 It was good talking with the students, not all of them were brave enough to speak. Ah, good, good. I'm glad to hear that it went well, yeah. I think in person it's a little bit better, yeah. On screen it's even more intimidating. Okay. I think we can start now. So thank you everybody. We are happy to continue with the Salam, this is the second lecture in the Salam Distinguished Lecture Series. And our speaker is Professor David Spurgle, one of the leaders in Microwave background observations. Currently a director at the Computational Astrophysics at the Flatiron Institute and Emeritus Professor at Princeton University. And this series, as we know, is funded, as I mentioned yesterday, is funded by the Kuwait Foundation for Advancement of Science. And we are very grateful for their support throughout the years. And today is the second lecture. So yesterday we heard about what the sort of the cosmological standard model, how it has emerged from the observation. And today it will be about what the universe's baby picture reveals about fundamental physics. So what we can learn from about the fundamental physics. So, David, please. So what I want to do today is I'm going to start by reviewing some of the things we talked about yesterday. And then turn to looking more deeply at the physics and trying to give it a kind of zoom in on some of the new physics that we can go to a full view. So what I want to do is begin by just reminding you of the simple model that we talked about yesterday. And, you know, while it's a simple model, I think it's very important to realize that already just what we know in the simplest model with no evidence for physics beyond what we need for that model, requires a lot of physics beyond the standard model, and provides important evidence that there must be physics beyond the standard model. First of all, as we've discussed, it requires dark matter. One of the things we can tell very direct populations that the dark matter is in a form that does not interact or does not interact much with electrons, protons, photons, or helium. Because we see fluctuations that are generated by two effectively different fluids, if you like. The tightly coupled fluid of protons, electrons and photons, and the dark matter component. So this says that the dark matters there and has does not have significant electromagnetic interactions does not have strong interactions and only interacts with gravity. So we know dark matter must demand new physics, it cannot, as people thought many years ago, be in the form simply of low mass stars or planets or clouds, very dense clouds of hydrogen. The second piece that requires new physics is dark energy, right, and this given its scale, given its uniformity is probably, but we don't know what it's telling us, but most likely telling us something quite deep about the connections between gravity and quantum physics. The next piece that demands physics beyond the standard model and physics as we'll discuss on energy scales well beyond that probe by the current generation of accelerators is the fluctuations we see that grow to form galaxies. And the final piece that requires physics beyond the standard model, and it's not something I will delve into today, but is just to think about as part of the picture of where we know it must need new physics is bariodensis. There needs to be the standard model does not provide for why there is an excess of protons over anti protons electrons over positrons. As I emphasize yesterday some of the cleanest evidence to interpret for the standard model comes from the observations of the microwave background, and we looked at observations of temperature polarization across correlation and decompose the polarization observations into e-modes that were symmetric under mirror reflection and e-modes, and we'll delve more into this in today's lecture. So let's talk about what we see in the fluctuations. All of the fluctuations in density in the early universe of fluctuations are linear fluctuations, and they're fluctuations the density of all the different components we have redshift 1100, studying the microwave background. There are actually several significant components. There's photons, neutrinos, dark matter, protons, electrons and helium nuclei. One of these components contributes significantly at redshift of 1100 to the energy density of the universe. Each component is a contribution of order tens of percent. So all four of these components affect what we see in the microwave background. Now there are a number of possibilities for what the fluctuations could have looked like. One possibility are isocervator fluctuations, where the overall density of these four components are constant, but what varies over space is the ratio, for example, of photons to dark matter. So some regions have more photons, less dark matter, others have more important matter, less photons. And similarly there could have been ratios, variations in the ratio of photons to neutrinos, photons to baryons, any of the components could have varied. Those are what we call isocervator fluctuations. What we see instead and what the data really demands is that the fluctuations are primarily what we call adiabatic density fluctuations. With adiabatic fluctuations, the ratio of photons to dark matter, the ratio of photons to baryons are constant through the universe. Whatever mechanism is responsible for baryogenesis is generating the same number of baryons per photon everywhere across space where we observe. And that by the way is very interesting to think about if we realize that we're looking at regions that are completely causally disconnected. And these adiabatic fluctuations, most interesting to me are adiabatic super horizon fluctuations. What do we mean by that? What we mean is that we look at two parts of the sky, say separated by 90 degrees. The correlated temperature fluctuations across these very large scales, the sort of biggest as we look about, you know, two or three degrees. And on those scales, there's, if there was not a period of inflation, if we had a universe that only went through a radiation and matter dominated upon the horizon size, the distance that information can travel is only about two degrees. And we would not expect to see any fluctuation on scales bigger than this if causal physics would generate the fluctuations we see. So we talk about these fluctuations as being super horizon because they're on scales larger than the horizon size in the standard expanding universe. And the strongest evidence for this comes from the observations here of temperature polarization cross correlation. And in particular when we're looking at polarization because we're seeing scattering off of electrons, we're seeing a signal that must be coming from redshift of 1100 that must be coming from the surface of last scatter. So this signal is applied in terms of multiples and you can see that what's predicted and I'll show you next the data. What we see is correlated fluctuations on scales of, you know, multiple holes larger than 100, which corresponds to much smaller than 100, which corresponds to scales larger than two degrees. So these large scale coherent fluctuations require one of two possibilities. I didn't have a period of superluminal expansion like inflation that can causally connect this region of the sky and this region of the sky. However, you paint on super horizon fluctuations in the initial conditions. And, you know, there are models that take the second approach. There are several models in which there is a bounce in the early universe that the universe did not begin with an initial singularity, but that, but if you generate the fluctuations during the collapsing phase. And I'm going to mention for the other possibility for explaining that those models have their own challenges, but remain, you know, an interesting area of study and speculation. Most of the community is focused on the inflationary models, but there's interesting work by people like my colleague at Princeton Paul Steinhardt, who is exploring these alternative models. The key piece in our story is that these fluctuations that are generated, you know, most likely during inflation that produces these super horizon fluctuations grow and evolve. And this picture that I'm showing on the graph gives you a sense of the basic evolution that happens. We have two components. One, the barrier on photon fluid, the protons, electrons and photons tightly coupled by electron photon collisions. That behaves like a fluid. If you start out higher pressure as shown here, the pressure, the higher pressure region expands and oscillates like a sound wave. This figure here shows in black, those oscillations in the barrier on photon fluid. The dark matter on the other hand is pressurized. It's why we call cold dark matter. So once the universe becomes starts to become matter dominated, the self gravity of the dark matter fluctuations can drive them to grow and grow an amplitude. If you look at the microwave background, we're seeing fluctuations primarily at redshift of 1100. And what we're seeing is a combination of a contribution for the dark matter and a contribution for the barrier on photon fluid. The regions that have more rotational potential well, that makes those regions colder. On the other hand, regions that have more photons are higher. On the larger, if we're looking at a lens scale like the one shown here, the barrier on photon oscillation happens to be close to zero. On this lens scale, we would get primarily a cold spot driven by the dark matter for this initial condition. On the other hand, if we were looking at a fluctuation whose characteristic lens scale was a little bit larger, you might have the barrier on photon fluid undergo only half an oscillation. If you look more like that, then you would have a cold spot from the cold dark matter, a cold spot from the shortage of photons and baryons was the oscillation. And on that characteristic relations be larger, the two turns would add coherently. That scale associated with the photons undergoing half an oscillation is the acoustic scale. That's the scale that's going to be associated with the peak in the microwave background spectrum. Just remember that we have that characteristic angular scale here. And that that anger scale here is associated with the baryons and photons being on a lens scale that they've undergone high oscillation. And those later acoustic peaks you can associate it with undergoing three pi and five pi and seven pi and so on. And we see that ringing if we look at the picture in for your space. When we do microwave background analysis, just to remind you what we're, we do is we take the sky. And these pictures of the sky observe from W map and the pictures are from plank and again just emphasize that to me this tremendous experimental success of the different instruments on plank and W map and the ground based experiments, all the pictures look like. And when we look at the sky, what we do is we decompose it into spherical harmonics. Look at the amplitude of the spherical harmonics and the plots you see look usually plot this combination that's been traditionally written this way was getting back to some paper by bottom to the south the standard unit notation we use that weights the C C actually by a factor of L squared. And this term corresponds to the amplitude of fluctuations the average variance in micro Kelvin squared on this anger scale associated with the moment. As it is, as you'll notice that even in this picture we can't with the multi frequency data fully remove the contribution of the galaxy. So we do analyses we almost always end up masking the region around the black the claim where black the foregrounds are brighter. So we need to account for cuts in the sky and variations in noise level and so on when we do the analysis but there's now a standard approach and this agreement between the two experiments you could really just look at quantitatively and this plot in black shows the cross correlation between the W map and 94 gigahertz data the plank to 17 and in red between the plant to 17 gigahertz data in the plant 100 gigahertz data and the papers on this plan to some more sense of experiment. That's why we've followed on and has given us improved numbers and you can see at the higher multiples, the lower noise in the plank experiment even across correlation is quite noticeable you get much more precise measurements of the higher multiples for playing. On the other hand that low multiples with signals are very strong the noise less important. You see really nearly identical results and if you look at this multiple by multiple part of the sky by part of the sky. The differences between the two experiments are consistent with noise there was some initial calibration offset but that's now been completely resolved and the experiments have read very well and this is true not not only the space based experiments but as shown here the various from based experiments. And as I have decided the temp the just remind people kind of what we look at we look at polarization, we look at polarization we're decomposing into the symmetric and anti symmetric parts. And here's a way of looking at polarization, we're looking at the signal produced by an individual K mode, and you can see that the emo polarization corresponds to gradients in the K mode. I like to think of the emotes, because if you look at what generates in the sky is actually tracing your electron velocity field at redshift of 1100. And when we look at the temperature polarization cross correlations, you should think about them as a density velocity pro cross correlation. Remember that the barrier photon fluid is oscillating like a sound wave. So the velocity and density fluctuations are 90 degrees out of phase. And that's why when we look at the bottom of the whole signal. Sorry, you'll notice that the temperature temperature signal is out of peaks are out of phase with the polarization polarization signal. These are peaks and density fluctuations. These are peaks and the velocity fluctuations. And when we look at the cross correlation between temperature and polarization, you see that it oscillates twice as often as you're looking here basically at something that looks like cosine squared. Here's something that looks like sine squared. And here's something that looks like sine times close up. And that gives the basic form of the signal we see. And you see this pattern again. When you look at this and for your space. Here's the cold matter driving the fluctuations here. Here's the barrier photon fluid. And to do and this is an analysis that came out of Bob's group of Toronto is you can actually look this is looking at the act data, and then asking, what would happen if we took what we see and remove the dark matter or remove the dark energy. You can see the pattern we see, which is matches very nicely with our standard theory just looks different when you look at what happens you have no cold matter or no dark energy. And you can basically see in the temperature and polarization patterns, the evidence of dark matter on the sky. You're just seeing it there. This puts very strong on any alternative gravity theory to fit the polarization data and fit the large scale structure data is very demanding. Chris part of when I wrote a paper last year that appeared on the archive of the girls that looked at what those constraints do. And these cosmological constraints that you've got to fit the suboptimation data is constraining any alternative gravity theory in an important and different way from things like the like observations. So, you know, for me this is part of why I think there's a very strong case with cold matter. And these fluctuations and don't emphasize or something that predicted long ago this is from the abstract of the seniority and so does it's 1970 paper. A detailed investigation of the spectrum of fluctuations may in principle lead to an understanding of the nature of the initial density perturbations, since a distinct periodic dependence of the spectral density of the perturbations on wavelength is peculiar to a divided perturbations. So, what's in your eyes and so don't which predicted a 1970 of this set, you know, the sound waves oscillating with this periodic dependence is now something we see as I saw temperature temperature here you see in temperature polarization with the plank data here with the polarization polarization, but the sound waves also because they're there in the balance end up in large scale structure, they're written in the large scale distribution of galaxies. And this shows the multiplied by the smooth component what you get for the galaxy power. This is not this is large scale structure. This is from the CMAS survey from Sloan, looking at the large scale distribution of galaxies, now not as a function of multiple across the sky in the two dimensional sky that we see in the three dimensions with large scale structure. And the curve here is this model fit to the microwave background data projected to large scale structure. And you can see this remarkably good agreement between what we see the microwave background structure. The large scale structure observations and have the advantage of providing another way of constrain the evolution of the universe. And we kind of look at this as measuring sound waves in the sky. And on the left this just shows you can undo some of the effects of non linear gravitational evolution, improve the p, but we can actually because we've got this ruler that we've got can calibrate on the microwave background of what the sound horizon system is, how far the sound waves can move. What is the characteristic scale and printed in the large scale structure. This correlation in the galaxy function, you can think of it being physically very similar to the correlations we can make for those hot and cold spots that sound wave that ring you saw in the microwave background sky produces this correlation in the large scale distribution of galaxies. And we can measure the size of that ring as a function of redshift with different galaxy surveys. Compare that to the predictions of land to CDM as it's giving us a measurement of distance versus redshift. And this lets us probe the expansion history of the universe. And this is a one of the plan papers where they looked at the data to date, then the different galaxy surveys years long surveys, the we will see the 60 f galaxy survey, and you can see as a function of redshift, the data we have is very consistent with land to CDM. Now, if dark energy was dynamical, we would see a curve here where the distance redshift relationship look different. And if we had dark energy evolving with redshift, it would show up in this plot as deviations from this line with that's equal to one. One of the major thrusts of observational cosmology in the past few years, but also in the coming decade is improving this plot with higher precision data. And surveys like the dark energies, but Desi and Euclid will be reporting evidence, often truly by close to an order of magnitude. That, you know, had a minimum will give us better constraints. I think what we're all hoping that we'll see deviation from land to CDM and see evidence for new physics and looking towards later in the decade. The NASA led Roman space telescope, formerly called W first will measure this potentially even higher precision so we will improve this font and make use of this acoustic ruler. So let's turn to what can we say about the properties of fluctuations. First, as I emphasized earlier, the fluctuations are super horizon and the T is a very odd and I emphasize the importance of this temperature polarization signal large angler scale at showing that the fluctuations were either generated, so phase. There were a number of attempts and we're clever papers by people like Neil Torok that had causal models that would generate much of the temperature spectrum without inflation, but those models do not produce this temperature polarization correlation of large scales and are constrained by these models and this shows already with this plot here is the first year data from W data from that. So back in 2003 we had pretty compelling evidence already that the horizon fluctuations were super horizon. Another important hint we have about the properties of fluctuations is that the fluctuations are not quite scale invariant, and this looks at what you can get by measuring the power spectrum as a function of scale. And statistically, there's now a more than five sigma evidence for the fluctuating from scale invariant and s equals one is the same amplitude of fluctuations on all scales, the fluctuations are a bit redder than that. It's more close to about 0.96.97. And if you look at the, you know, that's close to one, but not quite one. And that's what you would expect an inflationary model. If the infleton field is rolling down the hill, and we saw this at WMAP and with Planck we've measured this with higher precision, and looking forward to some of the upcoming experiments like Simon's observatory, we will further improve our precision to the measurements of the spectral index, which is the context of inflation is really telling us what's happening with the infleton field at the moment of that moment of expansion. Another important property we can observe about the microwave background fluctuations. One of the nicest ways is to kind of, if I just visually look at that, if you haven't looked at this in detail, is just look at the PDF, the number of fluctuations as that you see as a function of temperature. What's shown here, and this is from the early WMAP data, looking at fluctuations on the angular scales of four degrees, one degree and a quarter of a degree. And what's shown in black is the histogram of fluctuations. What's shown in red is the, what a Gaussian looks fits, fits to this distribution once you've normalized by the variance. We have a zero free parameters of fitting a Gaussian. So you can see it's just really well described and variance by the Gaussian, right, we see equal numbers of hot and cold spots. We don't see the five or four sigma points or just what you expect for a Gaussian given the number of points. And this gaussian 80 has held up as the data continued to improve from WMAP and then from plank. There were detailed ways of quantifying the non gaussian 80 one that I'm fond of is looking at various forms of three point function, or we take the temperature decompose it into the spherical harmonic amplitudes and cross it that since the universe doesn't have a preferred direction, it could be reduced to a three dimensional function that we call the bispectrum. We can look for the bispectrum various features of non gaussian 80 in the bispectrum. I think the one that's the simplest is what's called local non gaussian 80 where the variance in the field. There's overall amplitude. This could be generated if there was a non trivial three point function in the infotain field that drove inflation, or we can generate this if we have multi field inflationary models. So, the non gaussian 80 the form of three and four point functions is something that has just fascinated me for, for many, many years. We've been looking at this right guys in various forms over 25 years hoping to find some hint of new physics through gaussian 80. And, you know, there's a very nice detailed analysis of the plan 2018 data. In this paper you can see on the archive, and they've looked at many forms. And I could summarize it by saying, we don't see it. Right, of course, it's zero plus or minus some error bar, but there's, there's no signal there. Another interesting way to look for non gaussian 80 is through topology. functional fluctuations. Look at the number of the, the area hot spots and cold spots of the areas of function of the amplitude, the perimeter length of the hot and cold spots the genus the number of hot and cold spots. These are all topologically in various ways of looking at non gaussian 80. Again, we've been looking at this for since W map days, the data continues to improve this is I think the current state of the art. We don't see it. The fluctuations look remarkably gaussian. There could have been much more information in the fluctuations that could have been a second term other things going on, but the fluctuations really do turn out to be as simple as they can be. We expected an inflation. Right. And, you know, right now we can look and say, at the predictions of the simplest. inflationary models, they said the universe should be flat. And this was at a time at which we, you know, the evidence suggested a universe whose total matter density was less than once. The prediction actually contradicted the observations as we understood them at the time the inflationary model was proposed. If they've approved we've seen we live in a flat universe. The data predict this shows a nearly, but not precisely scale invariant spectrum of fluctuations the slightly red spectrum is predicted. The fluctuations are adiabatic and gaussian. So the next big prediction after we check these four off the checklist, I think, not seeing any of them would have been a challenge for the simplest model of inflation. The next case would have ruled out the simplest model in comparison modifications or alternative model is that there should be a stochastic background of gravitational waves. And you produce gravatons at the decision temperature. So the expansion rate of the universe during inflation is going to determine the amplitude of the gravitational waves. And you can see the characteristic scale for this is set by this ratio of the expansion rate to the plant scale. So as you're looking at things at very high energies and very high scales, we often talk about the aptitude of these fluctuations in terms of the ratio of tensor to scalar fluctuations, how big are the gravitational wave generated fluctuations, compared to the fluctuations generated by the scalar modes. And that ratio depends on the scale of the infotain potential. And at the period of time, the present today normalized by a scale that's pretty big, you know, what are 10 to the 16 GB. So one of the exciting things about studying the microwave background fluctuations and looking for gravitational waves is we are prone to physics at this very high energy scale and I think of this in this analogy, really talking radiation where you're seeing gravatons upon an excitation of mass loads modes at the horizon. And that's one way to think about what's going on when you're generating this. Let me again remind you when we look for these what we do is we decompose the polarization pattern into EMB modes. Gravitational waves actually generate both EMB modes, as well as temperature fluctuations. But since they're sub dominant as to the scale of fluctuations driven by very. We want to look for, so we can see them in temperature and see them in polarization potentially, but emo polarization, but they tend to get swamped by scalar modes. So the distinctive ways to look for B modes. Now there are challenges of looking for B modes, many challenges. There are other ways of generating B modes. And this plot here shows the predicted amplitude that we expect of these modes as a function of angular scale, where blue shows the gravitational wave signal. The red circle shows the signal that we know ought to be there we've actually now seen due to emotes generate a redshift of 1100 having to propagate from redshift of 1100 to us. And as they move along the line of sight they get distorted from emotes into B modes. As we would say 11 and lemonade. If you're interested in seeing gravitational waves. This lensing signal is a big foreground that you have that stops you from getting information on small angular scales. On the other hand, if you're interested in measuring the large scale distribution of matter. The signal is telling you what the large scale matter distribution is. We look forward to kind of observations be able to make with assignments observatory and CNBS for measurements of this amplitude of the signal will be a very direct measurement of the amplitude of matter fluctuations and tell us about things like that some of the this purple curve shows what we can do if we deal ends the signal we can use the path either the large scale. Or the lens except it's itself in the CNB to clean up the signal so potentially we can lower this year and there's actually now been measurements first measurements done with modesty lensing. The challenge with looking for the signal of course is we don't know his amplitude and these different curves show different levels of signal that we might expect to see. And as the signal gets weaker, it eventually starts to go drop below the gravitational wave signal and a large angular scales get swapped from the black. Now if we think about this in terms of inflationary models, different inflationary models will make different predictions for the tilt. And for the cancer just scale the ratio and already with the W map data. And that's from temperature measurements alone, and that was enough to be able to rule out models like lab of lab of five four models and strongly disfavor at square plus with any large scale structure data was able to rule out already those two models. I think this represent, you know, was already representing I think the tremendous experimental progress we've been able to make in constraining cosmological models, and that the two versions of inflationary theory that I had first studied when I was a graduate student land of far far and are actually ruled out by the data. And we need models like a step in ski inflationary model, they are split, or models with flatter And the subsequent years we've been able to look for them in the beam of pattern. There's been some excitement there was a lot of excitement about five six years ago, when this map taken by the Harvard group suggested that there were a pattern of gravitational waves. I, a number of others pointed out the time that the signal was very likely due to dust, and unfortunately as the data improved it turned out to all the dust. And that will be a significant forward that but since then the data is continued to improve. And this shows the polarization polarization data here, the bicep tech data here. The fact that we're not seeing the signal so our was point one, we would expect the points to go up this way. You can see they continue to draw data already constraints the amplitude of gravitational ways. And what's shown here is both the constraint on the gravitational wave signal and the amplitude of ways. And as you can tell from the data, there's a very nice detection of the lens in signal, which is telling, as I mentioned about the large scale structure, but we only have constraints on the gravitational wave signal. And, you know, while things continue to approve, you know, the constraint is all from polarization are about point oh eight is not actually not yet that much better than the temperature only constraint. This is an area where I, we can anticipate significant improvements in the coming years. I think within the next set, you know, several years, we should see constraints grow to closer to point oh one. And looking forward to CNBS for and we can see constraints. Experiments like constraints grow to what are 10 to the minus three. And of course will be the most exciting result is not a constraint, but detecting gravitational waves. And if we were to see them, this would be awesome. It's a probe of physics directly at the plane scale, a glimpse into the universe and so the first 10 to the minus 30 seconds, not 10 to 30 seconds. PowerPoint over on Pino there. So it's 10 to the first moments. Really direct. You're actually seeing individual graviton excitation. There's probably the quantum nature of the gravitational field. So one could look again at things like non gosh Navy there so there's a lot to be learned. In the final 15 minutes of my talk, I want to look at ways to search for new physics in the microwave background. About the possibility of the signatures of neutrino physics detecting the signature of early dark energy by looking at how that might modify the microwave background. A lot of this has been motivated by this interesting tension or conundrum people use different words for this. That we look at the observations, the microwave background, and make our measurements from whether it's plank or W map or act, we find a Hubble constant around 6768. Just from large scale structure observations using those very acoustic peaks. Those that characteristic sound wave scale, even without using the microwave background, just from large scale structure, one gets a very consistent number. So if we calibrate with this sound wave ruler, we get a Hubble constant. We're doing measuring expansion rate of the universe using more classical methods, using sephiates is a distance indicator gives a Hubble constant of around 74. And most other methods give consistent numbers. This is from a paper by the ship led by Verde et al. We find that there are some hints of lower expansion rates. When the Freedman's group using tip of the red giant branch, a different calibrated the sephiates gets an expansion rate that's much more consistent with the microwave background observations. And these holy cow observations, which are based on time variation and gravitational lens and these have been re analyzed looking with more carefully. The dark matter distribution around galaxies and those re analyses actually push the Hubble constant down to here. So no longer have I would say a consensus among the measurements of low redshift. So it could be that there's something suddenly off in the sephia data. Sephia measurements are hard. These are measurement. The sephiates are in relatively dense regions of galaxies. Nevertheless, the groups that have done these analyses are very careful on their high quality work. So I think we are really obligated to take them seriously and think about what physics could explain this. But what we need to do is recalibrate the ruler and we'll look at different ways of recalibrating this in the next few minutes. And when we're looking at the cosmic microwave background, while we think about this is telling looking at right at this. We're actually sensitive to physics all through the evolutionary history of the universe. You know, we're very sensitive to what's going on here. If there's a physics of nutrient that the neutrinos are energy or doing something non standard. And we're sensitive to subsequent evolution of the universe. So let me move forward to look at how things actually show up in the spectrum. If we do things that change the way the universe behaves at redshift of, say, 2000 or 3000, that's going to change how those sound waves oscillate. Anything that changes the relationship between redshift and distance will shift the acoustic piece. So neutrino physics will shift the location of these higher multiples. Most distinct in the emails, as you can see that the email signal in these higher peaks is actually sharper than the signal in the temperature piece. And one of the directions in terms of where the data will improve within the next few years is improved measurements of emotes on these scales. And that's going to be sensitive to the effects of neutrinos and the effects of early dark energy. So we've already learned a bunch of things about neutrino physics. As we anticipated more than two decades ago, one of the interesting things we could measure is the number of relativistic degrees of freedom. Remember the way the fluctuations appear to us, depend on the expansion rate of the universe. We're actually, think about our microwave background measurements as being sensitive to the evolution of the density of the universe. And since neutrinos are contributing over 20% of the energy density of the universe at redshift of 1100, their effects are pretty significant. And we can count the number of neutrino species. And we can get a measurement of the number of really not just the neutrino species, but of relativistic degrees of freedom, any light particle will contribute that. And what we see right now with our current best days is consistent with three that there's just the electron you want in town neutrinos that we expect to have generated in the early universe. Now the early universe of course is a wonderful accelerator. It was very hot and very dense. So if there's any other white particles, we would have seen them. One model that people have often thought about is could we have a symmetric universes started out motivated I think largely by thinking about E8 cross E8. Could there be a mirror universe that had the same properties as ours. I think we can now firmly say no, we can just count out the relativistic species and what we expect based on the width of the Z is what we got. And I think, and this is an important constraint on kind of any new physics that generates light particles. We also can measure the combination of the microwave background, the large scale structure, how it affects growth, the seven neutrino masses. And this is something that's going to improve a lot. And we'll tell us about the neutrino mass hierarchy. Let me just remind you that the neutrino oscillation measurements whether we're looking at solar neutrinos or cosmic brain neutrinos. The oscillation experiments coming from accelerators are always measuring mass differences. They're measuring the mass differences between the different masses. And we have measurements of the difference from solar neutrinos and atmospheric neutrinos between the different items. We don't know whether we have this kind of normal hierarchy, or this inverted hierarchy. When we look at the effects of neutrinos on the microwave background, and on the growth of structure, what we're sensitive to is the sum of the neutrino masses. So we're measuring a different quantity than the oscillation experiments. As we do this, we can start to put interesting constraints. And this plot shows what we know about the current constraints from Katrina on the lightest neutrino, the constraints from cosmology on the sum of the neutrino masses. And with the current data, we can't distinguish between the inverted and normal hierarchy. But looking at where we will be a decade from now, with this sort of wonderful next generation of satellite missions and ground based observatories that are already being constructed will either be in the blue region, or the green region will see evidence for the inverted hierarchy, or the normal hierarchy and ruled out inverted hierarchy. So I think we're going to see some very interesting progress and really know more about neutrinos. Now the last few minutes, let me just mention a few final part of physics that we can look for the microwave background. One is neutrino interactions. And these are some figures produced by Christina Christ, a graduate student at Princeton working with me, who has been studying the possibility that we pretty strong interact in the neutrino center, that the neutrinos scatter off each other. And you've got a very large neutrino neutrino scattering process. This scattering will delay the neutrinos from streaming out of those density fluctuations and have an imprint on the microwave stuff. And one can look at and given the time I may not delve too deeply into this, but changing things like the strength of that interaction, and that will shift the phase that shows the deviation of the model from the standard as we do things like change the effective interaction cross section, change the neutrino mass, and by making these changes, what one can do is take the microwave background data and shift the values of the Hubble constant. So what we expect for the amplitude of matter fluctuations, which we can compare to the gravitational lens experiments. And this shows what happens when you have strongly interacting or less strongly interacting neutrinos. And you can see by adding these new parameters, we open up more parameters space. And while there's some tensions between the measurement lambda CDM and some of the ground based measurements, there are regions in parameter space with these interacting neutrinos. That's consistent with this data. Now, of course, we added actually three new parameters, and with three new parameters of course can fit data better. But for me, the exciting feature of these models is that they make unique predictions for the high multiple polarization spectrum. Correct. There's actually data, we have in hand now, we've now surveyed with the act experiment about half the sky at five times Planck's resolution and more than two times Planck's sensitivity. So we have data, which is still blinded, but we've got it in hand, we're working on the now that if this is the right explanation, we'll know that. So that that's really exciting to me. And similarly, we can look for early dark energy. And this is a nice slides and work by Colin Hill and his group of Columbia. And you can understand how the early dark energy solves the this hubble tension by looking at the fact that the sound horizon different distance is the distance of sound wave could move in the age of the universe. And we can rewrite that as the sound speed is a function of redshift divided by the. So if we change the universe by adding an early dark energy component, we change the evolution of H of Z. This is from beginning of the universe to recombination. And if we change that would we recalibrate the ruler and can get a consistent answer. And what we want to do in these models, you have a model where the dark energy is initially frozen. So it acts as you have a component that acts like dark energy. And then as the universe evolves, it rolls down the hill. And I saw surprises is more important matter and there's been a bunch of papers exploring this class of models in the last year. And just to give you a, you know, a sense of the changes is that it takes the temperature spectrum and some way the polarization factor and shifts it modestly. What's shown in black is shown in red is predictions with early dark energy that fits the recent model. And while this doesn't show up well in a log plot. If you look at a linear plot, it changes the multiples of the function of L by a couple percent. This is as times 10 to the minus two. So this represents a 1% change and a somewhat bigger change in polarization. This is the level of error due to statistical noise in our current measurements. So right now we're in a situation where we can possibly see this early dark energy physics. So let me conclude. Let's take some questions. I hope that I've convinced of two ideas. One that the measurement might play back on or this powerful probe we've got the standard model that fits just the standard model demands new visits. And some physics to generate the fluctuations, inflation is a beautiful model, but we do not have a well established, you know, the theory that UV complete that is sort of the accepted inflationary model. So for those of you thinking about the physics of the highest energies, this is your laboratory. I hope I've conveyed that the coming years, you know, it's been a great time for CB experiment, but the coming years should also be very exciting that kind of guaranteed measurement in the next 10 years is going to be a detection of the southern neutrino masses. And with that determination of the neutrino mass hierarchy. So we get lucky and we could see evidence for some new physics, early dark energy neutrino interactions into examples, but there are many other pieces of new physics that we can use. This is a laboratory detection. And this is very exciting possibility and the experiments are really now in the process of improving their limits of detecting promoting gravitational waves. So I hope I've conveyed to some sense of the excitement of what we're learning have learned and I think we'll learn from our observations the likely background. So thank you. Thank you, David. So, we have a bit of time for questions. I see that the power that compare raised the her and so maybe she can just speak. Paula, are you there. I think you are muted. Sorry, I think it is a misunderstanding. Okay, no problem. Okay, no problem. Yeah, so there is a question, a very technical, yeah, in the sense of a unique some Sengupta is asking a suggestion from you about a textbook or a coursework on CNB. Um, there's a number of good textbooks. Just in terms of the basic sort of going through the relevant equations and and understanding them. I found Donaldson to be a very, you know, it's a little old but it's, it's quite complete is a good place to start. For those of you who like so far more formal treatment, Ruth Doris book was a nice book. Um, and there's a, you know, what I, there's a nice, let's let Ellen, who I have a nice undergraduate level book that wants sort of a quick read on these days and actually don't, you know, I haven't looked for them. They're, I suspect people have done like some nice lecture series. Um, Dan Bowman is some very nice notes. I don't know if those are recorded online, but he, but those are notes that I've encouraged my colleagues who are, you know, I often have former postdocs who are common assistant professors need a place to start for their own lectures. And that's a good place to look. And another question about from Gerardo Morales, Navarrete, and he's asking whether there could be some connection between non-gaussianity and the neutrinos. Well, there's two forms of non-gaussianity broadly. There's non-gaussianity that's generated during inflation or whatever mechanism generates the fluctuations of early universe. That kind of primordial non-gaussianity that will could exist on very large angular scales that can only be generated during the accelerated phase and neutrinos are not important there. And there's a second form of non-gaussianity that's generated at later times through the gravitational interactions of the fluctuations with large scale structure. So, that takes the form of the gravitational lensing signal. And while I've talked more about the detecting gravitational lensing through looking at this BB signal, we can also see gravitational lensing effects through looking at a non-trivial four point function. I've talked about the fluctuation being gaussian, which would mean you should have a non-trivial, no non-trivial four point function. And that seems to be true initially. But as the fluctuations propagate towards us, what happens is, if you have a denser region, so let's say you have a cluster of galaxies. I have two microwave background photons. And again, this is the moment one wishes you have a blackboard, so I'm going to wave my hands. The fluctuations are converged around, the photons converge around dense regions diverge around large regions. That takes my hot spots in the dense region in front of them, or term. It makes them smaller. If it's a low density region in front of them, it makes them larger. That generates a non-trivial four point function. We know exactly the form to look for you can take your maps, measure the four point function, and then infer the gravitational potential. Why is this important for neutrinos? Because if the neutrinos have mass, they contribute to the expansion rate of the universe, but they're light enough they don't cluster on small scales. That has the effect of making the universe expand quicker and suppress the amplitude of density fluctuations. Since my non-gaussianating depends on the amplitude of density fluctuations, the more massive neutrinos are, the smaller the four point function is, the smaller the non-gaussianating is. So it actually has this effect on generating neutrinos that neutrinos mass suppresses the non-gaussianating that we would anticipate in a universe with the lowest possible neutrinos. Good. Then there is a question from Khalil Bitar. The question is, is it possible to modify gravity and remove the need for dark matter and or dark energy? Do experiments necessitate for both? So we have the simplest model consistent with all the data has dark matter and dark energy. And we now have, one can write down, people put a lot of energy into this alternative models that modify gravity in various ways. We don't have a successful alternative model, fits all the microwave background data, all the large scale structure data, fits the rotation curves of galaxies, fits, modifying gravity. The fact that LIGO saw gravitational waves arrive at the same time as the optical signal, of course, tells us the gravitational waves exist and propagate at close to the speed of light. So you can't have alternative models that change the way gravity waves propagate. And if I think about gravity as graviton exchange, that sort of tells me a lot on the large scales pulled by cosmology, gravitational waves behave the way that we think they ought to in GR. So it's a constrained problem. What Chris Pardo and I showed is that if you want to fit the large scale velocity fields, so when we see, we know what the electron velocity is doing at red 100, because we can see that in the polarization. We know what the galaxy density fields are doing at redshift zero, because we see that large scale structure. So any alternative theory of gravity has to get us from redshift of 1100 to redshift of zero in the same way as standard gravity does without the dark matter. And that requires an alternative gravity theory with effectively the sign of the gravitational force changes sign on the scale of 100 megaparsecs. So it looks to me like it has to be pretty contrived to fit all that data. There are variants on things like Tavis, this Tetser vector scalar theory that does fit the temperature data alone, but there's not something I've seen in the literature that's published that fits temperature polarization of large scale structure with any alternative theory. Okay, let's take a couple of more questions. I see that Dependu Bandari asked, raised his hand, so maybe he or she can just pick out. Dependu, are you there? You're muted. Okay, as we wait, maybe I can take another question. The question about the limits on sterile neutrinos. Yeah, so if the neutrino number density is the same as the electronic relativistic neutrinos, we know they're actually rolled out the constraints are good enough. There can't be another neutrino species whose abundance is the same as electron-mealing termitrinos. On the other hand, is sensitive to the reduction mechanisms and how things oscillate. If you can arrange that a coupling between ordinary sterile neutrinos are weak enough that they don't oscillate back and forth at a rate at which you have equal numbers of both, then you could have potentially evaded the limits. So energy density in this addition or in any additional species. So the two-sigma level, three-sigma has to be less than about half of the neutrino species. Okay, then there is a question basically asking whether gravitational wave observations will tell us something about the dark matter. You know, there are some constraints. I guess so far I've told us more about compact objects when I close in neutron stars and ones from the old universe are going to tell us more about physical addition in its first moments. I guess there's probably a constraint and I haven't actually seen this work out, because I think most models would not predict something very significant on gravitational wave interactions with dark matter. As I mentioned already, we know that gravitational waves travel at very close to the speed of light because we, LIGO saw the gravitational wave signal from a neutron star to neutron star merger very close to the same time as we saw the optical signal. So that constraints interactions that way. As I mentioned already, I think one of the important constraints that waves signals produce is they really rule out not all but broad classes of alternative gravity models, and that makes it more difficult to develop alternative models for dark matter. That would be good. So one last question that I can read it from Dependu Bandari is basically about possible cosmological constraints on dark photons. There are a number of constraints and there's been some active work on this. I don't know the most recent papers well enough to give you the limits off the top of my head. There's come in a number of forms, you know, from. I can think of how I would go about doing it but I don't want to let me not invent constraints on off the top of my head when I know there's actually a very good literature on that so let me just refer you to that. So thank you very much, David. I think we can conclude here. It's good to remind that tomorrow we're going to have the third lecture of the series. But before that we're going to have the celebration of the Iraq prize starting at 130 center European time. And that's it. So thank you again, David. I see you tomorrow. Thank you for the questions and look forward to the prize and then speaking to you again tomorrow. Thank you.