is hopefully not as hard as the first time we do this. I see you can tell which one are the first groups, second group, third group, fourth group, group five to eight all the way. Hopefully when more people come in, there will be more people for certain of the groups, otherwise it will be smaller in number of people in some of the groups. The group numbers, as you can tell us like this, I will be calling randomly in terms of group numbers for some of the answers or the questions I asked you in the last lecture. I hope some people had time to do this or otherwise it will be a little bit embarrassing. I find peer pressure to be one of the best driver to work sometimes. Okay, let's start a little bit because the beginning would just be about last time. So okay, the lecture series, last time we have basic introduction of larger structure to bearing because of the oscillation of register space distortions. You haven't had much of register space distortions, but we'll talk about it today. Today we'll be talking about clean probes across creating larger structure and CMB. Would you like to move to the central two columns? We're having people that lacking group members down here for example. And as you can tell the fun time require you to sit in the middle two columns and form eight groups right here. Yep, everyone's looking at their own group members. Okay, good. So you know who you are and where you are and what group number you are. If done this before, so I know we can do this again. So homework questions from last time. We have three big questions. I wonder if people have time to think about this a little bit. The first question is the phase shifts between CMB and larger structure. The second question is how would you do reconstruction? The third question is calculate the correlation function of galaxies and how? So I think I'll quickly just make you guys familiarize with each other and the group members. Can each group send down one answer on their own? So each group will have a piece of paper right on your group number and the best answer you can have and do it in five minutes. Cause I'm assuming you already did this. You just need to figure out who has the best answer within your group. All right, we have five minutes to do that within each groups. So okay, let's do that now. 1140, we want those pieces of paper down here. You already have the questions from before. Hi everyone. So I realized there's enough questions on the questions. I might try to at least do one of the question with you together, okay? I happen also happen to have those slides. So keep writing the answers, but I just wanted to say that I think the correlation function question was a little hard. So I would like to clarify and also the reconstruction question, okay? So let me just give you the answer, or at least the partial answer to correlation function. What is the correlation function? So in bearing acoustic oscillation, we usually calculate something called a correlation function, and how we look at it is using something very simple. Let's look at what's the correlation function of the population during the day. There's a much easier question than what the heck is bearing acoustic oscillations. So let's look at what is correlation function first. So we consider a normal or typical American family by my opinions, probably not correct. For those who don't know what that is, it's probably good for you. And moment that goes to work, this is a very typical family quote, quote, the kids and past day at home and nearby school in Gaussian distribution. So now the next question I ask you is, well, moment that on average commutes about 20 miles, so actually Americans commute 22 minutes on average, so you can calculate how far they commute, say all of them, say all American family, the parents commute 20 miles only and they stop. They don't commute more or less. And the kids' day and past day and nearby school and home in Gaussian distribution, what is the correlation function of population during the day? So you need to start thinking, what is the correlation function, right? So statistical measure of basically if I have one person here, what's the excess probability of having another person x distance away? Okay, so that is the correlation function. So in this case, for every single person, say you imagine you're American for a second, you'll be about 20 miles away from whoever family member you might be. So if you're in college, that doesn't work at all, obviously. But say if you're in high school, that's likely that you'll be 20 miles each away from your parents. If you're parents, you're probably 20 miles away from your kids. So on average, what you will do is that you'll go to every single person, calculate the number of person x distance away from you, and make a histogram. And stack all of the histogram for every single person. That is the correlation function of the population during the day. So now, let me back up one step and ask you the question. This is the easier question for the groups. What is the population correlation function during the day? Don't think about galaxies. Think about normal, everyday things. They only commute 20 miles away. Everyone only commutes 20 miles. So they take the bus or the bike, whatever. They get to work in 20 miles, and they stop. And the kids and pets stay at home in a Gaussian distribution. So what happens? So let's ask yourself this question first. Within the group members, don't think about cosmology for a second. Just think normal day life, okay? Give yourself like two, three minutes to ask yourself what that answer should be, okay? All right, start that. Okay, I'm starting to hear correct answers already from multiple groups. So that means some groups are starting to be ready. Do someone want to volunteer, the answers? Some brave ones. Do I need to call random number? Okay, someone do 173 mod eight, please, for me. I don't know what that number is. 173 mod eight, anyone? I have to do it on the internet. What was that? Huh? Yeah, I'm just doing it in my head, but I rather don't do it. But you guys know the answer, I hope. I'm looking at the group and they're not looking at me, so. Who is the, did you want to volunteer? I feel it's hunger game, except there's no death. Yes, hold on. For being brave, you get to use the microphone. So I believe we would have some power at the zero distance because there are some members that are staying at home, but then we would also have one at 20 miles, which should be of higher power because there are more pairs that would be on 20 miles distance than those that are on zero. So there is some truth in it, and it's quite good. I mean, there's any other suggestion of supplemental information? The peak at zero will be larger than that 20. Do you want to say why? Because there are more kids at zero distance than parents are just two, so they'll just go out. So they're both kind of correct, but not exactly, but they're actually combining, it's pretty close. So remember that there's, people always cluster at nearby distances, right now you're at a cluster, basically you're like in a galaxy because you have a lot of people altogether. So even if you're not at home or you're not the kids, you can still be at the company, you'll have a lot of people around you. So that center, zero peak, is very similar to the initial perturbation that you saw with the movie yesterday, where you have this dark matter and baryons and photons all starting from that central peak. So that's actually what the central distribution is. And a lot of it is so similar to the fact that the parents can only go X distance away. So the galaxies, in this case, it looks like they're going an X distance away, but there was pieces of this situation where the photon pressure was driving the gas out. Well, the photon pressure was driving everything out basically because it's inverse constant scattering with the electrons. Remember dragging electrons along and the electrons taking the protons along with it and so it drags everything out. At a certain point it stops. So that's that little peak that you were seeing. It's very similar to here except you imagine I guess the car stopped having gas at 20 miles. So that's very similar analogy, but not exactly. So you guys all get really similar answer, but remember, the gas is originally actually clustered to start with. So you are very likely to be in a distribution with a lot of other people to start with, okay? So that's something to remember. So yes, a bump in 20 miles, it drops dramatically. I did not put plot to drop on top because that's actually hard to block because it should be very dramatic. The scaling is not relevant because it depends on the number of people you assume. That's very similar to the bearing acoustic oscillation in the little peak right there. That's the little bump, right? Tiny, tiny peak at about 100 mega parts of an edge. And it's the huge drop that you see, okay? So at least I think I clarified one thing which is correlation function. We'll go back to reconstruction later on in today's lecture. So hopefully that will clear up what reconstruction is and the phase shifts between the CMB and the larger structure. I think that's something you guys might want to think a little bit more about. So write it down on your paper now. What's the shape phase shift? How does it cause the phase shift between the CMB and larger structure? Or about Raphael later before he falls asleep? I'm kidding. Okay, let's do the lecture today. Okay, so these are the three questions we answered. What's the correlation function? But now you can think about how to calculate it yourself. We will talk about reconstruction later on in this lecture today. So you will pay attention to that hopefully. And hopefully we answer the phase shifts between the CMB and larger structure at some point. This is more like a theory question, okay? Okay, so this is what we'll be talking about today is combining larger structure and CMB to join forces against dark forces. Well, like dark energy and dark matter. And what is the challenge here? I mean, people have been talking about this for a while. This is the last decade. We've been experiencing a good increase in amounts of data and precision, especially in cosmological background and larger structure. And we still don't know the answer to what caused accelerated expansion of the universe. Or we don't know whether Einstein's theory of gravity is correct at the larger scales. And if GR is correct, then what is dark energy? Because then you have to explain either one or the other. Either GR is incorrect or dark energy. It's something that we have to understand it somehow, I hope. So these are the challenges, I think that still face us now, which is quite surprising. As a cosmologist, there's still the same questions about a decade ago. So I would suggest that we wanna do multiple probes, not just one probe, because it actually will help a lot when you have multiple directions going into it. You want it to be based on clean physics. You want the system acts under control. We'll talk about what system acts are. You hear way too much about it. And they're highly applicable to future survey because you don't wanna do something that nobody is gonna do anything related to it for like next 50 years. So when you develop some new probe, make sure it's applicable at some level, right? So multiple clean probes, Raphael has talked about the Cosmic Earth Background. It's obviously very clean. Physics, early universe physics. It's leftover radiation after the Big Bang. You know all that. It's mostly Gaussian. The statistical properties can be described more or less 100% by the two-point correlation function because it's so Gaussian. And we know that it's so Gaussian to the level that we don't expect any, well, the clean map, not the one with all the foregrounds. It's very much described by the two-point statistics. How about the other probe that we just talked about the larger structure? We have traces of the density field that could be early type galsies. They're red star-forming galsies that are blue. Their quasars is supermassive black holes are creading. And there's neutral hydrogen traced by things like limon-apple forests that you might have heard of before. But for those who have never heard of what limon-apple forest is, it's basically the shadow casted by neutral hydrogen on the light coming from the supermassive black holes. Do you want me to rerun that again? So supermassive black holes on one side, observer on the other side, the light's coming in, basically the shadows casted by the neutral hydrogen on the spectrum of the quasar, okay? So that's limon-apple forest. For 21 centimeter, you probably heard a little bit more about it because you had the reanalyzation lectures. But that also traces the larger structure, the neutral hydrogen itself. And you might come up with other traces of the larger structure, so keep thinking. Physics are clean on relatively large scales. That's actually a really good thing because that means we can do analytical or at least simple calculations to predict what we should expect to see. So here is something that's the larger structure, but it's not just the galaxy points here. So we had a question yesterday actually about what we can do with larger structure other than the typical galaxies and stuff like that. And I wanna show you this is a video of going through all of the galaxies in Sloan from low ratio of like 0.1, actually yeah, 0.105, all the way to 0.7. All the little dots are real galaxies observed in this RI deck, right, ascension declination plane. This is real data. The colors here show something called the filaments. Filamentary structures that are basically ridges in the density field in the universe. The blue or the color actually tells you how uncertain the filaments are. So if it's blue, it's really certain. If it's red, it's really uncertain. So in between is kind of in between. So I'll start the movie. So you can see that they evolve pretty significantly and it depends strongly on how many galaxies are there at every single ratio range, right. Some of it is cosmological, how many galaxies are there. Some of it is really observational like how it targets which galaxies will get a spectrum. So every single galaxy here has a spectrum. And you can see that it changes quite a bit. Yes, you have a question. I think I will try to give you a microphone. Can't hear you. Okay, go. They don't understand your question. Say that again. Radiation? No, no. I need to give you a microphone. I don't understand. Radiation, I was talking about. The RI. Variation in the structure. Variation, okay. Go ahead. I heard radiation five. No, no. So it's like during the rush, if you go, if the rush shape increases with the rush shape, there is a variation in the structure of the filaments. Yeah, so somewhere they are less, somewhere they are more dense. And why is that? Because of the merger of the galaxy or some other things? So I mean, we were just saying part of it is the number density of galaxies we observe. Part of it was just the growth of structure throughout time, right. Because if you look at a simulation that you see everything like you have the aka gods view, you actually see the structure becomes more and more nonlinear as you go to low rush shifts. What I'm showing you is going from low rush shift to high rush shift. Let me finish. At low rush shift you just simply have more galaxies and more clusters. You actually see this. This is a high rush shift. Even though that we have way less galaxies, you can still see that the clustering is a lot less strong at high rush shift. At low rush shift it's much stronger usually. Yeah, but in this movie you can see around rush shift of 0.2 something, there is much less structure over there. But at the earlier rush shift there is more. Right, that's actually observational. So at some point we don't actually see those types of galaxies because we decided not to look at them. And we can actually tell exactly what galaxies we want to see. You can hold on to the mic. Okay, any other questions? Do you want to pass the mic up there? Is there a reason for the large hole, that specific hole in that area for the, you know? Like here? Yeah. So this is actually where we did not observe very much. So it's just the few galaxies there are actually not from the observation that we recently made but from the old observations because brighter galaxies was already made. We call it the legacy galaxies. So back in like 2002 we already observed it. This is like new observations. But that's very good observation. You actually see that hole before, see? This is actually consistently not there. Just observingly we don't actually see that, okay? Cool, very good. So multiple clean probes, we have radiation with density. We draw a matrix, that's pretty easy. Many correlations can be done right between the radiation and the density view. You can have auto-correlation of temperature-temperature. So that gives you the C and B auto-correlations that you have talked about. You've heard about from Raphael. And then you have the density-density auto-correlations which is the larger structure that you've all heard about the clustering, the correlation function, the barylchocic oscillation. That all came from the density-density auto-correlation. But you can also do cross-correlations like density and radiation cross-correlations. So that's something I will mention today and I'll give you one example for the many, many examples what you could do and what physics you can learn from these cross-correlations between density and temperature. And that also relates to Raphael's lectures about secondary anisotropies that you mentioned yesterday. I think someone asked the question whether, you know, what do we learn from temperature or the aftereplank? Do we learn something more? And then I think Raphael suggests that there is secondary anisotropies that we can learn a lot more. And a lot of the secondary anisotropies power can also be enhanced quite dramatically by using the cross-correlations between the density field and the radiation field because the density field is actually imprinting on the temperature field that you observe. Okay. Is your hand up for question or? Okay. You're just really tired. Okay, so the key is to identify clean probes and create the right sample and keep the systematic under control to make all these exercises useful for cosmology. Okay, so this is the angular clustering. You've seen it many times. I hope at this point you know this is a temperature field angular power spectrum and the fluctuation power on the y-axis and x-axis is L which is oscillations per 360 degree. We know have an enormous precision power on the universe if we know it's a flat universe, the omega baron H square, omega C H square is completely well determined to this extremely high level. I think this is actually even better now by a little bit. It's clean physics systemized under control so we believe that, that when we don't have to prove to you because Raphael already taught you everything you need to know. The partial structure is pretty simple also. It has the contents and the properties of the universe actually affects the phase space distribution of the density field. So to simply put x, y, z in all the velocities in different directions are functions of these following parameters, for example. The dark energy equation of state or the time dependence of the dark energy equation of state, how much matter there is omega matters of function of redshift, expansion of the universe H of C and you have, say, some of the neutrino masses, someone asked about the neutrino properties and how it affects the larger structure yesterday, for example, and gravitational constants, of course. So you have all these things that will affect basically the phase space distribution of the universe. So if you can extract the information from the phase space distribution of the larger structure, you learn about the stuff that is a function of, basically. Okay, so that's the idea of larger structure, the basic ones. There are many papers to read about this, but we talked about Barencus oscillation as one thing yesterday. We'll touch on something called the Russia space distortions today. Let me just show you how neutrino masses affect the clustering of the density field. On the left-hand side, there's no neutrinos. Some of the neutrino masses is zero. On the right-hand side, it's one EV and you can see how the clustering has changed quite a bit. The plot of color is density, gram per centimeter cube. So something physical that you can actually grasp and how you see neutrinos actually change things quite dramatically, how things cluster, okay? So that's how I will look at it and then I will do something called, we'll calculate the clustering of the density field and you're like, okay, what is clustering? So clustering is synonymous to the correlation function we just talked about. So the correlation function, we said there's a top peak in the middle and then it drops and it has a little bump at x distance away, whatever that distance is. That is only the monopole. We also consider something called the quadrupole later on and I wanna ask you guys, unless you already know, why do we consider quadrupole also? If there's a volunteer, we don't have to do five minutes. If we don't, we have to do five minutes to think about what is the monopole and quadrupole of clustering. Any volunteers? If no volunteers, that means it's worth the discussion. Is that, oh, the volunteer, do you wanna pass the mic down? It's a lot of physical activities to be a lecturer here. We have the two dimensional, two point correlation function thing that Shirley talked about before. So that's a function of the position, distance and the angle. So monopole is the angle average thing. You just average over all the angles. You integrate. So that's monopole. Quadrupole is when you take another moment of that. You integrate over angles but you use the second order Legendre polynomial. You multiply the two dimensional, two point correlation function with the second order Legendre polynomial and you do the integration. So essentially both these things are the angle average things of two dimensional, two point correlation functions which in itself is a measure of the over density. Very good Siddharth. But he's a little, what's that called? He's a little a fanatic in this situation because his thesis is on precious places distortions. So he knows this stuff. Okay, thank you. So why do we need to calculate monopole and quadrupole? That's the next question. Why do we need to look at anything other than the angular average? Any suggestions? Maybe not sit up this time because he knows the answer. Yes, do you want to pass the mic up there? Someone's talking. Who wants to speak? Yeah. I think someone else raised their hands before. Oh, nobody? So if you talk once today, you're not talking a second time. Okay, this is democracy. So it's his first research and break the anisotropy. It means isotropy of the signal. So that's why we need to consider higher order terms. Exactly. Exactly, there's anisotropy in the field that we're observing and that's because of something called racial space distortions and something you actually mentioned yesterday. A lot of groups talk about peculiar velocities and that affects what we observe in the field and it gives you anisotropy. So that's the part that why we need to look at a quadrupole. Okay, all right, let's keep going. We don't need five minutes now. So that is the clustering of the density of racial space and how it changes as a function of the neutrino masses. It's an animation so it might actually make people wake up a little bit. The model of quadrupole both changes as a function of the sum of neutrino masses, as you can see. So that's how you can tell, if you calculate the clustering of the universe, what you can tell about the neutrino masses. The answer is to yesterday's question in a more quantitative way, okay? Yes. Yep, that's a very good question. That's very good. I actually do not know exactly what the bentrack model is. I believe it's Planck 2015, and then he goes from there and just increases some of the neutrino masses. So that was actually made by my student, Sherda Balaam, who's graduating, yay. Okay, good. Good question. The next one is how the dark energy equation of stage will change the clustering of the density field, which has the monopole and the quadrupole again. So we were just talking about how dark energy is so important. And so why we do, we actually wanna look at that in the larger structure, but you can see how it's changing the clustering in both the monopole and the quadrupole. Mind you that the quadrupole scale is a lot smaller than the monopole scale. So even though the changes in monopole looks a lot less, it's actually quite a lot. We don't usually use just the amplitude of the correlation function to calculate what's the effect on the dark energy equation of states because we actually think that there's some issues in terms of calculating exactly up and down what's an amplitude because of something called galaxy bias because we observe only the galaxy correlation function and we don't know exactly how to relate that to the dark matter field exactly. So we usually use just the shifts of this VAO peak, which I cannot point to you here, but I can show you here. So right here, this is the VAO peak that we always talked about. Notice this is multiplied by r square, so everything is a little scaled differently. And this is shifted as you change the expansion of universe. That's the standard ruler that we talked about yesterday. Okay? All right. Have I lost everyone yet? You have a question. Do you want to yell really loud or do you want to pass the mic? That's a really good question. I actually haven't thought about this carefully in terms of why they shift opposite ways. When I saw it, it said I would look at the power spectrum, which is also only angle average. And that one is easy to see how it shifts up and down, but I haven't thought about the quadrupole why it shifts the opposite. Anyone has any suggestions? I actually haven't thought about this question, but I will think about it and tell you tomorrow. That's a good question. Yep. Anyone else? Okay. You want to use the mic? Could you please play this once more? Could you please play this once again? Okay. So for those who actually gain intuition from animation like this, Mestatmark has a whole webpage about what the power spectrum looks like, but power spectrum for all the varying cosmological parameters. So that's also where I gain the intuition, but it doesn't have quadrupole. So that's something that's about the velocities that I'm not a hundred percent sure. Next thing. So we have the contents of the properties universe affects the phase space distribution of the universe. X, Y, C, V, X, V, Y, V, C. So for the X, Y, C, it mostly affects the baryoncosic oscillation as you mentioned, we talked about yesterday. For the V, X, V, Y, V, C, that's what affects the registry distortions. And the effect is mostly coming in from the something called F. I will tell you what F is coming up very quickly. Baryoncosic oscillation, just to remind you guys what is the phase shift that we just talked about? The radiation and the matter, you can see the bumps actually shifted from each other. So that's what we would suggest asking the first slides of today. And it was talked about yesterday. This is a BO peak again. Each initial over density has excess pressure leading to outward going wave at recombination. This sandwich deposited basically all the gas in a spherical shell 500 million light years, which is 110 megaparsec from the original location. So that's something you've seen yesterday. Hopefully now it really gets to you. The over density in one location implies basically an increasing density. So this is artist's conception. You have a bunch of overdensity in the middle and then you have a ring around it. You have excess overdensity at 110 megaparsec away, but it's a very, very small statistical signal because what it is, this is an actual data set. You see, there's no ring around it. It's really hard. It's a very statistical measurement. We need a very large volume of sky survey to actually see and detect it. So that's actual data set at point two, which is actually way more cluster than the stuff we're doing at a higher shift. So how do we actually say first thing, how do we do berencosic oscillations? You've seen this a little bit before, but I wanna see what you actually would do. I'll show you how cosmologists actually work. So you wanna create a clean sample. So what are the potential issues in creating a clean sample for berencosic oscillations? As a volunteer, we don't have to go in for discussion. Otherwise, we're going for discussion, for potential. Just to create the gaseous sample. You already answered one, so you're not allowed to answer twice. Sorry. Anything else? All right, I guess we'll have to have a discussion. Okay, let's make it four minutes. I know you guys probably know the answers. All right, let's go. Well, I'll call on a group randomly this time. There's no volunteer allowed. So think about you creating a sample for the berencosic oscillations. There's a bunch of galaxies. So what are you gonna do with a bunch of galaxies? Okay, one GPC space. Oh, the galaxies are very solid, but I see. Then you make that sample more realistic. You have a big light bulb. Then you have a sample of a galaxy. Then you create a random catalog of galaxies. Then you put the convolution function in it. How you do this? Observation. Observation? Clean sample. Clean sample. Clear this. How do you do this? It's a large scale, I would say. Observing it. Large scale. Large scale. Large angle. Large angle. Large scale. A few is bigger than that. So you have a flat sky approximation. Then you have a variation on the sky. There are bright galaxies. Okay, assume you have x, y, z of a bunch of galaxies in the universe. What could go wrong when you calculate the correlation function? Think of it this way. We have done more observations. We've done sharpness. We've done a little bit like this. That's the only way we can do that. The galaxies will be distributed at large scale. Yeah, but that is the point. Yeah, but I don't know if they're large scale or not. So we have, we have rushes. So this is in data. It's not in simulations. Another question that's very good. We have all the rush shifts. We have the positions. But they are correct. Right, right. Because we need a big, we need a big angular scale. Yes. That is there. Short noise. Because you have a discrete sample. You don't, you don't have a continuous sample because of that there is an inner and short noise. To reduce that short noise, we need to... We need more number and more large scale. Large scale. More number and large scale. That is the reason. So you can volunteer. You can still. Yeah. Any of, any of... Any of the... But is that in the... Like short noise? No, no, just to... We need to write to lower the... Just to make sure that we have large volumes, more, much bigger than the AOR scale. To lower down the short noise, we need to sample more source. I don't think I'm gonna... I don't think I'm gonna... Caller. Caller. Yeah. So it's like to have... So like I said, told him, you need a bigger and bigger volume to lower down the cost of the variance. And you need more and more sample to lower down the short noise. Then you have a discrete space distortion effect and the other effect you're talking about. Okay, everyone. I think wrap up the discussion. I actually heard many, many good answers already. But I like to call out group eights because they have the best answers, I think, so far. Do you wanna pass the mic to the group eight? Do you wanna explain to them what you think? So, well, besides red sheet space distortion, that is something that we can model. We have also to consider all the systematics effects. So when you compute the angular correction function, you usually create a random map. So a map where all the points are randomly distributed. And in order to use this, you have to model all the systematics. So the geometry mask of your survey, for instance, or if you have some difference in sensitivity or whatever. And this has to be estimated and included in the random map. And the other problem? Well, you can also have stellar contamination in the sample or other problems like systematics maps. When you have the survey, you can have different air masks or seeing in different regions that can introduce also systematics. Yeah, so that's exactly what I was looking for. But there are all the other issues that you mentioned, like photometric rushes, possible lensing affecting the number density, and I think there are multiple people talking about similar systematics, actually. That's really good. I'm just gonna show you what I wrote down here. It's the variations of targeting sample caused by differences in targeting algorithm. That's something nobody actually mentioned. It's just human cost issues. The change of targeting data, which changes over time. The spatial pattern of missing spectroscopic data points. Sometimes you actually miss spectroscopic data points because, for example, in Sloan, you cannot put two spectrum very close to each other simply because you cannot put two fiber physically very close to each other. There are optical fibers that link, basically take the lights from the telescope to the camera. Then you actually miss spectroscopic data points because if there's a galaxy closer than, say, 52 arc seconds to each other, you cannot observe both of them. Change is a galaxy density due to observational systematics, stuff that they really just nailed. And here is one example about stars. So number of galaxy targets as a function of the distance away from stars of different brightness. So this is a very funny fact that people didn't really realize until we looked at this. It's that number of galaxies divided by number of average number of galaxies on the y-axis. On the x-axis is the angular distance from stars. If you have a very bright star in the middle, you actually would not see the background galaxy x-distance away very well. So this is basically telling you that if your projection distance is very close to a star, you're very unlikely to be targeted just because our imaging software is not very good. So that actually happened in Sloan. Very big effect. So stars are crazy. Good. Reconstruction. So that goes back to the second question that we asked yesterday. Reconstruction is a way to move the galaxies back in time to increase the signal-to-noise of the barycosic oscillation measurement. So this is the plot we showed yesterday. I know as many plots you've seen yesterday. We have the spatial clustering, the correlation function on the y-axis. The x-axis is the distances. At Russia 49, the peak is very sharp. Resuming into this tiny peak here is the black line. And then at Russia 0.3, you see that it's already very flat. So it decreases the signal-to-noise of this pao peak, which we really want to measure because it's a cool standard ruler that we talked about yesterday. So people can do something called the reconstruction that brings it back to Russia 0.3 and make it really sharp. The red line and the magenta line is a slightly different way to do reconstruction. So I want to ask you is that what are the potential problems of the current reconstruction scheme since the homework problem is how do you do reconstruction? I'm going to give you one example of how to do this. What you do is that you know there's a lot of galaxies everywhere. You can reconstruct a density field automatically by some kind of smoothing or whatever filtering you want. Then the next thing you do is to calculate the potential at every single point you care about. And once you have the potential field, you will be able to calculate the displacement of the velocity field that each galaxy should move at point x. And once you have that, you can move the galaxies backwards one step in time. So that's how the current algorithm is doing to remove the nonlinearities, to bring basically from the blue line here, the blue dash line to the red lines. So that's what the current algorithm is. So let me just take one step and ask, is there any question about the reconstruction algorithm? Yes, you're allowed to ask questions. What is the systematic noise you're talking about exactly? So let me generalize the question a little bit. Let me just repeat this question. He said, basically how do you deal with the noise of the density field that you observe when you do the reconstruction? So that's one great example of a problem in reconstruction is that you don't have the exact potential of the universe where you only have approximation and an estimated potential of the universe. That's a good problem. Yes. Any other questions? Otherwise, now think of problems of this reconstruction algorithm. What are we assuming here when we do this reconstruction algorithm? Think of it this way. What do we need to know to get the potential field from a galaxy field? So how do you do that? How do you get some potential to the velocities? Is that something we need to do? Or what assumptions are we assuming? Is GR assumed if modified graph is correct? What do you do? So talk for five minutes, okay? Talk to each other. Okay, I've heard multiple good answers already. So let's just randomly pick a group to answer that question. Or is there any volunteers already? Someone has to mic. Anyone wants to volunteer or we just pick random group? Oh, the group can. Okay, you have a volunteer. Let's pass the mic down. This is like reality show. Thanks. So one thing we were considering is sort of like a density of galaxies in the space. And so if you are looking at say, in your example Z equals three and you are observing this, you have this observed density of galaxies and now you're gonna simulate back in time. Well, an obvious assumption would be you're assuming no galaxies formed in between Z equals three and Z equals 49. So maybe you could also observe, so you do this simulation, but also maybe you can do some other forms of observation actually at Z equals 49, but that might be out of our limits. But then you could compare your simulation and this observation, and that would give you understanding of how you know how like going backwards in time actually works. So that's very interesting. Similar to what one of my students working on, but really actually moving backwards in time by using physics equations. Trying to involve everything that's including all the physics. But the current algorithm is much simpler than that. It's a linear perturbation theory. So the problems are slightly different, but what you suggest is actually a much more interesting way to do reconstruction. Okay, any other suggestions of the current problems? You guys both talk, did you talk today? You have, have you talked? No, no, but the one behind. Okay, you can answer. So that's a very good suggestion. Do you want to pass the mic over? Thank you. For two. So a few things. So a few things. You have to assume a model for your galaxy bias in order to move from your galaxy over density field to your matter of a density field. You, during reconstruction you have to smooth over the density field, which so your reconstruction is very much dependent on your smoothing scale and function that you use. And I think the model dependency on GR may come in, does it come in through the kind of growth rate that you assumed? Yeah, it comes in through basically the cosmology assume. Yeah. You assume a cosmology assuming a model. And I guess also redshift space is an issue as well, but obviously some reconstructions now say they deal with that in some ways. Okay, very good. Also hint, hint, he actually works on reconstruction. So don't feel bad if you don't get all of the points, but that's really good. I heard multiple groups coming up with very similar interesting answers. So perfect. Thank you. Yep, we actually only check a few things in BOSS. It's the choice of cosmological parameters that includes whether it's GR or modified gravity, doesn't matter. The density field smoothing links that he just mentioned. And understanding galaxy bias, how do you map from observed galaxies to the underlying dark matter density field? Thus the potential. So that's very hard because we just have no idea. So all of this turns out did not matter so much in BOSS because our position is still quite low. I mean, even though it's a 1% measurement. So let's go forward. So after reconstruction, you can see the peak actually sharpened. It wasn't just a joke entirely. We moved the galaxy's backwards in time to increase the signal to noise of the measurements. So the new ways improve the reconstruction and that's one way to do it. I'm not gonna talk about exactly how we do it, but basically we iterate the original method until you basically hit a point and you're not moving the stuff around. So that's one way to do it. If you want to know about new ways to do it, I mean, the students actually suggest the very similar things that we're looking at. My students, you've been looking at something similar and different. We also have to test the fitting methods of the BAO, because you actually go from this little bump to a distance scale, right? A distance scale, which is the standard ruler distance scale. So how do you do that? That's actually something fairly difficult and you want to make sure you're not dependent on galaxy bias. You do not depend on what metapile spectrum you assume. You do not depend on the cosmological parameters you assume. So all these things have to come in and that's actually also quite hard. The cluster analysis of the BAO's galaxy sample has produced a pretty good one. It's actually the best late-time acoustic peak. What's the early-time acoustic peak? Anyone? Exactly, so you're not completely asleep yet. The CME is the best early-time acoustic peak measurements. The peak locations measure to 1% at the high-reshift sample and 2.1% at the low-reshift sample. Why do we have worse error bars at low-reshift? Gestions? Well, there's so many. Go ahead. That's one interesting way. So if you assume dark energy, then you want to observe a certain area. But there's more reason than this. Well, you talked once before. Anyone who hasn't talked today? Please. Well, they feel gases, but that was not exactly the reason. But that's a good guess. Yes, another one. Yes. That's another good reason, but not because of that we have a smaller worse error bars. Yes. Because basically they're more non-linear at low-reshift. That's what you're saying. Yes, go ahead. Non-linear growth, another good reason. So you guys have many good reasons. One more. One more that I was hoping for. Yes, it's about. I can't hear you. Exactly, this is non-linear growth also again. So one more. Why is the low-reshift having worse error bars? Usually low-reshift is easier. Yes. Effects from reconstruction. It's true, but it's not the answer I'm asking for. It's really cool. Great. So that relates back to the reconstruction question. But that's non-nearity also. Good. But not this one. One more. Okay, I feel like I'm... Say that again. Exactly. So there are more volume at high-reshift universe. So you have more sample of this big ring or big sphere of BAO peak. At low-reshift you have smaller volume. So you have less BAO peaks that you can sample. That's why you have smaller error bars. So that's the major reason. But all the other reasons you mentioned actually are very, very good reasons. Like the non-linearities. You have trouble doing BAO reconstruction a little bit, but all that stuff comes in. But the major reason is they're just not as many BAO peaks, BAO rings in that volume of the universe. Good. So this question actually tripped multiple faculty members. So don't feel bad about this. Taking into account the observation of the anisotropy, we can also improve our constraint. So if you only look at, remember the monopole? You actually get the gray contour. But if you actually look at the model and the quadrupole, you get the orange contour. So it actually matters that you look at anisotropy and the rations phase distortions effect into calculating the distance scales for the BAO. All right, I think this is actually a really good time to stop. We play very strong constraint on cosmological parameters because you actually observe distance versus rush shift. And you can use that to constrain how fast the universe expands, how much as I spend it over time. And so you can place constraint on the dark energy equation of state and the time dependence of dark energy equation of state right there. We have very different answers, for example, from the supernova plus Planck. So keep stay up in tune. So I'm actually gonna just stop around here. We have talked about beringkissing oscillation as a clean probe and systemized under control. So I'll be actually going into rush shift phase distortions if we had had more time. But since we're actually about to do lunch, I'll do that next lecture. And let me just fast forward to a homework problem. Just one, don't be scared. Just one this time. Okay. You have about like 20 more slides we haven't gone through. Homework problem. What are other interesting probes of the universe using a combination of CNB and larger structure? Describe one probe per person who I will have a lot of PhD thesis. Whether and say whether it's clean and has the systemized under control. Yeah, he's very smart. He took a picture of the homework problem. Apparently I need to email this slide to someone to upload the slide. So it's better if you just write it down right now. Because I don't think it will be online by tonight. Okay, so one more probe about combining LSS and large and CNB and describe the probe and why it is clean or relatively clean or the systemized is under control. Just take a picture. You have your phone. I know that people have been texting forever. All right, thank you everyone. That's it for today. Have a good lunch.