 Okay, I'm gonna go ahead and get us started. Okay, that's great. Okay, welcome everybody. I'm expecting kind of a mixed bag of people connected online. I know we have like eight, nine, 10 people connected online last time I checked. I'm expecting sort of a similar number in the room. People are in various degrees of comfort with Omicron seeming to maybe be hitting its crest in the Dallas Fort Worth area, but not yet really on the down slope. So let me welcome everybody virtually and in person back to the SME Physics Department speaker series for the spring 2022 series which we're kicking off today. And I'm extremely pleased to be able to introduce our speaker today. I think he's known to most everybody in the audience. This is Professor Joel Myers is an assistant professor in our program. And he is a theoretical and a data-driven cosmologist. So concern both with data and theory when it comes to understanding the large scale structure and history and potential fates of the cosmos. His research focuses on developing the means to maximize the impact of data collected by cosmological surveys, especially surveys of the cosmic microwave background, which is essentially the light that's leftover from near the birth of the universe. He earned his PhD at the University of Texas of Austin under the supervision of Professor Stephen Weinberg who were very sad to lose last year. He then went on to be a senior research associate at the Canadian Institute for theoretical astrophysics, CITA, right? CITA, yeah. Before joining the faculty here at SMU in 2018, he's the co-chair of the science council of the CMBS4 collaboration, which I'm sure he'll explain more about today, which is the next generation ground-based cosmic microwave background survey set to begin taking data around 2027. Joel has just completed and approved faculty leave granted by the university where he was intensely focused on his research. And I think we're all very excited to hear him share the work that he accomplished during that period, but also the broader context and efforts that surround everything in which he's involved. So please join me in welcoming Joel to present our first talk of the spring 2022 term. Thank you, Joel. Thank you. All right, thanks very much. Thanks, Steve, for that introduction. So as Steve said, I'm gonna talk about the research I've been doing over the last few months or so focused on the CMB. And I'll start off by saying that we're in a really exciting period of time for the field of cosmology. Cosmology has matured into a precision science over the last few decades. And yet we still have a couple of decades to look forward to a wealth of data coming in. And in particular in this talk, I'm gonna focus on the wealth of data that we expect in particular for from CMB surveys. Here's an outline of my talks. I'll start with a brief overview of what is the cosmic microwave background and how do we learn about the cosmos by studying it. I'll talk a little bit about the timeline for the near future of CMB science and what we hope to gain from the upcoming experiments. And then I'll shift to focus on one particular aspect that's gonna become an important piece of what we do with upcoming CMB surveys, specifically the gravitational lensing of the cosmic microwave background. And I'll address a few different topics associated with CMB lensing. As I'll discuss CMB lensing is both a blessing and a curse. And so I'll talk about ways we can utilize it to learn about the cosmos, ways in which it hinders our quest to understand fundamental physics with the CMB. And then also how in practice we deal with lensing at the map level. Let me start off then with an overview of the CMB. And I should say that some of this will go pretty quickly. Please do feel free to interrupt in the middle of the talk with questions if I'm going too quickly. Here's a snapshot cartoon of the history of the universe. Galaxy surveys mostly probe the structure of the universe as it exists in the relatively nearby universe in a cosmological sense. The focus of this talk is going to be on the cosmic microwave background which is the most distant and oldest light that we can observe. The basic idea here is that because light has a finite travel time, the farther out we look, the further back in time we're looking and the CMB is sort of the ultimate limit of that progression. It's the farthest away we can look because at times prior to the emission of the CMB, the universe was filled with a hot dense opaque plasma. And so the CMB really is the earliest and most distant light that we can observe in the universe. The information content of the CMB can be broken down into a few different chunks. We are looking at a snapshot, when we look at the CMB, we're looking at a snapshot of the universe as it was at the time that the universe became transparent. And so the universe was filled with this hot dense plasma. And when we look in different regions of the sky, we see very slightly different properties of the cosmic microwave background. In particular, different directions of the sky have very slightly different temperatures of the cosmic microwave background. And that reflects the density, roughly speaking the density of the plasma at that surface of last scattering. In addition to that, the CMB photons are weakly linearly polarized and we can break that linear polarization down into two different pieces. So-called E mode polarization and B mode polarization. I'll have a little bit more to say about those in just a moment. But that polarization pattern reflects the motion of the plasma as it existed at the surface of last scattering. In addition to these primary anisotropies, that is the things that are encoded on the surface of last scattering, we also get information from observations of the CMB through the influences of all the stuff that exists between us and the surface of last scattering. In particular, the structure, the cosmological structure that exists between us and the CMB deflects the paths of the photons, that's gravitational lensing, that imprints features on the CMB that we can extract and observe. That'll be a big part of the second half of this talk. But there's also the possibility that CMB photons will scatter on free electrons that exist in collapsed objects like galaxies, galaxy clusters, et cetera. And furthermore, there's emission of stuff that is in the microwave band. So galaxies, stars, et cetera, give off light in the microwave band. When we make observations of the CMB sky, we're seeing the combination of all of that stuff. Now, CMB polarization will feature prominently in the ways that we can move beyond the current state of the art in CMB observations. And so let me just take a moment to describe a little bit more detail about the physics of CMB polarization and also this distinction we make between so-called E-modes and B-modes. So first of all, linear polarization of cosmic microwave background is produced due to the existence of temperature anisotropies at the surface of last scattering. And so the little animation here is showing that there's more intense light coming from this side than from this side. And when those things impinge upon an electron, excuse me, it causes the electron to preferentially wiggle up and down and emit light that is linearly polarized up and down as it's scattered toward you out of the page here. So that linear polarization is a natural consequence of Thomson scattering in the presence of anisotropies. Now, when we measure that linear polarization across a map of the sky, we can break down that linear polarization into two different chunks. There are the so-called curl free E-mode polarization patterns which are shown on the top here. These are distinguished from the divergence free B-mode polarization patterns on the bottom here. Due to the parity properties and also this curl free and divergence free nature, if you look at a pattern of E-modes in a mirror, you get back the same thing. If you look at a pattern of B-modes in a mirror, you get back the opposite sign. Now, this distinction is really important because there are no primordial, excuse me, the only primordial source of B-mode polarization is primordial gravitational waves. And so one of the key goals of upcoming CMB experiments is the search for primordial gravitational waves by looking for this B-mode pattern of polarization, which would be a smoking gun of inflationary theories which predict the existence of primordial gravitational waves. I won't have too much to say about inflation in this talk, but this notion of E-modes and B-modes will become important in what we say a little bit later on. Now, most of the statistical information that comes from measuring those fluctuations in the temperature and the polarization can be summarized in the so-called angular power spectra. The reason for this is due to the fact that the fluctuations are linear and very nearly Gaussian. And so all of the statistical information of a Gaussian field is contained in its two-point function. And the angular power spectrum is just a convenient way to represent the two-point statistics of those Gaussian fluctuations. The way to read a plot like this is that large angular scales are shown toward the left. You can see the angular scales labeled on the top axis. Small angular scales are toward the right. And a higher amplitude of these lines means that features of that particular angular size are more prominent on the sky than others. So for example, this first peak in the temperature power spectrum indicates that there are spots speckles on the CMB pattern, sorry, the pattern of the CMB sky of two degrees are more frequently occurring than those spots of say 10 degrees or of 0.1 degrees. And you can see the power spectra predicted in a standard cosmology for the temperature fluctuations, for the emode fluctuations. And then you can also see predictions for models that include primordial gravitational waves predict a spectrum of B mode polarization. And then finally, I'll come back to this later. There's also B mode polarization that is generated due to gravitational lensing. This is predicted in standard cosmology due to the conversion of emode polarization to B mode polarization by the deflection of light by large scale structure. So what do we do with all these measurements? Well, first of all, what is reflected, the physics of what's contained in these bumps and wiggles that you see in these angular power spectra are the physics of sound waves that propagated through the plasma that filled the early universe. If you change the contents of that plasma, you change the physics of the way the waves propagate through the plasma and therefore you change the shape of these bumps and wiggles. We can turn that around and ask what were the properties of the plasma that led to this spectrum of bumps and wiggles? And therefore we can infer the contents and history of our universe. These spectra are also sensitive to the initial conditions. What did the initial spectrum of density fluctuations prior to recombination look like? And then the evolution is dictated by the contents of that plasma. Analysis of these CMV spectra has done a wonderful job at constraining our modern physical model of cosmology which has come to be known as the flat lambda CDM universe. It's a model that's defined by just six parameters. And those parameters are all constrained to better than a percent except for one of those parameters which is not so important for today's talk but it's an astrophysical parameter which is mostly a nuisance for what I'll discuss today. But the rest of the parameters are constrained to better than 1%. And it reveals a universe which is strikingly different from what we would have thought say 30 years ago. We find that the universe to accord with modern cosmology must be dominated by some form of dark energy consistent with the cosmological constant. The next most significant contribution to the energy budget is some form of non-barionic and non-luminous dark matter. And only about 5% of the total energy budget of the universe is made up of ordinary matter. All of the stuff of everyday experience accounts for only about 5% of the total energy budget of the universe. So that leaves open some pretty big puzzles as far as what is the nature of dark energy? What is the nature of dark matter? But on the other hand, this is a crowning achievement of modern cosmology. We have a very solid understanding that accords very well with the observations that we make. And this is the precision with which we measure these quantities is very largely due to the measurements that we make on the cosmic microwave background. Now I also said already that we have a lot of data to look forward to. But that data will not primarily be used to further constrain these parameters. That would be a pretty boring couple of decades to look forward to because there's not a whole lot qualitatively new that we can learn from tighter constraints of these parameters. And so looking forward, most of what we're looking at is going beyond this concordance model of flat lambda CDM cosmology. Okay? So with that being said, let's look ahead and see what are the experiments? What's the timeline? And what are the data that we hope to and what is the physics we hope to constrain with upcoming CMB surveys? Here's a pretty detailed timeline of the last few years and future, near future of CMB science conducted from the ground. I should say the results I showed here came primarily from the Planck satellite. So there's a satellite that observed the whole sky, the whole CMB sky and extracted almost all the information you can expect from the temperature anisotropies and a big chunk of what is being done by these ground-based experiments is measuring polarization for one and then measuring things on smaller scales. The ground-based CMB effort can be broken down into two geographical sites. There are measurements taken from the South Pole shown in blue and measurements taken from the Atacama Desert in Chile in green. We can further subdivide the efforts into large aperture telescopes designed at measuring the small angular scales. Those are at the South Pole SPT, SPT-3G, et cetera and in Chile Act Pole Advanced Act and part of Simon's Observatory. And then there are measurements of the large angular scales that are primarily aimed at looking for primordial gravitational waves by measuring B mode polarization of the CMB. Those are at the South Pole by Sep and Keck and in Chile Polar Bear, Simon's Array and then part of Simon's Observatory. Now, obviously we are here on this timeline and we are moving forward toward a merging of the technologies and of the teams with the future laid out to us that we will eventually combine all of these efforts and all of this expertise to construct CMBS-4 which I'll use to frame a lot of what I say in the rest of this talk. CMBS-4 is a dual site experiment. So it will contain telescopes at the South Pole and in Chile. It will have about an order of magnitude more detectors than the previous experiments. And it will allow for really high fidelity measurements of the CMB. Here is a quick snapshot of the layout of what we expect CMBS-4 to look like. So there are several different telescope designs. There are two six meter telescopes, six meter aperture telescopes that will be cited in Chile. These are of a cross-stragon design. You can see a person for scale here. And so this is the primary mirror and then the cryostats contained off to the side here, sorry. And so there'll be two of those cited in Chile. There will be another large aperture telescope of a different design, cited at the South Pole. This is a five meter aperture. It's a different design for reasons that I can discuss if anybody's interested. But one of the main reasons is that this thing has to swivel around. And if you tried to have a design like this, it would collect too much snow. So that's one of the simple reasons that you have to have a different design for the South Pole version. And then in addition to those large aperture telescopes, there are a set of 18 small aperture telescopes with three per cryostat. That's why you only see six of these ground shields shown here. And these small aperture telescopes are doing the same thing as the previous and current generation, again, looking for primordial gravitational waves by measuring primordial demodes. Now we can divide the broad, so the science program of CNBS4 is really broad and this maps pretty well to what the generations of experiments between now and the start of CNBS4 are also aimed at phrasing things again in terms of CNBS4 because that's what I'm, well, I'm the science council co-chair. So this is kind of my jam here. So there are four broad themes, primordial gravitational waves and inflation, which as I've mentioned a few times, this is aimed in particular at measuring the B mode polarization, but also of measuring primordial density fluctuations which helped to constrain inflation. There's measurements of the dark universe trying to understand the nature of dark matter, dark energy and whether there's additional physics beyond the standard model of cosmology. There's mapping matter in the cosmos which has both astrophysical and cosmological implications. We wanna find out where all the stuff is in the universe, both the mass density and also the hot gas density which is relevant for a lot of astrophysical applications. And there's another category which I won't have a lot of time to say of anything about today. It's an exciting new discovery space for CNB experiments, for CNB surveys. It's the time variable millimeter wave sky. The basic idea here of that last category is that we have instruments which will be scanning the sky, the same patch of sky again and again every day over and over and over, measuring very deep in the millimeter wave. And this allows for natural possibilities to look for things that change in millimeters in the sky. It's a regime that has not been carefully studied previously and opens up new possibilities to look for variability. This includes variability of stars, variability of galaxies, one-off events like fast radio, well, sorry, not fast radio bursts, but gamma ray bursts. It also allows us to look for things in the solar system. So for example, a hypothetical planet nine which moves across our maps would change and therefore would show up as a variable source in our maps. That's all I have to say about time variable stuff today but again, it's another kind of exciting aspect that I won't have a lot of time to touch on. Now, one of the key ingredients for the rest of the other three of these categories is going to be the focus of a big chunk of what I have left to say, which is gravitational lensing on the cosmic microwave background. So as I alluded to earlier, what we actually observe when we look out and measure maps, so the CMB is not a pristine view of the last scattering surface, but rather it's those CMB photons that have traveled to us across the whole universe. And because there's stuff that's in between us and the last scattering surface, those photons can get deflected. And in particular because the universe grew all sorts of cosmological structure, there's a big cosmic web upon which all the clusters and galaxies and everything else formed, there are the gravitational potentials of those things will deflect CMB photons. And so what we view when we look at the CMB is the lensed CMB, that is the CMB distorted by the effects of gravitational lensing. Now to see how this looks, this is a simulation performed by our own Eric Guzman of the unlensed CMB B mode polarization. You'll notice that this map is blank. So this was a simulation done with no primordial gravitational waves. And again, in the absence of primordial gravitational waves, there are no primordial B modes. So this map is blank. And on the right, you see E mode polarization. And what I'm going to do is just show you what happens when you... So this is the primordial versions of those things. What we actually see is the lensed version, which looks like this. And so there are some striking changes on the left panel where you started with no primordial B modes. You definitely see lensed B mode fluctuations. And that's due to the conversion of E modes into B modes due to lensing. And if you look more closely, you can also see that there are changes in the lensed E modes as compared to the unlensed. So if I flip back and forth, you can see that there's some subtle changes in the E mode polarization map. And if you look at specific areas, you can see, for example, at this region, the features change their size and they change their size in a different direction over here. So roughly speaking, there are various regions in the map that get magnified and other regions of the map that get de-magnified. And so this leads to a change in the statistics that we see in the CMB. And furthermore, if you are very astute, you can find actually the pattern of B modes that you get over here is some function of the lensing map and the E modes. So these changes to the statistics that result from CMB lensing allow us to infer the lensing potential, infer the lensing deflection. And so that will be important in what we say later that we can just by measuring this, we can guess that what this must have looked like, okay? Now, as I already alluded to, CMB lensing is both a blessing and a curse. On the positive side, CMB lensing, because it is due to the imprints of all the cosmological structure that exists between us and the surface of last scattering, it carries information about that structure and in particular about structure growth in the universe. So by measuring CMB lensing, we get access to information about structure growth in the universe, whereas otherwise, the CMB would only give us information about a snapshot of the universe and then the integrated expansion history. But here we actually have measurements about the structure itself imprinted in CMB lensing. So that's a positive thing. On the other hand, if what we care about is imprinted on the surface of last scattering and not in the large scale structure, then the way that the lensing distorts what we see acts as a hindrance to what we try to extract, okay? And so again, lensing is both a blessing and a curse. This will become even more true as we go to future CMB experiments. So the Planck satellite, which has made so far the best measurement of CMB lensing has detected its effects at about 40 sigma. So it's definitely detected at very high significance, but we expect that with future generations, we'll be up into hundreds of sigma where sigma's don't even really make sense anymore. It'll become an extremely important aspect of the features of the maps that we measure. And so we need to deal with lensing, both for good and for bad. And so the remainder of this talk will be focused on how we deal with lensing. All right, and so the first of these topics, I should actually pause here. Are there any questions up to this point? This was probably a very rapid introduction if you haven't seen a lot of this stuff before. Yes, Sully, that's exactly right. Oh, I'm sorry, yeah. Yeah, so Sully's question was, by reconstructing the map of the lensing, does that tell us about the density of structure that exists between us and the surface of last scattering? And so that question spot on, it's exactly what we hope to do when we make use of the reconstructed lensing maps. In particular, in this diagram, we can see that if there's a large deflection, that means that very nearby, there's a large integrated mass density along that line of sight. And now mostly what we're interested in is, well, there are exceptions to what I'm about to say, but generally speaking, what we're interested in is not so much, is there a large blob here or there, but rather what are the statistics of large blobs and small blobs? What is the amplitude of the lensing power spectrum? We're ultimately interested in the statistical information contained in that lensing. And as I'll discuss, this allows us to extract information about structure growth that impacts the clustering of matter. Good, okay. So the question is, do we get any distance information of the sources of the lensing? And if we do, how do we get it? And is it useful to have it? Did I catch anything that you... Okay. So you're absolutely right to say that the way I've just picked it so far, this lensing map or the equivalent on the whole sky contains only the integrated mass density. Now we do know a little bit of distance information because the way that things get lensed depend upon the distance of the lenses. And so there are an object of the same mass at a distance that's about halfway to us in the last scattering surface has a stronger effect on lensing than one that is either farther away or closer to us. And so we get a weak sense of where the structure is just from the lensing map. And furthermore, we can cross correlate the lensing maps with other probes that do contain distance information. So for example, we can take a lensing map and cross correlate with a galaxy survey and say, look, there's a big pile up of galaxies in the same region that we have a big lensing potential that must be due to the same large structure that formed in that region. And so in that way, you can pick out some of the redshift information. But if we're focused only on the CMB, the only information we get is a so-called lensing kernel which tells us that certain distances contribute more strongly to the lensing than others. Great questions. Thank you. Perfect. Okay, thanks. Great. Okay. So let me then move on and talk about how we can use lensing as a tool to learn about the universe. I should mention that this little section of the talk is based on a paper I wrote this fall with Dan Green at the University of California, San Diego. And for this particular section, I'm gonna try to tie it into the talk which means I'm gonna leave out most of the thrust of this paper. So I encourage you to go and look at it if you want the rest of the story. But with that being said, let me talk about how we can use CMB lensing as a tool and in particular, how we can use it as a tool to infer the physics of neutrinos and neutrino mass in particular. All right, so all sorts of things can affect the growth of cosmological structure. And these things can include physics beyond the standard model or it can include relevant aspects of physics within the standard model. I have a list of examples here, neutrino mass which would be the focus of what I'll say today. But in addition, dark energy can affect the growth of structure either due to changes to the expansion rate or the way things actually collapse and form bound objects. Similar comments would apply if you didn't believe in dark energy but you wanted to test modified gravity theories. Typically you can actually disentangle the effects of dark energy and modified gravity through their effects on things like structure growth. Dark matter interactions, either self-interacting dark matter or interactions of dark matter with baryons can affect the way that structure grows in modified cosmological models. And if dark matter is made up of axions as opposed to wimps or purely cold dark matter in the traditional sense will also affect the way structure grows in particular that typically shows up on small scales, small physical scales. There are a host of other examples. I've highlighted just a few here just to show you that I'm focusing on one particular example but there's a lot of other physics that you can extract from the CMB lensing measurements that we will make with upcoming experiments. So neutrino mass, which will be the focus of this talk or this section. So neutrino mass is a relatively novel feature of particles that we know exist in the standard model. We don't know what the mass scale of neutrinos is but we do know that they have mass and we've measured the mass squared splittings very precisely due to flavor oscillation experiments. Now measuring the absolute mass scale is a really big challenge in laboratory experiments because the effects of neutrino mass are small and the typical energy scales at which we deal with neutrinos is much larger than their mass scale. I can say that relatively confidently despite not knowing the mass scale because we know that we have upper bounds that make that hierarchy large. We also don't strictly know the ordering of the masses. We don't know the sign of one of the delta mass, delta M squareds. And so there are two options. We can either have a normal ordering or an inverted ordering, but in either case because we know the mass squared splittings we can put a lower bound on the sum of neutrino masses. Now the sum of neutrino masses is an interesting quantity for us for this discussion because it turns out it's the sum of neutrino masses that is cosmologically relevant, okay? In the normal ordering case, the minimum sum of neutrino masses when you take the lowest mass eigenstate to zero is about 60 millilektron volts. And in the inverted ordering, it's about 105 millilektron volts. So we know that a prediction of the standard model along with measurements of the flavor oscillations is that the sum of neutrino masses must be at least 58 millilektron volts. Now cosmology provides a really unique window into the physics of neutrino mass because much like the cosmic microwave background there exists a cosmic neutrino background in standard cosmology. So the same way that the photons had been in thermal equilibrium in the early universe when there was a plasma of electrons and protons, the photons rattled around and we're in thermal equilibrium with the plasma. If you, and then as the universe expanded and cooled the universe became transparent, photons were free to travel. Therefore we have the cosmic microwave background. If you run the clock back far enough to about one MEV, one mega electron volt, then neutrinos also would have been in thermal equilibrium with the plasma of the early universe through weak interactions. And neutrinos therefore would have frequently scattered, interacted, annihilated and been produced due to interactions with the plasma. And again, then as the universe expanded and cooled those neutrinos didn't disappear but rather they began to freely propagate throughout the universe. And therefore we predict that in standard cosmology there exists a cosmological neutrino background. There's a huge number of neutrinos passing through your body for every second. This very abundant source of cosmological neutrinos is particularly important because it has expanded and cooled along with the expansion of space. And its temperature today is such that at least two eigenstates are non-relativistic today. And so cosmology provides us with an abundance of non-relativistic massive neutrinos. And that's a very unique thing for neutrinos because their masses are so small that typically they're very ultra relativistic when they're produced in laboratory experiments. Now those neutrinos, those massive neutrinos which are non-relativistic today have non-trivial effects on the growth of structure. This is due to the fact that we know that they were highly relativistic in the early universe and they are non-relativistic today. And due to this they act as so-called hot dark matter. That is there are things that contribute to the matter density of the current universe and thereby contribute to the expansion rate in the same way as cold dark matter but they contribute to structure growth in a very different way due to their high velocities. Specifically neutrinos free stream out of potential wells and roughly speaking you can say that they do not cluster they do not form bound objects but rather they free stream and they kind of do their own thing. And so a universe that contains massive neutrinos will predict less growth of structure on scales below the free streaming scale of neutrinos than one that does not have massive neutrinos. In other words, clustering is suppressed compared to a universe that has no massless neutrino sorry no massive neutrinos excuse me. This suppression is shown in the statistics of the so-called matter power spectrum. The matter power spectrum by the way you can think about in a very similar way to the CMB power spectrum but the matter power spectrum is a 3D object rather than a 2D surface. But the idea is the same you're looking for the two point function of density fluctuations of the matter density throughout the universe. The effect of neutrino mass is shown here as compared to a universe that contains only massless neutrinos. And as promised you can see a suppression of the clustering which is represented by the matter power spectrum. And so for the minimum mass of neutrinos shown here in the blue line that is the sum of neutrino masses is 60 MeV for the blue line. You can see that the matter power spectrum is suppressed by a few percent as compared to a universe which contains only massless neutrinos. And again, the basic idea here is that the neutrinos contribute to the dark matter that is they are non-relativistic matter today but they're not cold dark matter they're hot dark matter and so they don't cluster the same way as the matter of the rest of the matter in the universe. And so this leads to a suppression in the matter power. So this is all great. What does this have to do with CMB lensing? Well, as we said CMB lensing is sourced by the matter density throughout the universe. And so this suppression can be viewed through any probe which is capable of telling us about the clustering of matter in the universe. There are several such probes that we have to look forward to in the coming years of cosmological surveys. This includes CMB lensing. It also includes things like measurements of the galaxy density which are biased galaxy number counts are biased tracers of the underlying matter density in the universe and also galaxy cluster counts. So big, the largest bound objects in the universe called galaxy clusters maybe super clusters if you wanna distinguish it format peaks of the density field. And so they tell us about the clustering of matter as well. What's being shown in this plot is the way in which these various observables CMB lensing measurements of the galaxy density and measurements of galaxy cluster counts probe the matter power spectrum as a function of redshift which corresponds to distance or time and also as a function of wave number or length scale. So small scales are over on the right, large scales are over on the left. This purple line denotes that free streaming scale which in this plot is this vertical line at redshift zero. So we should look for a suppression to the right of this line as the signature of neutrino mass. And so we want to look to the right of this purple line to look for a suppression. There's one more line I wanna draw your attention to which is this sort of dark red line here which denotes the scales where the fluctuations are linear where we can make prediction, definite predictions of the fluctuations without doing simulations we can basically do it analytically. And then to the right of this line we have to worry about non-linear corrections due to non-linear structure growth due to gravity and then also baryonic feedback effects that come from things like supernova feedback, AGN, et cetera that can affect the matter power spectrum. That's kind of a subtle issue that I'm glossing over but feel free to ask questions about it. The basic idea that I want you to take away from this is for the purpose of this talk that CMB lensing gives us a lot of weight for measuring the matter power spectrum in a regime that can reveal information about neutrino mass. Specifically it gives us a lot of weight between the free streaming scale and the non-linear scale where we can trust our calculations and where neutrino mass has suppressed the growth of structure and it does so over a wide range of red shifts. And so CMB lensing is a good place to look for neutrino mass for the effects of neutrino mass, okay? And to be a little bit more specific here is a forecast of the uncertainty with which we will measure the CMB lensing power spectrum with an experiment like CMBS4 shown for the suppression expected to the CMB lensing power spectrum from non-zero neutrino mass and in particular from the minimal 58 millial electron volts of the sum of neutrino masses. So again, you can see that there's a suppression on the order of a few percent due to the fact that neutrinos don't cluster but they do contribute to the expansion history, the expansion rate. And we can see from this plot that CMB lensing from CMBS4 will measure at very high significance this suppression. And so CMB lensing gives us a window into this effective neutrino mass. Now, as I said, the point of this paper that I'm referring to here actually goes well beyond that and focuses on how a measurement of neutrino mass that would be consistent with this minimal set of masses has really broad implications beyond just the particle physics of it. This would be a very powerful end-to-end test of Big Bang cosmology. The thermal history that went into this story would have to be accurate at the level of a few percent all the way up to one mega electron volt which occurred at a time of about one second as opposed to the fraction of an electron volt and 380,000 years at which the CMB formed. And so a measurement of neutrino mass, if it's consistent with what we expect for the minimal mass of neutrinos and the standard model predictions gives us a very thorough test of cosmology and actually very strongly constraints beyond the standard model physics. Okay, so that was CMB lensing as a tool but CMB lensing can also be a nuisance. It hinders our pristine view of the surface of last scattering. And in a paper that I'll now describe done in conjunction in particular with Cynthia, either in the audience focuses on why CMB lensing is a hindrance for certain things and how by reversing it, reversing the effects of CMB lensing we can improve the precision with which we can do various cosmological analyses. So the basic idea of this aspect of the talk is that the change to the statistics that I discussed earlier that appears at the map level allows us to reconstruct a guess at the CMB lensing deflection. Once we know that CMB lensing deflection because we know the physics of lensing we know how lensing works we can reverse engineer what were the fields when they were unlensed. And in particular in this paper we actually explore how iterating this procedure improves these constraints, improves the fidelity with which we can reconstruct things. So once you've delens once you've taken your best guess at what the primordial maps would have looked like you can repeat this process and take another guess and say what is the residual lensing left after the lens? You can continue this process until things converge and improve your guess. What we actually do in the paper focuses on doing this process at the level of the power spectra. And we do that to show what the effects are without actually having any need for the maps. We don't need to simulate anything we don't need to have real data in hand but we can demonstrate what is the value of the procedure that I'll discuss. So delensing has a very wide array of benefits. One of them is that it sharpens acoustic peaks. Remember acoustic peaks refer to these bumps and wiggles that appear in these power spectra. Lensing has the effect of smoothing out those peaks making them less prominent. And the reason for this can be pretty easily understood. If you have a sharp feature in the power spectrum that corresponds to something that happens on a particular angular scale because lensing has the effects to magnify or demagnify different parts of your maps, that effect will appear at different angular scales if it appears in a magnification or demagnification region. And so statistically that will blur out what was once a sharp feature. So lensing smooths acoustic peaks. Undoing the effects of lensing reverses this and sharpens acoustic peaks. Sharper features are easier to measure. And so that is a benefit that you can more easily extract the positions and heights of these peaks if you de-lens. And this is showing that quantitatively that if you de-lens, you get smaller errors. So this is the error on a particular feature as compared to the error if you do nothing. On the left panel, you see peak positions. That's the angular scale at which a given feature appears. On the right, you see peak heights. How high is a given peak? And so smaller numbers are better. And you can see from this plot that de-lensing improves your ability to constrain the angular scales and heights of acoustic peaks. De-lensing also improves your ability to reconstruct lensing. Now this sounds a bit weird. How can it be that by removing lensing you can better measure lensing? This basically comes down to this iteration idea that I was discussing. So by iteratively improving your guess of the residual lensing after you dig out the lensing you can actually show that you get improved measurements of the lensing reconstruction. And this is showing how that works in our iteration scheme as compared to some other iteration schemes. This by the way has been tested against some map-based procedures and it matches really well. So this is a fairly technical issue that I might skip for the interest of time. The very quick version is that in the absence of lensing you can treat every scale of the angular power spectrum different L's as being completely independent. In the presence of lensing that's no longer true because in part of this blurring effect that I talked about, de-lensing removes that blurring effect and therefore makes the scales independent again. This simplifies analyses allows for tighter constraints on certain parameters that I won't discuss. Okay, so that's great, but you might be asking why do you care? Why do we care about doing all these things? Where the rubber meets the road is that at the end of the day you can get tighter parameter constraints by de-lensing. So for example, these are just some specific parameters. This is the so-called angular scale of the sound horizon at the surface of last scattering. It corresponds, if it's a specific parameter in the CDM to guide your eye. So on the horizontal axis is the noise level. This characterizes basically the depth at which a given CMB survey observes the sky. Simon's observatory falls roughly at five micro K arc minute on this scale. CMBS four falls roughly at one micro K arc minute. And so the idea here, oh, and sorry, the vertical scale is the error on any of these given parameters. If you're just trying to measure this parameter with Simon's observatory and then you add a bunch of detectors, you add a factor of 10 more detectors observed for seven years, that will bring you down to here and improvement roughly speaking on the order of 15%. However, if you just work with Simon's observatory data and you de-lens, that is just take the data you already have and guess what the lensing spectrum, what the lensing map looks like, undo the effect of lensing, our analysis says that you'll improve by a factor close to 30%. So at no additional cost to the experiment, just analyzing the data in a different way, you can get a bigger improvement than you would by spending hundreds of millions more dollars to try to achieve the same thing. There's one more aspect that I was going to try to touch and I think I'm gonna have to skip it in the interest of time, but it's very interesting. The last thing I'll say is, so I've said a lot about why you might hope to measure lensing and why you might hope to remove lensing, but I haven't said much about how you do any of this. So as a practical matter, we need to address the question of how do you analyze the CMB lensing in the maps that you actually acquire? And what I'll mention in this section relates to a pair of papers that I did with my grad student here at Guzman, here at SMU, of a machine learning approach to identifying and isolating the lensing in CMB maps. Now I should say that with current data, the problem of reconstructing lensing is basically solved. In the near future generation of CMB experiments, we have pretty good strategies for both getting a good lensing measurement and doing the delensing to the fidelity that we require. However, at the CMB S4 type noise levels that we expect in five years, we have more work to do because lensing will be a much more prominent feature and because other things start to become important at the same noise levels. In particular, if there are other sources of statistical anisotropy, that is other sources which cause things to be distorted on the CMB photons paths towards us, those effects can get confused and can interfere with one another. So for example, patchy reionization may lead to such a statistical anisotropy. So first of all, what is reionization? Reionization is the process by which the universe transformed from a neutral hydrogen gas to being in the ionized state that we observe it now. This process unfolded due to the turning on of the first stars and galaxies that caused the neutral gas that filled the universe and the dark ages to become ionized. And it happened in a way that is not totally uniform. Because it's not totally uniform when you look at different patches of the sky, you see different effects of reionization. In particular, the presence of free electrons that result from reionization have different densities along different lines of sight. And that patchiness in the reionization process leads to different amounts of modulation of CMB fluctuations in different directions in the sky. And that also leads to a change of CMB statistics in a way that's very similar to but distinct from CMB lensing. Another such example of this is so-called cosmic polarization rotation. This, the basic idea is that when you look in different directions of the sky, it may be that polarization vectors are rotated. This can happen for a number of different physical reasons. One is if there is primordial magnetic fields that cause Faraday rotation of polarization vectors. Another possibility is an example from physics beyond the standard model. If there were an axion that coupled to photons existing throughout the universe and if that axion field, excuse me, changed its value throughout the history of the universe that would cause left circularly polarized photons to propagate at a different speed than right circularly polarized photons, a concept known as cosmic birefringence. And that would also imprint a statistical anisotropy much like lensing, though distinct in its effects. Now, if you want to try to search for these things, lensing becomes a challenge because the way that you search for these things would be the same basic idea of the way you search for CMB lensing. You look for a change to the statistics of the CMB maps that you observe. But because lensing is a much larger effect, you have to deal with the fact that lensing is there and try to extract all these things simultaneously. This is the type of problem for which deep learning is very well suited. Deep learning is capable of doing these nonlinear, non-Gaussian statistical problems all at once. And that's what Eric and I did in this pair of papers. So here is, so Eric built this deep learning network which we call Resinet CMB. Here's a snapshot of the model architecture. The basic idea is you pass in for now simulated polarization maps of the CMB and it spits out an estimate of the lensing potential, the modulation field and the unlensed CMB polarization maps. And then similarly, we extended this in a second paper where it can also do the cosmic polarization rotation field. And it does so very well. In particular here, as an example of some of these maps, some of the outputs of this Resinet CMB network, showing that it does an extremely good job at reconstructing the primordial CMB that is removing the effects of lensing and in this case, modulation. It does a very good job of reconstructing the lensing. And it does, even though it doesn't look like it, also a very good job of reconstructing the modulation. Here you might say, oh, this doesn't look anything like this, but this is due to the fact that this signal is inherently small. And even though it doesn't look very impressive at map level, this is the best you could hope to do, as I'll show here at power spectrum level. There's an additional complication when you're trying to reconstruct modulation due to the fact that the effects of lensing are not totally independent of the effects of modulation. And so not only is the lensing a contaminant for your signal, it also biases the signal that you try to extract if you're looking for modulation. And what we're showing here is that Resinet CMB both avoids this extra variance, as you can see by the difference between the dashed red line and the dotted red line. And it also avoids, mitigates this bias due to lensing, which would result if you use standard techniques, techniques which is shown in this light blue line. The quick takeaway is that the best you could ever hope to do is this dotted red line and Resinet CMB performs in this dark blue line. And again, even though it's above the signal, you can see that this would allow for a statistical detection of patchy realization, which is the best you could ever hope to do. And so this network, this machine learning network is performing nearly optimally on this very complicated inference problem. Similar statements apply for the reconstruction of cosmic polarization rotation. Again, the best you could ever hope to do is this dotted red line or approximation thereof. And the blue line shows what Resinet CMB does as compared to standard techniques which are shown in the dashed red line. And so again, Resinet CMB is performing nearly optimally for this very complicated inference problem. Okay, so let me summarize. So cosmology and CMB science in particular is at a very exciting point. We have a lot to look forward to with the wealth of data incoming from future surveys. Gravitational lensing of the CMB presents new opportunities and also new challenges with the next generation of CMB surveys. It's a blessing in that it allows us access to the structure growth of the universe from measurements of the CMB, but it also hinders our pristine view of the CMB. And so removing its effects can also be useful. And I showed a machine learning network that's capable of doing some of those things along with reconstructing other secondaries at the same time. So I will stop there and I'm happy to take questions. Thanks very much. Sure. The podium, Mike, yeah. Okay, so we have time for questions here. I was gonna start and see if anybody online had a question since no one from the online contingent took advantage of your previous request for questions. So I'm looking for hands being raised here. Okay, I don't see anything. So from the room, anybody have any questions in the room? Oh, yeah, sorry, Kristen. Thanks, Joel. This was really nice way to finally understand something that I've sort of halfway understood for a long time. I'm curious when you talk about massive neutrino suppressing clustering, a lot of intro cosmology classes use the existence of substructure in halos like dwarf galaxies as evidence against hot dark matter. But what you're talking about here is something else, right? It's not quite that dark matter is neutrinos, but that neutrinos behave like hot dark matter in that they, is it that they free stream out and take mass out of the potential, which smooths it out to some extent and prevents clustering or what is the mechanism there? Yeah, so great. So that's a really good question. Hot dark matter has a similar effect. If all of the matter, all of the dark matter were hot, what you'd expect in a plot like this is a very sharp suppression of this matter power spectrum below some scale. What we see from massive neutrinos is a few percent suppression below some scale. And so the reason that this is only a few percent is that massive neutrinos make up only a very small fraction of the total matter density today, even if they're very massive. In other words, we know that there exists a form of cold dark matter in addition to neutrinos. Neutrinos cannot make up the total of the dark matter, but you're exactly right to say that warm dark matter is measured in a similar way and it would also show up in CMB lensing. The way it would show up would be a much, much starker drop on a much larger, more prominent scale in this kind of fall. So the mechanism by which then that massive, a more massive neutrino would suppress clustering would be that it carries away its mass out of the potential well and prevents clustering in that way. That's right, so exactly. The warm dark matter or neutrinos do not cluster. And so their mass density does not contribute to the clustered fraction, but their mass density does contribute to the expansion rate. And therefore you get this summation. Okay, thanks. Okay, let me see if we have any questions online here and then I'll come back to the room again. Oh yeah. Is that Richard? Yeah, go ahead. Does the d-lensing is always treated as a one-time effect or do you include multiple lensing? Good, so there's a couple of levels at which you might be thinking about the effects of lensing. We iterate the procedure of d-lensing, but we treat lensing in the regime that only single deflections are important. So to use a technical term, we are treating lensing in the borne approximation, but we iterate the procedure of d-lensing to remove lensing. So to come back to my cartoon of lensing, you might be worried about the fact that there are multiple deflections along the line of sight. This is a drastic exaggeration of the size of the effect and so-called post-borne corrections to the lensing are negligible across most scales. They do become important post-borne corrections or multiple deflection scattering becomes important at very small scales, but those are scales smaller than the ones that are important for the reconstructions I've talked about here. The origin of the question was essentially the time dependence in a sense at universe expanse. So the probability of the density of large density, fluctuations probably decreases with time, isn't it? Oh, good. So structure becomes more and more non-linear at late times, but it does get farther apart. So if we were to ask a civilization in the very distant future, would they have to worry about post-borne corrections? The answer is more likely, yes, because there are more non-linear fluctuations and more prominent scattering effects would be likely to appear in your lensing maps. So in other words, we live at a time in which the multiple deflections are unimportant, but say 15 billion years in the future, it would become important that those effects are included. Thank you. Okay, any other questions? Oh yeah, Zoe. So my question relates to how you were doing your neural network construction. You were trying to reconstruct the different structures that you had. So the lensing and the different polarizations, but if I were to try to make an autoencoder like this, I would train it on a set of dogs or not dogs, but to figure out what you wanted to do like this in terms of anomalies, but if you only have technically one picture, like we only have one cosmic ray microwave background, how did you determine a proper target to then figure out how you can reconstruct what you're trying to reconstruct? Yeah, good question. So the training is done on a very large data set, but you're right that at the end of the day, all we have is one set of CMB maps. And sorry, just to be a little bit more specific, Eric simulated a very large collection of both truth maps, the outputs and inputs, the lensed, modulated, rotated CMB maps. And so for every step of the training, the network got these inputs, this mimicking what we would observe, and it got the output so it knew what the truth was. And the learning takes place by making adjustments to the parameters that define the network until it can accurately or as accurately as possible, take a given set of inputs and make a prediction that matches closely to the truth. But you're absolutely right to say, in the real world, we only ever have one set of maps. And what we really need to understand is how to quantify the uncertainties of the predictions. We get a, so far the network as I've described it gives a point estimate. It gives, in a formal sense, it gives what it thinks is the maximum likelihood estimate of these quantities, of these maps. The next step of what Eric and I are working on is actually addressing this question of the uncertainties. There are ways we can do it with this network, but it's not ideal. And so we're working to improve the uncertainty estimation that comes out of a network like this. Okay, so the data that you're training on is mostly simulated. So you would know the structure of how it would create lensing. That's right. Okay, that's what I was worried about. Yeah, exactly. So everything is simulated, both the inputs and outputs are simulated for what we've done so far, that's right. Yeah, so then if you were to look at the CMB, then you could figure out your structure based on how well you know your simulation to work. That's right, that's right. So yeah, you're touching on something which is important in all machine learning tests. Of course. Which is you only trust the outputs in so far as you are confident that you've modeled all the uncertainties that may arise in real data. And so if there was something that was surprising in the data that mimics the effects of say, lensing or of modulation, that could potentially be a pitfall for our machine learning methods, that's right. Okay, thank you. All right, and I will do two more questions or comments. The first one from Roberto online. Go ahead, Roberto. Oh, you may be muted, Roberto. Sorry, sorry. Perfect, yeah, no problem, we all do it. Gerald, thanks for this wonderful talk. I had two related questions on the neutrino suppression of clustering. Isn't that a function of the abundance of the neutrinos and dependent on the mass of the neutrinos? How do you estimate that? Yeah, good question. It is indeed a function of the abundance, but in standard model cosmology, there is a definite prediction for that abundance. It's parametrized by a quantity we call ineffective and it's predicted in standard cosmology to be exactly, or not exactly, but very, very close to 3.046, which roughly corresponds to the three families with some non-thermal corrections. But you're absolutely right that a non-standard thermal history could in principle change that density and therefore change the suppression and that relates closely to what I was saying that if we are to measure the suppression that matches with the standard model prediction, it gives a very comprehensive end-to-end test of big bang cosmology. Very good. And the other question I had was, these neutrinos are massive, then they would have a magnetic moment which would then give you neutrino photon interactions that could affect these neutrinos coming from the cosmic wave background. Has anybody looked at that? There have been studies of like large magnetic moments that is enhanced beyond the prediction you would make in the standard model. And those things lead to non-trivial effects. So for example, if that coupling is large enough, you get predictions which differ from what I've said here, not so much in the neutrino mass, but it shows up in the way you would expect to measure ineffective from the CMB. And so it changes, I probably don't have a good image to show you, but it will change the T and E spectra in particular in this high L or large, sorry, small angular scale region. Okay. You have references on that? You can share with me? Yeah, absolutely. Okay. I'll email you. Okay, perfect. Okay, very good. All right, and then we'll do our last question or questions from Pavel. So Joel, actually very good that you pulled out this slide. And by the way, thank you for this talk. So you mentioned that there are improvements from using neural nets and deep learning in reconstructing the multiple moment dependence. What, where do you see the major promise of this new technique? For example, if you look at this plot, what do you expect to learn better using this new technique that is based on the CMB for which multiple moments, for example, or which physics issue that you will be able to address? Yeah, good question. So yeah, where are the benefits from something like machine learning? So one place on this plot that it would show up would be in removing this green line, which serves as a contaminant for measurements of these blue lines. Now we have, sorry. So yeah, we have some techniques to do that. Machine learning may improve, well, it does improve upon standard techniques like the basic standard techniques to D-lens. And then furthermore, D-lensing can also be applied to these high L, in particular the high L regimes of the T and E modes where what's shown here doesn't really demonstrate very clearly, but lensing kind of cuts off this exponential suppression due to the transfer of power from large scales to small scales. D-lensing can also help to dig down into the stamping tail. And that's particularly useful for measuring quantities like N effective, which I brought up in response to Roberto's question. And so that's another region that it might help for primary CMB science. But realistically, probably the better use for it is the simultaneous reconstruction of other sources of statistical and isotropy. And the reason I say that is there are other techniques, there are existing techniques, which are roughly speaking, people have more confidence in because people get worried about the black boxes that sort of inherently enter when you use machine learning. And so if lensing is the only problem, then I don't expect machine learning will be the primary way in which we deal with it. Though I think work by Eric has shown that it's a viable path that could actually be adopted. Okay, thank you. Thanks. Okay, and do you have time for one more question? Yeah, sure. Okay, then I lied to everybody. Let's do one more question. Suzanne, you had your hand up, then down, then up, then down. Do you wanna ask a question? Yeah, sorry. Yeah. I had a question about if the real world CNBC data is blinded to the neural net or not, or is it partially blinded? Yeah, good. Right, so the real CNBC data would never be used in the training. There are a few exceptions to that, which would I think probably not make it a true blinding. So specifically, what you can see in these simulated data are that we've applied kind of a smoothing on the edges of these maps. Now real CNBC data will have similar features due to the way that we cut out contaminants. And so for example, we observe across the whole sky, but regions that look through the Milky Way galaxy, we remove from our data because there'll be all sorts of stuff that we don't want, non-CMB emission that we want to remove. And so those cuts would show up in whatever CNB maps you have. And so it might be more worthwhile when you're training a network to make sure it works on the sky cut that you actually hope to use in a real analysis. And so that's not a totally necessary thing to do. You could imagine training on a different random set of sky cuts and make sure it works on anything. But I could imagine things like that showing up in your training where you use the same sky cut that you hope to use to make sure that your network is optimized for that cut sky. Similar other observational effects like anisotropic noise that matches the experiment would probably also show up in a pipeline that use this on real data. But you don't actually require the real data for any of those things. What you require are simulations of what you anticipate getting from the real data if that makes sense. Okay, thanks. Okay, all right. Well, thanks everybody. Let's go ahead and thank Joel one more time for his presentation today and we'll close up the event. Okay, you're all free. Enjoy your Monday evening. Thanks everybody. Thanks to folks online as well. Thank you.