 Okay. Maybe we won't be waiting for everyone who's coming back from the coffee. Um, this is the last lecture for a larger structure. Um, the plan of this lecture is to A, finish up the discussion of the EEG that I introduced earlier in the last lecture. So for people who haven't seen the EEG, you probably haven't either slept through the first lecture or, you know, you haven't heard about it. But hopefully this will give you a little bit of background so that this lecture is not completely wasted. Um, also for those who missed the last lecture, you should talk to your friends who have the notes from the last lecture, who, um, can show you what you missed a little bit at least as we go through, because we will refer a little bit back to the last lecture. So, sorry about that. But the first lecture is always very hard to get to. I mean, the morning lecture is always very hard to get to. So let me start with that. After we finish EEG, we'll take a little break to ask you some fun questions. And those questions, it will be not the similar types of questions we have before, it will be more astrophysical order of a magnitude estimation question. So when we, when we went through grad school, one of the last exam we have to take before we get our PhD candidacy, it's a half an hour of order of magnitude estimation. And they could be anything. So I will try to see if you guys can do that too, because that will be pretty fun. And then after we finish that, I will start doing a completely new probe, a larger structure called Lamanava Forest, that illustrates all the different properties you've heard about throughout, you know, the whole three other lectures we talked about. So including, you know, barynchusic oscillations a little bit, how do you do that with this completely new probe? We'll talk about that probes. And how do you understand, say, primordial on Gaussianities, looking at large scale power differences in larger structure using Lamanava Forest also? So that's also kind of new. And then we'll look forward to other experiments of larger structure that's in the future. So it gives you a sense of what, you know, your generation might see in the future. Okay, so that's today's outline. I didn't have a slide on it because it's sort of jumbling off everything. Okay, so let's go back to a little bit to Yeezy. So we talked about this before in last lecture, but I just want to remind people what that is. It combines gravitational lensing, the philosophy view from register space distortions and the clustering of the density view to probe basically the metric potentials. So lensing probes both of the metric potentials, the metric written down here, the phi and psi, while the philosophy is only sensitive to one of them. So that's why you can break some degeneracies when you do that. So this is a quick review for people who have actually been to the first lecture. It's independent of bias, this Yeezy. And you can see that because they basically, the term on top is proportional to bias because it's galaxy cross-querying with the gravitational lensing. Term below, there's the philosophy is probe by register space distortions, beta is proportional to f of a bias. For those who've seen this before, it's fairly easy from this morning. And then the galaxy clustering proportional bias square, they all cancel out. And these are the dependence of EG on different gravity models. So this is Einstein's theory of gravity as a function of scale or distance versus time, f of our model and chameleon model. You see the time, well, the scale dependence very strongly. And of course, there will be time dependence because of that. And the first detection actually ruled out something called a Teffas model. And at that point, Teffas was actually a fireball model. So it's a pretty interesting probe, but it hasn't been done again until 2015. We actually had a discussion why that's the case. But that's basically because it requires both good imaging. So you can do a galaxy lensing and spectroscopy measurements on a fairly large area of the sky because you need to get the retrospective distortion measurement, which requires the spectroscopy in kind of high number density in a fairly large volume. Because you remember in retrospective distortion, our discussion we all did today is linear theory. So all that stuff that we just learned today that came down to this equation, and thus this one, is only valid in large scales. So you actually can only derive the constraints on F or F over bias, basically this parameter beta. If you assume this model, when you assume this model, it's only working in large scales. So you need large area of spectroscopy also. So this is the 14 pages of stuff that you might not have seen this morning if you haven't got here this morning, okay? So that was hard. So we decided to replace it by CMB lensing, it's a galaxy lensing. There's many good things about it. So we've discussed a few of those. One of them is dramatically increases the range and number of traces we can use. Basically anything in front of CMB is a lens. So you basically can use anything as a lens as long as you can do retrospective distortions with it. CMB lensing is quite a lot cleaner because there's no astrophysical system acts like intrinsic alignment. There are other problems with CMB lensing but it's very different. So at least complementary. They're well known source plane because we know where CMB is. We don't have to worry about what's the ratio of distribution of the sources for the weak lensing, the gravitational lensing for our galaxies. So what we did, so we actually did this, not just wrote the theory paper. One of the authors is actually in the audience. You can ask her. I don't know where she is. But anyway, so we have the Planck lensing map. We use the boss retrospective distortion measurements and we use the boss galaxy clustering. So you see the three plots. The lensing map is on top. This is actually, I think the potential map and then the galaxy clustering and the retrospective distortion measurements. So you first, this is actually how you do this. You calculate the angular power spectrum of the galaxy on the y axis is angular clustering on the x axis is the L that you've seen many times in CMB. But this is, I think might be the first time we've seen it in angular power spectrum of larger structure. And the model and the data looks actually very, very similar. This is using something called a minimum variance quadratic estimator for people interested in data analysis. This is a way to do it that will create the minimum variance, which is very interesting. And then we compute basically this is the galaxy lensing cross correlations and we use something called a pseudo CO estimator for people who haven't heard of a pseudo CO estimator before it'll be good to look at what the hell that is. And it has a slight deviation from the prediction on large scales. So let me just move this a little bit for you to see clearer. The prediction that we had shown before is the same model as this one. So we say exactly the same model that fits the low reshift galaxy angular power spectrum but it does not fit the angular clustering of galaxy C and B lensing cross correlation by quite a bit actually. There's about two ish sigma, 2.5 ish sigma below what we see. So we wonder what's going on actually here. We've talked too many things. I'll show you what we have done or what we have to do to test all these possibilities but similar deficit actually seen in other cross correlations in other experiments. So we might be okay. Maybe something this is real but maybe not necessarily extra galactic. We don't know yet. So growth of structure measurements. That's the one we talked about before the monopole and the quadruple. If you have not, if you don't remember already what we just talked about this morning go back to your notes. That's the monopole and the quadruple you've seen before and combining all of that. We also want to look at the system X related to galaxy sample. So what are the system X? We talked about this before such as the stars that we talked about that will affect how galaxy density appears around bright stars. There are things about the seeing of the sky might affect the number of galaxies you see, all that stuff. We're in there, we put all of them in there and find that they don't actually change the signal at all for the EEG measurements. So that's a good thing. Very different. The small differences is very comforting at least from the galaxy survey side. And then we do something kind of fun. We try to see if there's any CMB lensing systematics and look at cross correlations with the foregrounds also. So the first thing we test is to take the data release one subtracted by the data release two of Planck and cross correlated with the CMAS galaxy sample and see if there's any residual effect that's coming from the change of the CMB lensing map over different data release consistent of zero. The next thing we try is that we try to take this is a map 545 gigahertz that's more like dust related. You've probably heard it from Raphael before and cross correlated with the difference map between the Planck lensing and don't see anything. And then we try many other things. So EB minus V is a galactic dust map basically. Compact sources at 143 gigahertz we have actually many other tests and then to test with the SC also. So none of it has a significant contribution to possibly contaminate our EG signal. So here's the results. We're just gonna show you a little bit what we have done. We have the EG on the Y axis and the X axis is the L parameter again. The previous larger scale measurements this is the point that we have shown. Smaller scale is on the right hand side larger scales on the left hand side. The GR theory will show up as a blue line and the measurement will be green dots, green crosses. So that's what we got. You can see that we have very, very large scale measurements of EG which is really good because that's when we can interpret things easily. The small scale things we have difficulty interpreting because you remember what you did the calculation earlier Kaiser theory for example is only valid in large scales and so is true for the galaxy, galaxy clustering. We can only do it properly more or less in large ish scales. So this is probing gravity bias free at the larger scales, you know, scales are actually 150 megaparsec large. So that's good because we actually can use all of this signal to make some conclusions. So that was good. And then we say, okay, so what do we do with this? There is a slight tension with the larger scales. We actually still don't know what that's going on. We're still trying to figure out what could be the case. We're hopefully using the new lensing map from Plong to see whether that clears up something. But if you have any ideas of why there's about 2.5 signal deviation from GR, let me know because that's something kind of exciting or could be very wrong, but at least we know it's happening. So hopefully looking forward, now combining these probes you have seen that both probes has dramatically increased the power over the last decade. So it's nice to start thinking about combining them together. So when I say dramatically increase the power what does that mean? This is approximate experimental sensitivity over the year. I know some of you might be born in year 2000, I suspect. Well, maybe not. But it's dropped exponentially, basically over time. Yes. That's a good question. Where would Bicep2 fit on this map? I just don't know what to do with Bicep2. This stage two. So, Plong-ish. Yeah, Plong-ish. Is that stage three in between Plong and CNBS4? So that's happening right now, I found that. I mean, you work on it, so you don't need to ask me. And then, number of spectra also increased dramatically over the years. Okay, some of you might have been born the first, you know, 1995 and around that era, right? So you can see that how things are shot up. This is a lot, lot plot. This is a lot plot, it's a lot linear plot. That's pretty cool. So I would like to encourage you to start thinking about combining these things and individually, you know, looking at them individually, to looking at that matrix and start to think what to do with them. Now I'll stop here for fun question time because these are the questions that I want you to try and see if you can do it. For orders of magnitude estimation. So I know you have not had an exoplanet discussion, but that's why the first question might be fun. How close would you need to be to detect a Jupiter analog in a Jovian orbit around a solar type star? I will post the results online after. And the second question is a little longer. I should have very long answer for this one. It's a dark matter discussion, which you have had lectures. So I think some of this might be fairly easy. Suppose a weakly interacting mass of particle has a certain mass, a certain cross section when it's not relativistic. So what temperature does this annihilation freeze out in the early universe? So try to answer the next three questions. Well, give yourself like 10, 15 minutes to pick one of the questions and work on it. I think the second question is more, it's a little bit more complex. The first question a little easier. So if you can work with people around you, that will be great. Because I know there's not enough people for some of the groups. So give yourself 10 minutes. And I will post the answers later, okay? Okay, everyone. I just wanna quickly show some steps for the second question, because it's quite fun. And I think since you had a dark matter lecture, you should be able to do that. I've heard correct answers already on the first question. So I figure I don't have to show you guys. But basically I'm working in a very simple unit. So you'll see an H bar and K all equals to one. And once you do that, you probably wanna think about the freeze out temperature by looking at this equation. So I've seen that equation earlier from someone. So that's good. You have a right direction already. And implying a bunch of this. So this is not that hard. Because once you have the right equation, everything is not so bad. And just to give you a sense what you would do. Oh, let me try that. This might be much harder than you think. Much better? Freeze out temperature. If someone gets something close to this, I see similar equations. I don't know how well you get to the answer. I've seen people with the right equations, that's for sure. How many people has got to the second question of the second question? I'll just show the first part. I will post the answers to the second and the third part of the question later on to the lecture program website. So it should be fine for everyone to look at it themselves. After maybe, you know, after you can see this one, you can probably work on the second and third easier too. Because it gives you a sense of what you're assuming and what equation you should look at. Okay? All right, this is just to give you a taste of how you would approach it if you were me. Back to lecture, that's not as well. I think it's fun, but it's not the same type of fun. Okay, this is the original larger structure for lecture because we actually had to just finish larger structure three. So this is a population density map of Japan. And I'll be asking you a question, which is what can be a trace of the Japanese population if I cannot do the census of Japan? Okay, so if I cannot do a census of the Japanese population, what's the next best thing it would do? Suggestions. Do you want to mine, can you yell? Lights is good, yeah, very good point. Especially if Japan is a very well-developed country, so it's a good one. And another one, something you all have on yourself. Cell phones, yes. Any other type of stuff? Basically, a trace of Japanese population can be volcanoes even. Apparently, volcanoes correlate positively with the population density, which shocked me. I will think it's anti-correlated, but it's actually positively correlated. Yucatos is something you wear after you bath in Japan if a few have been to Japan, or Pokemon posters when it's popular. Okay, so that's actually a really interesting thing because you realize that it's not obvious that these will trace the density of Japan, but they do. And so we can use something called a limon, I hope for us to trace a larger structure. This is my Pokemon for now. I know you might be too young to know what Pokemon is, I'm sorry. So how do you find the equivalent of Pokemon for a dark matter at high-reshift, right? At low-reshift, you can use normal telescopes to look at bright stuff like galaxies, quasars, stuff that emits light. At high-reshift, it's a little easier, especially in a rush of larger than two, so we're gonna do that today. So we're gonna try to do something which is explaining to you something a new cosmological probe of larger structure, and how does it, you know, what can you do with it? And so some of this you already learned, but this is really applying what you've learned for the last three lectures on something that's not a normal galaxy, not a normal point source in the sky. Introduction, you know all that. But basically we have a motivation because observation of how gas clusters, CMB distance supernova, and gravity plus observing movements of local galaxies tells you there's this wrong percentages right now because Planck has changed those numbers, and what happened at the beginning universe is also unknown. And also what happened at the beginning universe, like something people might have talked about at FNL, I think at the inflation lecture, he hinted many times that we can use that, use larger structure to tell you what FNL local is, especially from just normal clustering measurements that you actually learned over the time of last three lectures. And if you can measure FNL to different numbers, you can actually prove whether it's canonical inflation, high order derivatives, some of them are FNL not local, like other shapes or triangle, and ghost inflation, curvature models, all that stuff. So I'll tell you some new pro, which is the limon hour forest. So we have a bunch of quasars at about redshift two to three to four to five sometimes if you're lucky. And if you take a quasar spectrum on the left hand side and you have a telescope on the right hand side, and you pass it through a bunch of basically H1, hydrogen. This is a simulation of gas that I just put in the middle. What does it do? You have the emission lines of the quasar, which is normal, the emission lines on the top, and you have one, if you have an absorbing cloud close by, you actually see an absorption. And you have many, many absorbing clouds, or you can think of it a field of absorption, then you can see many, many, many dips. So that is the limon hour forest. It's the shadows, this is more romantic way to say the shadow casted by neutral hydrogen on the light coming from supermassive black holes. So that's, I think the most romantic way I can describe limon hour forest. But really technically it's just absorption by neutral hydrogen. This is a real limon hour forest on the lower left corner, right down there. This is a real data set, completely normal, nothing like spectacular, but just a normal quasar spectrum. All these emission lines is expected. You use this to find the ratio of the quasar, and then you see this limon hour line of the quasar itself, and this is limon hour forest, left word of it. So what does that mean? So that's the limon hour line of that quasar. This is where the quasar's sitting. But if you go to the next limon hour forest, what it means is that you actually have lights coming from this quasar, I guess, absorbed by a neutral hydrogen blob in front of that quasar. So that's the neutral hydrogen blob, the yellow dots. And you have more of them because you have many, many neutral hydrogen blobs casting this shadow, this little dips, the absorptions. Going further, further, further. It's basically a field that's more similar to a CMB temperature field in some sense than a normal galaxy clustering or galaxy something, or quasar, because these are not points. These are really a field of neutral hydrogen, okay? Or even the 21 centimeter actually, it's much more closer to that. And if you have many, many quasars, say they're all in the same red shift, where the blue dots are, and you're at the line of sight, looking outward, you'll see that there's many, many larger structure that you're probing using neutral hydrogen, okay? So this is limon hour forest. Any question? Because this is a pretty cool concept. This is using basically the noise, the depth and absorption of a spectrum to probe all the stuff that's basically absorbing it. Okay. So you can do a lot of stuff with it. Baryonucleosic oscillation, you've seen this before, but how do we do that? We know this, we know that baryonucleosic oscillations is fluctuation from CMB that grown into order unity fluctuation today. And we've seen the family guy probably only remember this from a lecture after two years, and it becomes the baryonucleosic oscillation peaks for the gaseous correlation function. So we know that you can do it in photometrically. So people who do photometric surveys can do it with baryonucleosic oscillations too. And I think DES should be able to do it very well, very soon. This is spectroscopic, much easier because we don't smear out, we don't smear all the rush shift. So the position of the gaseous is exact on the radio direction. If you have a photometric survey, the position of the gaseous is not exact. So it just smears it out. So the position is not as accurately determined. It's a little harder to do baryonucleotometric survey. So what happens when you use malign amount of force, right? I talked about photometrically, we talked about spectroscopically. Now we talk about using the noise, there's little dips in the spectrum. So another way to do this. So we try to simulate this, actually we're the first one who simulated it. We put a bunch of lines of sight through this simulation box. What's this simulation box? This is the old cosmology with a huge number of particles, a pretty big box because this is at rush of two inches, it's all really big distances. Fairly good, well gridded so that we can resolve small-ish scales. We're assuming something called the fluctuating computers and approximation which basically said the optical depth is a function of density. So that's the second to last equation. And you can calculate the flux which is basically proportional to, this is normal, flux is exponential minus up to the power of minus tau which is the optical depth. So now you see a very nonlinear transformation from delta which is the over density that you're very used to see. From all the equation you just saw today, the delta S, the delta R, like all that stuff is first taken a power, then you take an exponential again. It's a little interesting. And then we get skewers of neutral hydrogen. I'm glad you guys are not hungry anymore because you only get skewers of kebab here. But these are neutral hydrogen clouds instead of whatever the meat that is on it. So we take the correlation function of these skewers. Remember this, nobody has done it at this point when we were doing this. We were like, okay, what do we do with these skewers of neutral hydrogen which will be imprinted on the spectrum of quasars. The first thing we did is I would take a correlation function of this flux for low resolution box divided by the high resolution box. And we realized that we cannot go much, much worse if you change the resolution too much. If it gets a lot worse, then you might actually start imprinting some scale dependence there. You don't want to introduce a BAO peak basically, no matter what you do. So you want to make sure the resolution of your simulation is enough that it doesn't change where the BAO peak might be. So the first check. No off your scale dependence, that's good. So that is the correlation function. What we get from taking the correlation function of the skewers, that's what we get. Nobby actually expected this because we kind of said, okay, we're taking a nonlinear transformation of the over density field, bringing it back to a flux field and then trying to do coarse correlation of the flux field. So this is a pretty nonlinear situation here. And we realized that we can still do bearing acoustic oscillation with it. At 2009, Nobby has done it before. And we were quite surprised. We were like, okay, we must be doing something right sometimes. The real space correlation function is the one in the red dots. The rational space correlation function, which is the one we could measure, is different. As you can see, it's actually high. It has enhanced power. If you look at your notes, you have enhanced power because of the velocity field in the universe. Remember that this one plus F mu square term, that's where it came from. So that's why it has the extra power with the blue dots. And you can scale with the matter correlation function. So that's good. You can actually link what this looks like to the matter correlation function. Remember, we did a nonlinear transformation in between. So it wasn't necessarily expected. And we have rational space distortions, stuff that you actually learned just this morning about the squashing and about the squashing on the large scales and the squeezing on this very small scale, this finger of God effect. And so we look back at the anisotropic correlation function. Remember, you've seen these squashing plots before. So now we want to understand how Lyman alpha four's correlation function looks like in not just real space, but also rational space. We start with the matter field, which is on the left-hand side. You see the BAO feature. And then we transform it to flux, which is a nonlinear transformation already, twice actually. You take an exponent, you take the power to get exponentials. And then we go to rational space correlation function. This is all simulated. There's noise. You can see that. On the matter field, this is the stuff we understand, stuff that we actually just did the discussion earlier. You can prove it with the Kaiser theory. You can do all the nonlinear perturbation theory, all that stuff. This is on the left-hand side. We understand this part. The flux field, we don't know so much, but surprisingly they look similar. So we're very happy when they look similar. We're like, okay, there's something we can do. We can model it. Because it's a completely new probe. We don't know what it is. So flux traces matter quite well. Even when we include the rational space distortions, mind you, even though the color scheme is the same, the amplitude is completely different here. So you cannot actually predict from the matter what it looks like entirely without some interesting scaling. So we took this, which is the cross correlations between the flux and the density field divided by the square root of the two auto correlation ratios. That looks very flat. No scale dependence. That's good. So we don't wanna destroy the BO peak. And it seems like that's something we could actually try to do because they trace each other quite well, which was surprising. So how should we deal with this rational space distortions? What would you do if you were me? So we non-linearly transform a matter field into optical depth, and then you take an exponential into flux field, and then we take cross correlation and auto correlation, all that stuff with it, and find rational space distortions, distorted correlation function. How would you... The first thing you would try, what would you do? Just learn it this morning. Just to hint, it's the Kaiser theory again. So we took the Kaiser theory, which is in your lecture notes that you can derive. It was surprising why it might even work. Let me just tell you why it shouldn't work. The Kaiser theory depends on the fact that the conservation number of galaxies, right? That's the first principle that's depending on. If you look back, it's like one first line. This does not have a galaxy number. There's no conservation galaxy number at all, right? This is a flux field, which depends on some optical depth. So why does it work? We still don't know. We apply the Kaiser linear theory. We take a very theoretical curve, which is a BAO peak, right? And we apply the Kaiser formula. It has something like this that looks similar to what we saw before. So we actually put it side by side to something actually in the same scale and everything. This is the flux, which is simulated, that one we can simulate. And that's the theory. Just using Kaiser. We were quite shocked, actually, to be honest, because the theory is not the same theory at all. We still don't know why this is the case. We actually don't have a theory of Russia space distorted, laminar, or forest correlation at all. This is still unsolved problem, by the way. So if you wanna work on it, this is a good time. Let me just check the next thing. So we understand approximately, we think it's approximately how to model the Russia space distortions. Mind you, the two, magnitude is very different. So what you can get from the theory, the magnitude is off. And, but the scaling, once it's divided by a ratio, it works. So how about possible systematics? So I just described a completely new, larger structure probe. At 2009, nobody's has done it. Nobody even had data to look at it until we look at boss back then. And what are the possible systematics when we try to do baron-cosic oscillations with it? What are the systematics when we try to do Russia space distortions with it? If you guys, five minutes, is that okay? Five minutes, talk to someone? Or you have already good systematics you can tell me about, laminar for forest. It's related to the 21 centimeter you've been talking about a lot, right? So there are similar systematics, so you might want to think along those lines. Suggestions? Do you want a mic or do you want a yell? Yep, yep, yep, that's actually very important. You need to make sure you don't get the laminar beta contamination. That's very good. That's one possible systematics. Perfect. That's another one. I definitely cannot hear you. Hold on. You guys can hold the mic. Inwardening due to thermal and Doppler-wardening like thing. No more broadening. Ah, interesting. So, wait, exactly what it is. You said the line is broadens because of the various. Yeah, velocity, thermal, and... So that's an interesting one. We didn't actually look at this, but that could be something interesting to look at. There's another one in two rows behind you. Some absorptions are saturated. So, you see the... Yep, so, then laminar for systems basically saturated laminar for line. Very good. So, the broadening will also help into those guys. If you have that laminar for systems, basically a saturated system that has huge amount of nitrogen, it will make this huge, fat laminar for forest region. That's a huge dip like that, and it has a lot of wings. So, you need to make sure you remove those correctly. That's perfect. Yes. Do you need a mic? Do you want to yell? Exactly. Estimating continuum. So, a lot of people, you know this. What is a continuum? Do you want to say it? Do you want to pass the mic down? They can't hear you. Okay, here, because I'm so close. The origin quasar continuum flux that's emitted from that quasar. Exactly. So, remember the first plot I showed you of the quasar? Look, look, look right here. You need to estimate the continuum, which is basically where that is. So, what is the continuum? So, you know how much absorption there is. So, that's actually really, really hard to estimate. It's a very good point. So, you guys get all the system acts. That's really good. I was going to show you just one thing, which is UV related to something about quasar. UV background fluctuations. So, what does that mean? You're like, what is that? So, many, many possibilities. So, metal-length contaminations is the stuff that you guys just talked about and the continuum of subtractions, you also mentioned it. The damn laminar force is similar to metal-length contaminations. But what I'm going to talk about is one thing is to look at the UV background fluctuations. Why do I say that? UV background fluctuation is that, it's basically a situation where you have quasars lighting up and ionizing stuff around it, right? So, you can actually have extra ionizing region around each quasar. And that could actually throw things off because quasar's cluster, just like large-year structure, because it traces the dark matter, it could have some kind of signal at the VAO peak. So, you don't want to mess that up. So, what we do is that we put a lot of quasars at various different reshifts and you put in the right luminosity function because you want the quasar to be right at the right level. And you put in an ionizing background and you put it and calculate the correlation function from the simulations. So, what if I have a lot, a lot of UV background fluctuation versus very little? So, there's no UV background fluctuation where you get, when you have a lot of UV background fluctuation, that's what you get. These data points are the simulated observation, simulated observation, and this is a fitted line. And you can see that the UV background fluctuations actually does affect, we can actually model this whole thing. We actually figure out how to model this because you want to remove this properly and only get the VAO part. But the two changes are the biases changing and the width of the peak is broadened. You can see this is much wider. So, you don't really want a lot of UV background fluctuations because of that. So, that's one way to do VAO. So, to conclude for laminar of force VAO, we approximately understand how to model versus phase distortions and what happens when we include simple systematics like the UV background fluctuations. So, right now, laminar of force VAO is a way to get very nicely a high reshift, expansion of the universe. So, people have done this now and that was part of the team. But the next thing I want to show you is that something people haven't done. And also, I want to mention that the russian phase distortion part, nobody has done it yet because there's no theory to it. So, encourage you guys to think about, this is an open problem. I want to mention the next thing is about scale dependent bias, how you actually probe something called the primordial non-gaussianities that Enrico has mentioned at the inflation lectures. So, we mentioned this, we don't know which version, maybe even which version of inflation models it should be. Is it this multi-fuel inflation or is it single field? This is a sort of summary of what larger structure tells you. We have the VAO the wiggles on this side. You have the matter radiation equality actually determining what scale this was actually picked at. And then you have the standard inflationary scenario is this slide, while all these other inflationary scenarios actually gives you excess power at the larger scales. So, this is sort of summary of larger structure. No matter what larger structure you use, you pretty much have these kind of properties. And say the neutrino masses, it will actually change the whole shape, it kind of change the whole thing up and down. I mean, actually tilt like this. And the bias of Gauss is matter because if you have different biases, you have completely different signal to noise and it moves things up and down. This is linear bias, I'm assuming. So you have scale dependent bias, you have to be very careful. You have scale dependent bias, you can mess up what you can learn on inflation or what you can learn about neutrino masses. Okay, so this is sort of a summary of any larger structure probe. Lemon alpha forest is no different. So this is something we've done a long, long time ago. Oh, sorry, long time 2008. For different larger structure sample, you can place constraints on primordial non-Gassianic parameter called FNL local. So for those who studied this, you probably heard of this. Planck has measured it exquisitely well, but this is before Planck. When you have all these different larger structure sample from photometric luminous red galaxies, quasars, spectroscopic luminous red galaxies, different types of modeling of quasars, and you can combine all of them with WMAP-5. This is back in the days. This is a pretty good competitive constraint back with WMAP-5. But now Planck is amazing, so that is bigger error bar than we should even be able to show. And then you'll be like, okay, why do we want to go to larger structure? Because, well, Planck is basically, as Raphael has mentioned, for the temperature side, you've done a lot already. You might not be able to do a lot more with the primary anisotropy. Well, I think in larger structure, we still have a lot of room to expand. We have a lot more modes. Or 21 centimeter. That's another thing people have talked about a lot, using 21 centimeter. There is another experiment that might be from the Cospheorex, that is sort of looking at photometric galaxies with very, very, very good photos, over a huge chunk of the sky. They're also aiming directly measuring the non-gallium anis, primordial non-gallium FNL loco, using larger structure. So what happens is you use laminar force, not normal galaxies. The Skewer is again, we do the same thing as before. You've done this again. I take the power spectrum. So what I do is that I take the ratio of this dash line to the solid line. So I take the ratio of the power spectrum, when we have primordial non-gallium anisotropy versus nots. Okay? Fun stuff happens. So this is taking the ratio and subtracted by one. So this is the difference from the basic percentage difference from one you have no funny inflation models, I guess. I shouldn't say funny, but different. FNL equals to minus 100. FNL equals to plus 100. They actually flipped. The sign is flipped. It's kind of fun because laminar force is actually negatively biased. It's something that people haven't quite understood when we were doing this until now, I think we get it. But back in the days, we don't. And so the signal is actually inverted. So it's a great way to test any systematics, especially in the same survey. If you say, I think FNL is, I don't know, probably plus minus 100, it doesn't matter. But like plus minus five, for example, you really want to make sure that the tiny difference in excess in power is not because of some systematics. If your laminar force measurement is the other direction, that's hopefully not something systematics related. And we have preliminary theory predictions, which actually also predicts the negative 100 and plus 100 going in opposite direction from what you expect from galaxies and quasars. So it's kind of cool way to look at things when you get a completely different signal. And with retrospective distortions. So we can also predict that. Well, we cannot predict the retrospective distortion one. This is kind of preliminary. The retrospective distorted one is different, is smaller, the signal. So right now we have some theory models of what happened for retrospective distortions, but it's not complete. And this is recent SDSS3, there's not two reasons, that we actually see similar trends. So we're actually quite happy that maybe things are working from what our theory prediction is. But there's still many things to learn. So I just want to say that we approximately understand how to model the retrospective distortions. We're investigating what happens when we include other systematics, such as UV background fluctuations. And we think we definitely know how to do BAO because people have done it already. Let me just quickly conclude. You learn something very new today. You're learning something, if we have a new larger structure probe, what can you do with it? And how would you go ahead and model various theoretical model predictions for retrospective distorted power spectrum or correlation function? You can look at it when, whether you can detect primordial non-galarianities. You, of course, would be able to model the BAO because it's large scale, should be very easy to model. And I just want to tell you that it's cool that we can understand the BAO. You can do the retrospective distorted and the primordial non-galarianities. Boss Lime Apple Forest already made the first measurements of expansion of the universe at retrospective larger than two. And we'll get a really good result coming out very soon. The Desi Lime Apple Forest, which has four to six times more quasar will actually completely beat boss. And it will make a really good measurement if there's dark energy model at retrospective larger than two. And you basically map the expansion of universe at really, really high retrospect until 21 centimeter comes along. So I would implore people who would think about Lime Apple Forest, think about, you know, this is like a precursor, how you do 21 centimeter in some ways. Very different systematics, complete difference. So this plot again, we have a lot, a lot of data. Both Desi and Nebos will have this Lime Apple Forest skewers that I'll just talk about. And I think WFIRST is also thinking about using this as a way to probe actually intergalactic medium, not so much as a way to do cosmology. And looking forward, I'll just describe a few surveys of larger structure for you because it's important to know the field a little bit when you're going into, you know, maybe grad school or postdoc in the future. This is the Sloan Jones Geyser with four. We have three different, not instruments of three different directions. One is looking at the galactic archeology. So looking at the stars and understanding how Milky Way forms and why Milky Way is this way. Are we special as a galaxy? E-boss, which is using, this is where the boss galaxies are, is pushing out to really high reshifts. Using quasars, using quasar clustering, the first time that anyone has tried to do this, the E-boss galaxy, which are basically emission line galaxies and some high reshift luminous red galaxies and Lime Apple Forest, those are the skewers. Manga is very interesting. It's this way to take a thousand fibers and look at one single galaxy. So every single galaxy has this data cube of huge number of spectrum of stars inside it. So it teaches you a lot about the metallicity of the star. Every single galaxy is well mapped with all the velocities and chemical abundances and everything. So 10,000 of those galaxies like this. Desi, I've mentioned it multiple times and you're like, what the heck is Desi? Because I've mentioned it quite a number of times. It's talking to special scoping instruments. It, in principle, starts at 2016 right now, but it's commissioning sort of, at the very beginning, we were planning what the targets are and trying to figure out what we should be doing. But this is the preliminary plan. We have the early universe, the late universe, which is the stuff we have mapped using boss. And then we have more luminous red galaxies, the red and dead galaxies here. And then we have emission line galaxy, which are star forming galaxies. And you have about 1.7 million of quasars we can use for clustering. And then another 0.7 million of Lime Apple Forest, quasars that are very good to look at early universe, to look at dark energy, to look at, you know, growth of structure of Russia too, for example, using Russia's space extortions. With Euclid, for those who are European related, this, you might have heard of this before, this is a survey that's basically trying to understand the geometry of the universe, using Russia's space extortions, berenchocic oscillation, weak lensing. So weak lensing is something I haven't talked much about, but it's not my expertise. It's good that you know a little bit about galaxy lensing, but we have talked about CMV lensing, which I hope will give you a taste of lensing. It's imaging and spectroscopy together. So the stuff when we say we combine imaging spectroscopy, you can do all of them with Euclid. And it will start 2018, I'm part of the team. Finally, I'll talk with W first a little bit. This is a combination of both worlds. I'll show you a video instead of me talking, because it's more fun. This is recently, recently becomes a real project by NASA. And because of that, I think they have cool videos. Oh, hold on. I don't know if I can actually make the mic play the music. Is that, do you think it's possible? Oh, that's smart. Don't mind it might not happen, depending on. Yeah, I'm trying to find a cable. There isn't an obvious cable for the sound. That's why I didn't use it. Oh, maybe this one, hold on. Telescopes generally come into two different flavors. You have really powerful big telescopes, but those telescopes see a tiny part of the sky. Or telescopes are smaller. And so they lack that power, but they can see big parts of the sky. W first is the best of both worlds. W first is the Wide Field Infrared Survey Telescope. What I think of W first is doing as building on what were the two great successes astronomically of the 1990s in the last decade. That is the Sloan Digital Science Survey and the Hubble Space Telescope. W first is a NASA Observatory that has the top ranking of the National Academy of Sciences to launch in the 2020s. It has the same image precision and power as the Hubble Space Telescope, but with 100 times the area of sky that it views. Looking at a large fraction of the sky allows you to get a more complete accounting. For example, the stars in the Large Magellanic Cloud, which is the nearest galaxy to us, or the stars in the Galactic Bulge. So you can do a much more complete accounting and a much shorter amount of time. The particular thing I'm interested in using W first for is to actually do a statistical census of planetary systems in our galaxy. And what we're looking for is gravitational microwave events. These are cases when another star passes in front of our line of sight for a background star. And it makes that background star get a little bit brighter due to the gravity of that foreground star. And that allows us to find planets. What W first will do is it will have what we call a coronagraph. A coronagraph lets us image and characterize really dim planets next to very bright stars. The better how good a telescope that you build, it's always going to have some residual errors. This is going to be the first time that we're going to find an instrument that contains these high-formant deformable mirrors that are less correct for errors in the telescope. That's never been done in space before. W first will allow us to potentially make groundbreaking discoveries finding out what dark energy is. So this will tell us if dark energy is an unknown form of energy or if it's a modification of generativity. Single W first images will contain over a million galaxies. And we can't categorize and catalog those galaxies ourselves. Citizen science allows interested people in the general public to solve scientific problems. And so one of the things that I'm really excited about is enabling this bridge where the general public can get involved in doing actual science. For me, it's a really exciting opportunity to play a significant role in a mission that I think will be one of the most powerful telescopes that we have in the 2020s. And will be some of the most important things our country does in space in that country. Okay, so I'll leave you guys with thinking about what you might want to do in the future. Ending it with all the larger structure surveys in the future. I'm actually part of the team for the science investigation team for W first. And let you think about what you might want to do as you move forward as a student and as a physicist and as a citizen. Thank you.