Do You Fall at The Same Rate as Your Mirror Image?

STEPHON ALEXANDER: I'm going to ask this question, why parity? Why do we care about parity? And of course, what is parity? OK. Why do we care about that question? But to motivate all this, I want to make sure that we're on the same footing here. I know we have some physicists in the audience. So this talk is not really geared for you. It's geared for really smart people who want to get some footing on what the standard cosmology is and how that jibes with observations. Why could we make statements like the universe is expanding at this given rate? Do we have observational wiggle room to make any other statement about the universe as it stands today? But then part of this motivation is to show that our standard cosmology works pretty well. It really works well-- meaning the theory that I'm going to talk about here, works really well in the face of the precision data that we have. But there are problems. And these problems are actually mainly theoretical problems. And then I'll talk about something that you've all probably heard a lot about-- cosmic inflation. And how cosmic inflation alleviates some of these problems. But I'll point to yet another problem with cosmic inflation. And then I will bring in this original question here, why parity? And then hopefully there'll be time to talk about this. I will talk about the Baryon Asymmetry Problem. In a sense, that's the problem. OK. So what do we mean by this Baryon Asymmetry Problem? I'll introduce that idea. And then I'll provide a mechanism that will be related to this question about why parity. And then I will end, not with necessarily a conclusion, but with some open-ended questions. So first of all, why do we care about parity violation? Well we have to go back to like 1956. Before 1956 we knew from experimental data that the electromagnetic interaction and the strong interaction, for example, basically had the following feature. If I study the physical system in a given frame of reference, in this case-- if I study, for example, the decay of a particle called the pion so the pion is a particle that's made up of two quarks. It's a balancing of two quarks. And this pion has zero spin. And hence, it doesn't have a preferred handedness. So when we talk about the handedness of a particle, we're really talking about throwing a football. If I throw a football with my right hand, and it spins and goes in the same direction to you, versus throwing it with my left hand, and this goes in the same direction, this quantity, the product of the spin and its momentum towards you is a quantity called helicity. So I can have left-handed helicity and right-handed helicity. And that's what we mean by handedness here. So now the pion is a particle that actually has no spin. But when it decays it produces two particles with a spin. So a pion could decay into a heavy version of the electron, call a muon. And that has a given spin. And the other particle we'll produce is something called a neutrino, which is a chargeless particle with spin as well. And so because the spin is conserved, meaning that it had zero spin, the product of the spin of these two particles that are left have to add up to be zero. And it turns out that if I look at this particles that have zero spin and decay into particles with opposite spin, the electromagnetic interaction and a strong interaction will produce particles of equal spin all the time. That's what we mean by parity symmetry. The handedness of the system-- if I change it from a left-handed system to its mirror image-- the probability of those particles decaying in one handedness is this is the same as it decaying in the other handedness. OK? That's what we mean by parity symmetry. And so all of the interactions were thought to actually obey this basic symmetry of nature. For any laser physicists here, you understand that also in an atomic system, this is the case as well. These are what we call selection rules. Now Lee and Yang realized that when they looked through the data, there was no statement about the weak interaction. This is the interaction that's responsible for something called beta decay. And what they realized was that since there was no data, they should not assume that parity is violated. And they propose an experiment. And the result of that experiment, done by Madame Wu at Columbia, won them the Nobel Prize. So let me explain what the experiment is. So what we're looking at here-- where's the pointer? I guess I don't need it. So what we're looking at here is the following thing. We're looking at a neutron that's made up of three quarks. It's made up of an up quark and two down quarks in a balanced state. And this neutron would decay into a proton. And in doing so it releases, it emits, the carrier of that force, which is something called a W boson. It looks like the photon of a the weak interaction. And also produces an electron and an anti-neutrino. So let's look at this interaction here. We have an up quark that becomes a down quark. So that's here. Once that happens, the neutron becomes a proton. And when the up quark becomes a down quark, it emits this photon-- this W boson-- and then produces an electron and an anti-neutrino. This is a mistake. This should be a bar here for the anti-neutrino. If I do this experiment, and I look at these electrons being produced as pions as a neutron becomes a proton-- and this experiment's really carbin 60 becoming nickel 60. OK? If I look at this process, and I look to see the mirror image of this process, it'll now produce a right-handed electron and a left-handed anti-neutrino, I never see this. I only see this result. So the mirror image of this interaction-- here is the mirror image-- does not exist in nature. And at the time, we didn't have the theory for that. And the triumph of the standard model of Glashow Weinberg and Salaam, was figure out what that theory is. OK. So everything you hear about the Higgs particle, that's all part of the story. Why is it that nature does not have this? So today we find ourselves in a similar situation that, when I was a post-doc, we realized that we never did this test for gravity. So we now have to ask ourselves, what are the experimental situations that we find ourselves in? And gravity-- or apply general relativity, which is cosmology, to explain this. And that's sort of the motivational aspect of this talk. So for those of you who are string theorists in this audience, there are some aspects of this talk that does hinge on String Theory, but it's not necessary. OK. So I'm here to tell you that I'm a friend of the String Theories, but I'm also a friend of other people, other approaches as well. You've got to be friendly to everybody. Hi, my friends out there in string land. OK. All right. So now I want to put everything in a cosmological context, so let's move on. So the thing I want us to take away here is that cosmology is nothing more than applied general relativity. So I'm going to explain that to you. So the discovery of general relativity basically says that we should no longer think of space and time as this empty stage that we move about. It is dynamical as we are dynamical. We move-- we are able to be attracted to objects gravitationally because space does bend. So because of the dynamics of space, this happens. And this happens because of something called the Einstein field equations. I guess I can't write it [INAUDIBLE]. So the Einstein field equation, which is a set of field equations like electromagnetism-- electromagnetism tell us how the electric and the magnetic field bends in the presence of electric or magnetic sources. Likewise matter and energy sources, like planets and stars and black holes, likewise there is a set of fields that bend. And that field is a field of space and time. Sometimes we call that the metric field. OK. So there are consequences for this in cosmology because we can apply the Einstein equations to the entire space-time of our universe if we know the distribution of matter in the universe itself. So the big game in cosmology is to first of all measure that and make a couple of assumptions. And I want to tell you what these assumptions are. So what is standard cosmology? Standard cosmology are these three pillars. Two of these pillars are observational, and one is theoretical. The first pillar is a cosmological principle which basically is a beefed-up version of the Copernican principle. We are not special. Every point in the universe looks the same. Every direction in the universe looks the same. That's basically a symmetry principle. And we now have observational evidence of this principle. And we'll talk about that in a second. Is it really the case that the universe does look the same at all vantage points? And then the second principle is the Hubble Law, which tells you that if I look at galaxies far away from us, galaxies further away from us move faster than galaxies closer to us. And they themselves move at rates proportional to their distance from each other. And if I combine these two ideas, these two principles, and I use Einstein's field equations for the dynamics of space and time, which are ten [INAUDIBLE] non-linear differential equations, I find that that theory, this mother theory, spits out one unique solution, [INAUDIBLE] topology. So there's one unique solution for the space-time for these two pillars. And that's an expanding or contracting homogeneous and isotropic space-time. So let's turn to this little cartoon here. Imagine at the surface of this balloon, I tack on a coordinate system at every point on the surface. So I have XYZ coordinate system at every point of that surface. And then someone starts blowing up this balloon at a constant rate. So if I'm a galaxy here, and I look at this other galaxy, and this is the radius-- this thing I would call a of t, if a of t starts growing at some rate, I will actually see-- even though I feel that I'm fixed in my own coordinate system I will see another galaxy move away from me. And I will see another galaxy that's further away from me move faster because of the angular velocity. The tangential velocity at the point of the surface here. And what I've just shown you there is nothing more than the solution of the Einstein equations. What I've shown you there is the fact that Einstein's theory predicts actually that our universe actually is this situation. It's expanding in four-dimensional space-time. Or three-dimensional surface embedded in the four-dimensional space-time, where a of t is what we call a scale factor. And it's expanding. And the natural consequence of this is that we are co-moving with this expansion. And the natural consequence is that we will see other objects moving away faster the further they are from us. So that was the first triumph of the Einstein equation. Physicists immediately jumped on the bandwagon and started doing more calculations. They realized that actually there's a thermal bath there. So the universe is very hot and dense. And therefore the hotter it got, then all of the matter will ionize. All of the atoms, including hydrogen, will ionize. And the universe will find itself in a state. In fact if you do this calculation, 300,000 years after this initial time, that you should actually see the formation. The universe cools. And then I'll see at some time, as the universe cools, I'll reach the ionization energy of hydrogen. An electron will bind to the proton. It will scatter photons. And that photons will actually be in equilibrium with that situation. And there should be a relic thermal energy associated with that. And so it predicts something that we call the cosmic microwave background radiation. So physicists were looking for this background radiation as a consequence of this expanded space-time. And lo and behold-- 1967. So before I tell you about 1967-- so the picture we should have now is that at some earlier time-- I won't talk about this T is equal to zero. That's another talk. I could come back and talk about that in future, if you want me to. But what this theory does predict is that a universe filled with radiation will form hydrogen for the first time. And there'll be a relic background radiation that we can look for. And this actually has a particular spectrum. And it's a perfect black body spectrum. Two things to keep in mind. As the universe continued to cool, some of that stuff clusters and forms galaxies. So in 1967 this was measured. The Nobel Prize was given to it. And this was what was measured, where like a chicken inside of an egg, we've cut the egg in half and opened it out. And we're looking at at that time, 300,000 years. And we see exactly this radiation. And of course we saw more things. We saw deviations from that average temperature. Hot and cold spots correspond to troughs and peaks in the sea of this radiation. Because there's an average temperature, and then there are these fluctuations. Today we're going to talk a lot about that fluctuation. This is the WMAP satellite. I was fortunate enough last year to hang out with the WMAP group at Princeton on sabbatical and got intimate with this data a little bit, although I'm a theorist. What we're looking at here is a prediction from inflation. We'll talk about inflation in a second. So the red line is the power spectrum, or basically the Fourier transform of those dots, those undulations. OK. This is wavelength. So we're looking at the relative sizes of these fluctuations. And we're comparing them to each other in the sky. And we are looking at how similar or different they are from each other. And the prediction of inflation, which we'll talk about in a second. And the black spots is the data. So this is the best fit to the data using four parameters. And this is something called the power spectrum of the polarization of the photons. So this is kind of cute. You can actually associate these fluctuations with acoustics. So this is literally an acoustic peak, if you think in terms of sound, for those you who are more comfortable with sound. If I play an instrument, the instrument resonates at different frequencies. But there's always an acoustic peak associated with the length of a flute, for example. I bought my soprano sax here. And it turns out that the universe has that characteristic size. So from that peak we can deduce the size of the universe at that time. Coincidentally it's just an A note 50 octaves below middle C. And this is the latest and greatest, the Planck data satellite. And we are currently analyzing that data as we speak, we the community. And the Planck data is consistent with the standard model that we have. There are some anomalies, but that's not the purpose of this today. But it is interesting. So what do we learn from this data? We can look at this data, and we can see that some weird things happen. What we thought that was so special about us turns out to be-- so I always like to tell people if you ever felt like you were never a minority, this is the time to feel like you're a minority. Because this is you, all right. We are a minority. We share that in common. We're a minority in the scheme of the universe. These dark guys here are the majority. And we have no idea what this is. People say various things. There's "Discover" magazine article that came out on dark energy this month. And I was quoted at the end with my own crazy theory. I regretted actually interviewing with "Discover" because now all my colleagues think I'm even more of a crackpot. OK. [LAUGHTER] STEPHON ALEXANDER: OK. And so I won't talk about these things today. I'm going to talk about actually-- I'm going to give you the Minority Report. So who ordered that? I mean, who gave us this kind of universe? So my friend and colleague Sean Carroll wrote a book, a paper called "A Preposterous Universe" because it is preposterous. We always thought that we were the main stuff. So as I said, we have this standard picture of the universe that, as I said, these three pillars predicts an expanded universe with the features that we see in this cosmic microwave background radiation. It predicts that relic background radiation. We went and looked for it. All right, this was done by Gamow-- George Gamow and Fred Hoyle and people like that way before the '60s. And we found it. So we had a model that explained the Hubble Law but also predicted this cosmic microwave background radiation. But what it did not predict were these fluctuations. What it predicted was the smooth and featureless universe that's expand. But unfortunately we are those very wrinkles in the universe that made the standard cosmology a limited model. We need to explain observationally why these fluctuations exists. Because those are the things that grew into the structure that we see today, meaning galaxies, clusters of galaxies, so on and so forth. But there's actually a much more serious problem. So we can summarize the expansion history of the universe with this Penrose diagram. So a Penrose diagram is a conformal map that allows me to freeze out the time expansion and look at the expanding universe as a set of forward and backward light cones. So in other words, let's look at it the following way. If I'm looking back at the past, it's like me shining light on the back. Because meaning, the fastest anything can travel is with these photons. These photons will disperse out. OK, I'm just giving you an analogous picture here. And so there'll be a limitation, at the end of the day, how far those photons went back. If they're traveling at the speed of light, they can only cover but a certain amount of distance. OK. What is that distance? That distance is its velocity, which is the speed of light divided by the time of flight. I'm sorry, the velocity-- the time of flight is the distance divided by the velocity. OK. So in other words, there's a limitation as to how far back we can see. So when we look back at this cosmic microwave background, we're looking far back as light could travel to us. And we see something very weird. What do we see? We see that the temperature at antipodal points of the sky have-- the photons have exactly the same temperature. Well those who took thermal physics know that for something to reach equilibrium, you must have scattering. You must have interaction. But we know that interaction are limited by causality. OK. You need causality for me to bump into you. But we're talking about photons here. So that means that any other point at the back, the light cones is of maximum distance this photon can travel. So this photon has the same temperature as this one. But there's no way they could have been in causal contact. And this is actually an internal inconsistency with the expanding space-time. So while it predicts this one thing, it has the seeds of its own destruction. And cosmologists basically swept this under the rug, until Alan Guth came along. Alan Guth is actually one of my mentors. And coincidentally occupied the same office when he was at [INAUDIBLE] and came up with inflation. So I had this idea, I have to live up to his legacy. And I never did. I just happened to work on his theory more. So the basic idea of inflation is to solve this problem. This is what we call the horizon problem. OK. How it is that these photons can communicate with each other when they didn't have time to do that? They need to do that because we see that they have the same temperature. So Alan Guth had a really simple idea-- that assumes that the expanding universe expanded at the same rate at all times. So Alan just said, oh, we can fix this problem. Let's start off with a tiny patch of space-time, very tiny, microscopically tiny. OK. I don't know, very tiny. Sub-Fermi scale. Less than 10 to the minus 15 centimeters. A little tiny piece of space-time. And let's assume that that space-time had something with the same property, some form of energy with the same property. So there's no horizon [INAUDIBLE]. Again this is an assumption. And let's assume that stuff is so weird that it endows the space-time with negative pressure. So at some point, boom! This piece of space-time expands exponentially. And like economists, when you actually do inflation you actually have exponentially expanding functions as well. So likewise the universe actually becomes a very, very expensive-- it's on its way to a bubble. OK. Actually, I have colleagues that work on bubble inflation, so I'm looking forward to writing a paper about that. Bursting a bubble. If that happens, then what happens is that all of these regions actually become encapsulated. And you saw the horizon problem. If you can manage to set up a set of initial conditions with the same properties. We've got to figure out how to do that. How to order that, OK? Do we have the physics to do that? If that's the case, life is good. Dandy. But there's a bonus out of this. But before I say, I want to talk a little bit more about inflation. What makes inflation happen? What is the stuff that will do it? It turns out it's actually dark energy. But before I actually tell you what it is, I want to get something straight here. So we like to think about fields as things that are the carriers of forces, like the electromagnetic field. But as a person that's trained in field theory, as a field theorist, we know that the paradigms, that everything is a field. OK. When we write the standard model down, all of these things are presentations of fields. It's just that these fields are localized because they have mass. OK. But there's one electron field. We're just different states of the electron field. And likewise we must look at the paradigm, the field paradigm. So again, if we try to do inflation we are required to use a field because that's all we're left with. But it cannot be these other fields. These other fields don't work. Because these fields screen. They screen, and they like to cluster up. We need something that's homogeneous and isotropic everywhere. So it must be a field that has no spin. And we call these feel scalar fields. OK. So they're simple field theories. Like the electromagnetic field have spin one, and they have two polarization states. I could never do it properly, but. So yeah, field like this. So you really think about a field. So how does inflation work? The basic idea of inflation is that you have a field. The field has potential energy, just like the electromagnetic field could have potential energy. And if something has potential energy, is like sitting on top of a hill. And that potential energy could redistribute itself into kinetic energy at the end of the day for the conservation of energy. But in inflation, the field has a very interesting property. Meaning, the potential is very special. Potential is very-- what's the word for-- has a very low gradient. There's an easy word for that. Flat. It's a very flat potential. So that means a field rolls very slowly. So a field rolling very slowly is like something that has friction. There's friction that's slowing it down. OK? And it turns out that that situation-- if I give you a scalar field where the potential is flat, and I plug that into the Einstein equation, you have to believe me that the solution you generate is this expanding, this rapidly expanding space-time. You just have to believe me on that. If you gave me 20 minutes of your free time, I could actually walk you through the calculations. They are very simple calculation. OK. So I hope that. AUDIENCE: [INAUDIBLE] potential in different parts of space or? STEPHON ALEXANDER: That's right. This field takes values at every point in space. But it takes the same value. And then now the field evolves. So the field evolves differently than, it's like this potential is now not becoming flat anymore. So the fact that the potential remains roughly flat, it guarantees that this field remain constant at different points in space. And that's exactly the situation we want for inflation. So we have to-- you can actually set this up as a Markov chain, believe it or not. No pun intended. So if that was the case, cosmologists would not really care. I wouldn't care. But why I care, I remember when I was a grad student, and I went to the very first cosmology conference in Morocco in 1993. I saw a young cosmology post-doc doing a calculation for inflation where he was calculating the perturbations. So in other words, this field is rolling down. But it's a quantum field. So there are quantum perturbations. These quantum perturbations are nothing more than-- think of a little oscillator. The field is rolling down. And then there are little oscillators fluctuate because of the uncertainty principle. Is a quantum mechanical system. And so these things, you can't run away from. You must deal with it. It's a quantum field theory. So check this out. If you actually calculate these fluctuations of this field, in this rapidly exponentially expanding background, you get a spectrum of these oscillators, these fluctuations. And the spectrum has the following property. If inflation begins at some time that I give you because I'm God-Physicist-- I don't mean to sound like that. I mean, I'm not. Anybody wants to kill inflation, talk about this, OK. This piece here. So inflation is a very special situation in which the region that sets causality-- which we called the horizon, OK, all of the perturbations get generated in this region of causal contact. Because we're doing a local quantum field theory. Nice. But the rapid expansion takes these fluctuations, stretches it, but also amplifies it. So it turns this quantum thing into a large classical fluctuation with energy. So this gravitational dumps itself into these large quantum fluctuation that becomes classical. And they get stretched out of the horizon. Kind of magical. OK? Inflation ends and now we have an ordinary evolving cosmology. These modes, these fluctuations, become frozen. And they come back into the horizon now as classical perturbations. And they're nice and ready to source structures. And if I calculate this, and I calculate the spectrum, that's the red curve that I showed you. So what inflation does in solving the horizon problem, it provides a causal micro-physical mechanism for structure. So we can now come take a theory of inflation, do calculations and make predictions for these fluctuations of the CMB and compare it to the distribution of galaxies and clusters of galaxies today and come back to the drawing board and build better theories. So this is what it allows us to do. It allows us to do physics. But there are some caveats here. And I won't get into it now, but we should not drink the inflation Kool-Aid theoretically, yet. It's a paradigm that is the winning paradigm right now. OK? No doubt about that. But as a theorist, I still worry about this question here. So I want to leave it for the Google geniuses here. Maybe one of you can come and help me out with this. Here's a problem. You see those nice little fluctuations that I calculated? They're quantum mechanical. I go get Peskin and Schroeder. He teaches me how to do these calculations. I do the calculation. Boom! I get this beautiful spectrum, right? Life is good. Well these fluctuations not only affect the spectrum of the perturbation, they affect the potential. The potential also gets quantum corrected. Well those very same things that do a nice job for the fluctuation can spoil the condition of the flatness of the potential. So many models of inflation suffer from this problem. There are some models that get around it. We can do a little dance. But keep that in mind, that inflation is not a perfect theory as yet. So I want to now move on to the second third of the talk. What's the time? AUDIENCE: One-thirty. STEPHON ALEXANDER: Perfect. I'm right on time. So, OK. This is good. So inflation, as I said, does its night job, solves [INAUDIBLE] problem, gives us structure formation. All right. Let's do the dance. I'm going to quit my job at Dartmouth and come and hang out with you guys at Google now. But unfortunately I have to stay and continue working on this stuff because it turns out that these fluctuations that are generated during inflation, if you look at the formalism, couples to something called a gravitational potential. Remember this inflation field is the energy that's driving the space-time. The space-time itself is a field. The inflaton field couples to the gravitational field. A piece of this gravitational field is the good old-fashioned gravitational potential. You know, the one that the sun has on us. So the universe has a gravitational potential. And that's the thing that's really sourcing the infall of matter into what have you. But you see, if we're going to do that, we got to do it democratically. We can't say that the gravitational potential is this guy chilling out here, right? And the inflaton field falls into it because of the gravitational attraction. The gravitational field too must also democratically undergo fluctuations. You can't do one and not do the other. OK. Anyway, I'm not going to bring up any analogies for relationships. The metric field also undergoes a fluctuation. And the fluctuation of the metric field is something called a gravitational wave. So I want to talk a little bit about that. And just like how the inflaton field gave us a picture of what structure might look like in the early universe, how the primordial structures are formed, we want to ask a question about what is the physical role of these gravitational waves? And yes, it will be connected to parity. So that's kind of where we're going here. Just to reorient you to that. I don't want to take you too far. So what is a gravitational wave? What we're looking at upstairs there is a wave-- this wave has an amplitude. And I'm calling this amplitude "h". And as amplitude oscillates, in this case as a function of time. And this is a gravitational wave. So it's the fluctuation, it is the modulation of space-time itself. OK. And so if I look at the second line down here, I'm looking at a schematic of the LIGO, a LIGO gravitational wave detector, which are two ohms interferometer with laser light going back and forth, being reflected. And as a gravitational wave passes through, it actually stretches the space. And therefore the arms will stretched. And they'll get stretched in a way that as a gravitational wave passes through, there's a compression in the horizontal direction and a refraction in the vertical direction. So it does this, and this, as you see here. So if you're a tall person, you get taller a gravitational wave passes through. But as the gravitational wave undergoes an undulation, a refraction, it makes you a little bit chubbier. So that's what a gravitational wave does to objects in space-time. The space-time itself stretches and compresses as a gravitational wave passes through. OK. And that intuition should be consistent with space-time as a field. Because electromagnetism is a field that propagates through space-time. It needs space-time to propagate within. But the metric is space-time itself. So it supports its own fluctuation. So it must contract and expand space itself. So that's a gravitational wave. And what I'm showing you here is a first equation that I'm going to have. I'm going to have a few equations now from here on. But this equation is quite illustrative. What we're looking at here is a wave equation. Actually if I solved the Einstein equation for a gravitational wave, normally you see that middle term there? If I ignore that term, set it to zero, in flat space a gravitational wave would just be these two terms, which is nothing more than a wave moving at the speed of light. But you see that middle term there? You see that you have "a", which is a scale factor. And in an expanded background, da dt divided by a is a constant. That's the Hubble parameter. So that Hubble parameter's quite large, due to inflation. So what ends up happening, if I solve that wave equation, what starts off as an ordinary wave gets squeezed. Meaning that the phase of this wave-- I produce a distribution of these waves at different frequencies. And they all get the same phase. And is a phenomenon called quantum squeezing. And this is exactly how inflation surmises to amplify and stretch the gravitational waves. This is quite important. Because that means inflation predicts a spectrum of gravitational wave. And that's what we're going after now. When we say the smoking gun of inflation is to find gravitational wave. This is really a big part of story. That middle term is the thing that's creating special phase relationships between the spectrum of all the gravitational waves. So another place that you can imagine seeing gravitational waves are if I look at binary systems of neutron stars in this case. This is a computer simulation. Credit goes to LIGO, I believe. So maybe we can corrected later on. But anyway what we're looking at here is how a gravitational wave changes the space-time as a strongly gravitating binary system goes around each other. So notice you see the swirl in motion. But there's a problem here. As I told you, if we are to really believe this picture of structure formation and inflation, we need to understand not only the fluctuations of the inflaton field, we also need to understand the following problem. The universe is not just inflation and gravitational waves. The universe is us. It's made up of electrons and protons and all these nice things. But one of the things we know about our standard model of particle physics is that there are equal amounts of matter, of electrons and anti-electrons and positrons. So for every particle, we know that there's equal amounts of both. So what do I mean by that? If I look really far back, and I try to find where the equal amounts of what we are is, we don't find it. We don't see any antimatter. In other words, we don't see anti galaxies. OK. So here's a problem. The galaxies are the structures that are formed. So why am I not seeing anti galaxies? If the universe starts off in a symmetric state, and I believe the story of inflation, I have to confront the biasing of matter over antimatter, either due to inflation. Or something special happens after inflation where I got rid of all the antimatter. And so when I was at Slack, me and my boss and another post-doc, Mohammad Sheikh-Jabbari, thought about this problem in the context of inflation. We said, maybe there's something special about inflation that could do the job. And maybe the gravity waves are the hidden part of the story. So the story begins really in 1967. What we're dealing what is the genesis of leptons. So remember, electrons and neutrinos and muons are all leptons. So if you can form leptons over anti-leptons, you actually can produce Baryons much later on. So this is called leptogenesis. And so the name of the game here is to not explain the asymmetry. That's not enough. You have to explain that number. What is the difference between leptons over anti-leptons divided by the density of photons in galaxies. So this number is a universal number in every galaxy. And this number also-- so you could measure this number just by looking at galaxies. Or you could measure this number in the WMAP data. And you get the same number. So the name of the game is to not explain the asymmetry, but to explain the number. And that's the number right here. So even if you have a mechanism to explain the asymmetry, your theory could still be wrong. You have to explain this number. So 1967, Andrei Sakharov, in a home prison-- that's the legend, that a picture of him right here. He came up with the three necessary conditions to explain this asymmetry. So let me walk you through this because this is actually very important to understand the rest of the talk. So in our standard model, the statement that you have equal amounts of matter over antimatter is really a statement of the current. So every bit of matter, the electrons, all the fields, actually have a current. And the current is really-- in particle accelerator, that's what you're looking at. You're looking at the current-current interactions. And there's an equation for those currents. And the equation is that the rate of change of the current is zero. So the vacuum, the ground state of the standard model, all the currents are vanishing. The rate of change. So if I start with a situation like in the early universe, where the current is zero, because it's vacuum, then the rate of change of the current is going to remain zero. So the standard model doesn't have the physics to produce more current, or number density of particles. So that's really the problem. But the standard model has another statement, that you have an equation for the anti-current. And that is also zero. So the first thing you need to do is to come up with new physics that says that the change of the current is not zero. You have to figure out how to speak to the standard model or extend it in a way that that is no longer the case. But that's not enough to produce a matter asymmetry. You need to also bias the amount of current over anti-current. So if I produce current, if I produce more matter and antimatter-- imagine I can do that if I'm producing the same rate of matter and antimatter, they annihilate. So I need to simultaneously do something called CP violation. Which is, notice the word "parity" is in there? I need to bias, I need to have something like the weak interaction going on for the leptons. OK. The interchange of the charge and the handedness of the system has to bias one production channel of matter over antimatter. And while that is happening, the other degrees of freedom-- the photons and all these things, the radiation has to be out of equilibrium with that production mechanism. Because you learn from thermodynamics that if a system is in equilibrium with its environment, it will equilibrate back to its time reversal, which is matter becoming equal to antimatter. So this is the only page of equations because this is actually what we're doing in our model. So the theory that we're working with here is a theory of gravity that encodes parity violation naturally. What I mean by this is that this theory takes gravity, which is parity symmetric-- it doesn't care about a left-handed system and a right-handed system, it treats them the same mathematically. And therefore its predictions will be the same. And what I mean by that now is that gravitational waves-- I'm going to produce a left-handed gravitational wave. I throw a gravitational wave in my left hand. And a right-handed gravitational wave-- it will produce both of them at the same amplitude. But it turns out that I can do something to general relativity that biases that. And this is done by the great mathematicians Chern and Simons So this term here is Chern-Simons term. And this term seems to be very robust. And most approaches to quantum gravity has this term in it. String theory, loop quantum gravity-- so this seems to be a natural extension to general relativity. And what I'm going to show you is that if I solve for a gravity wave with this theory, something really cool happens due to inflation. And that's all I want to say about that. This theta thing here is the inflaton field that's coupling to this Chern-Simons term. Think of this Chern-Simons term as chopping off one hand and throwing the football with the other hand. So this is how the idea works. What I'm now going to say is, we're now going to talk about the possibility of producing leptons over antileptons and trying to see if inflation can give us all three Sakharov conditions in one shot. So here's the basic idea. If you guys get this, I'm going to be so happy. So I'm going to try. The basic idea is the following-- inflation is driven by a field called inflaton. This inflaton takes the same value at every place in space. But that's the amplitude of the field. It's a field, so the field also has a phase. And it turns out that the phase of the inflaton is that thing that couples to the Chern-Simons term. So if the phase couples, that means that phase is going to affect other waves that are produced, in this case, gravitational waves. So what happens is that the inflaton field has the same value. It couples to gravity through this Chern-Simons term. And as a result, the inflaton field, which drives inflation-- that means it's puting my system far out of equilibrium, because nothing can catch up with that rate of expansion. So you get out of equilibrium very naturally from just the environment of inflation. That same inflaton field sources gravitational waves. But it sources a gravitational wave in a way that biases the production of left-handed over right-handed gravitational waves. Biologists call this circular dichroism. Or physicists call it birefringence. It is the preference of one-handed of a wave over another one in the amplitude. So I have to show you that is the case. But it turns out that it also does something really cool. I believe in page 199 of volume two of Weinberg, it turns out that the standard model has something called a gravitational anomaly that people didn't pay attention to. Well, people did pay attention to it. They just couldn't find a use for it. And that gravitational anomaly is actually the statement that d of the current is not zero, but is proportional to the Chern-Simons itself. So if I have a non-vanishing Chern-Simons term due to inflation, I will naturally get the possibility of producing more leptons over antileptons. So what I'm saying, if you buy the story, the inflaton field does all three things at the same time, all through the Sakharov conditions. So let's see in detail if it works. For the rest of the talk, the picture you should have in your mind is that inflation is like this cup of coffee. And as you stir the coffee around one direction of over other, I can produce gravity waves that stir in one direction over another direction. And that stirring can pop matter out of the vacuum. And it does it in a way that's out of equilibrium. Well, it's a rapidly expanding cup of coffee. So if you want to put Starbucks out of business, you do inflation with coffee. So this is a statement. Remember I told you, you have [INAUDIBLE] of the J? J is the lepton and antilepton number. It's proportional to this Chern-Simons term. So if this Chern-Simons is non-vanishing, the left hand side is going to be non-vanishing. But remember, this Chern-Simons term is related to r, as a gravitational curvature. Right? So to calculate that thing I have to solve a modified wave equation for the gravity wave. Now this is very important. And it's also a very beautiful equation. It's the left hand side, if the right hand side was zero, I have the normal situation for inflation for gravity waves, that first equation I showed you? And so I'm going to produce equal amounts of left and right-handed gravity waves. But because of the presence of this Chern-Simons term, what happens is that the left-handed gravity wave is soft by itself and the inflaton field. So I notice here there's a minus sign here. So I'll get a wave with an amplitude that's proportional to this Chern-Simons term. So I can get an exponentially amplified, sorry, right-handed gravity wave, and at the same time an exponentially damped left-handed gravity wave. And that is a source of the left-right asymmetry. That is a statement of parity violation. Left and right no longer evolve in the same way. Well that's nice because if that is the case, then I find h left and h right-- if I plug it in, or RR dual, because RR dual depends on h left and h right, I find that RR dual is non-vanishing. So the parity violation immediately sources a production of leptons. So I can actually calculate that. All right, so the statement here is that the solutions I get are exponentially grown and damped gravitational waves. And it's parity violating because parity takes left into right. But in this case, because the amplitudes are different, it doesn't happen. All right, so these are some colleagues at work. Last slide. So I can now calculate this RR dual and plug it in. And I get this the answer. And guess what? It only depends on two things. So there's very little fine tuning in this model. And what I find is that it depends on Hubble over m-Planck which is actually an observable measured in the fluctuation spectrum of the WMAP and Planck data. And then it depends also on the value of the inflaton field, which is something that we can measure by measuring the ratio of the amplitude of gravity waves over the power spectrum of the scale of fluctuations of the inflaton field. It also depends on-- you can say, well, if I produce a full spectrum of different wavelengths of gravity waves of left and right-handed amounts, which ones contribute the most to the production of leptons? So the picture you should in have your minds is that I have these gravity waves that are interacting with the leptons in the vacuum, and they're popping them out during inflation. And they're popping them out so quickly that it catches up with the dilution of inflation and actually presents by expanding. So if I calculate that number, and I plug in the value of Hubble of m-Planck, and if the gravity waves that contribute are roughly 10 to the 12 giga electron volts, which is perfectly fine-- so it's a very high energy process --I could get the observed Baryon asymmetry. So what I've presented here is a theory that seems to be quite minimal if we believe in the standard model of inflation, and we believe in a standard model, and we believe that gravity interacts with the standard model the same traditional way that we expect as a field theory, then this seems to do the job. And what we've done is we've found a nice job for the gravity waves. It's not just hanging around there. Nature made use of it. So can we test this idea? So I should have about five minutes left. OK. And the answer is yes. So two ways to test this idea. So some colleagues of mine on the gravitational wave astronomy side are looking to see the effects today of these birefringent gravity wave-- and these are some of my colleagues that we've worked on this. And the basic idea is that when I look at a binary system, and I look at the distribution of gravity waves that we detect, I will see a bimodal distribution. I'll see two different distributions for the left and right gravity waves. If I look at a binary system, what happens when I look at a binary system that produces gravity waves, I can never find one that's completely in line with my line of sight. So there's always an inclination angle that I'm going to measure. So something really cute happens when you have parity violation. And this statement summarizes it. In the same way that we say that the curvature of space-time bends like [INAUDIBLE] close to a strongly gravitating body, we may say that the effect of a gravitational parity violating correction is to rotate the apparent inclination angle of the binary system's orbital angle momentum axis either towards or away from us. So it changes the apparent inclination angle as opposed to its true inclination angle. All right. And the other way that we can potentially test this is using this cosmic microwave background radiation. And yes? AUDIENCE: [INAUDIBLE] would you be detecting the difference in inclination angle as measured by gravity [INAUDIBLE] optical? STEPHON ALEXANDER: Exactly. Thanks for bringing that up. You have to also measure an optical inclination angle and then compare the deviation from the expected. Now the other way that I think is much cooler if we can do this-- and it will win my friend Brian Keating the Nobel Prize-- I'm just going to be the theorist. I just-- Hans goes to Stockholm because he's going to build the experiment. So what the cause of microwave-- what inflation predicts is this red curve for gravity waves. OK, this is what we call a B-mode polarization. What any theory that has a parody violating gravity waves produces a different curve, an order of magnitude larger than the red curve. I'm sorry, which is that black curve up there. So it produces a stronger signal, a signal that's more detectable. And right now my friend Brian Keating-- he's good buddies with Jim Simons. Jim Simons gave him like a crap load of money to build a satellite to actually look for this effect. Because, notice, it's a Chern-Simons term. So thank you Jim for funding Brian. Maybe you can fund me one day. He's a great guy, by the way. So this is the Simons Array telescope that my friend Brian-- you should invite him out here to talk about that design. Very cutting edge bilometry technology. Detectors that are way beyond anything available anywhere. You might want to use some of that tech. I don't know what you guys can do with detectors. So here are the stats on that. And I want to conclude. So one of the biggest questions in particle cosmology is a question of barrier genesis, or leptogenesis. It's not sufficient to just talk about structure formation without talking about how matter won over antimatter. It's a real observational question. And what I presented to you was a model that requires very little new physics, no extra dimensions, minimal fine-tunings. Of course you need to drink the Kool-Aid of inflation. And it may be testable by measuring anomalous parity violating power spectra-- last slide I showed you. And LIGO, or maybe one day LISA, if it flies, might be able to see these waveforms in binary mergers, like black holes and neutron stars and such. And this is a great opportunity to test a fundamental issue using cosmic microwave background polarization. And I want end to make my string theorist friends happy. Because the story actually started with a string theory investigation, looking at the Chern-Simons term. That it's possible that if you find this effect, we might be closer to actually making model independent statements about string theory or theories of quantum gravity. Thanks for having me out. [APPLAUSE] AUDIENCE: The parity violation depends on the Chern-Simons term, which depends on the inflaton field. Wouldn't it have vanished by now and only be apparent close to the Big ***? STEPHON ALEXANDER: That's right. So one thing-- there are two effects that could happen. One is a propagating effect, which is that you can look at a gravitational wave travelling to us from the CMB to us. So it was affected by this field back then. And it propagated to us. And it turns out, as it propagates that effect becomes stronger. And another one is a source effect, that if the field exists today, it may source. And you're correct that there are cosmological constraints that tell us that this field cannot exist. And if it does exist, at the very most it's the dark energy. And we know that it has to be like 10 to the minus 3 electron volts. Good question. AUDIENCE: What is the current state of the gravity wave detection experiments. And it seems like those have been online for awhile now. Are there any results coming out of it? STEPHON ALEXANDER: know they are very optimistic. I mean I was just visiting my friend Nico Yunes and Neil Cornish who are heavy into that game. And they're very optimistic. They are optimistic that they will detect a gravity wave. But the question is the background noise. Like, they have to always figure out how to get rid of the things that may appear to be a gravity wave. But because we already saw the binary pulsar, we know that there should be a gravity wave out there. It's not a question of-- so I'm optimistic. I'm obviously not privy to the real technical challenges that they're dealing with. Because it's not my pay grade. But the part of my community that deals with gravity wave, we're very optimistic. AUDIENCE: [INAUDIBLE] CERN, you'd really detected a real gravity wave as opposed to just some truck passing by, like-- STEPHON ALEXANDER: Yes. And this is exactly the issue. They have to figure out what that signal to noise is. So the question is how do you characterize that? So they have to understand what those foreground are. And so a big name of the game is to figure out what a fake signal is and then model it, to subtract it off. AUDIENCE: [INAUDIBLE]? STEPHON ALEXANDER: That I don't know. I think advanced LIGO and LISA would be designed to do that. Because if you had LISA flying and LIGO, and you saw the same event, then you'll have two different locations. AUDIENCE: Yes, the answer is yes. [INAUDIBLE] LIGO because there's some several of them scattered around the earth. STEPHON ALEXANDER: The answer is yes. Yes. AUDIENCE: Do we have any idea what kind of interactions the inflaton might have, whether we'd be able to produce it in an accelerator? STEPHON ALEXANDER: That's a good question. So the answer is that we should be able to do that. And that's why last year me and David Spergel and my post-doc worked on a new model of inflation that is not based on a scalar field. But it's based on something that looks very similar to quantum electrodynamics. And in that case, inflation is actually driven by ordinary fields in nature. And so we're working now-- that paper was recently published in JCAP. So you can look for that paper. It's called-- it's a model based on vector fields. So the photon and fermions are driving inflation. And so you could, for example, try to recreate that situation at the large Hadron Collider, the ILC and see if you see something that smells like inflation. I mean that's a forward-thinking idea. But we did that to show that, as a proof of principle, that you can do inflation with ordinary fields in nature. So part of that was to ask this question that you're asking. AUDIENCE: If an anti-galaxy were to exist, what would be the observational-- STEPHON ALEXANDER: Yeah. There is-- that's right. Around every galaxy there's gas, like hydrogen, for example. So you would see a lot of annihilation going on, if there was anti-galaxy. So you basically see huge flux of photons. So we can imagine that we do have anomalies in the sky. We have things called cosmic rays. And we have very high-energy cosmic rays. Maybe it could be that is a result of some huge amount of antimatter out there. It's not my pay grade, but so far every galaxy person I've spoken to tell me that there's no evidence of huge anti-galaxies out there. But I tend to keep an open mind about things that I'm ignorant about. So far I've been able to answer everybody's questions. This is scaring me. This is Google. I'm just kidding. AUDIENCE: In one part of the talk it said, one of [INAUDIBLE] part of the talk. You showed a factor of ten ratio between matter and antimatter. So I'm a little bit confused. STEPHON ALEXANDER: OK, good. I'm glad you brought that up. We saw a factor of 10 difference in ordinary left and right symmetric gravity waves produces inflation and a left-right asymmetric gravity waves. So that's a factor of 10. But it's interesting that that factor of 10 may be the same factor of 10, to give you the Baryon asymmetry. So what we're looking at is really the gravity wave power spectrum, the distribution of the frequencies that are gravity waves. And what we see is that we have higher power for larger wavelengths of gravity waves, if they are left-right asymmetric, and lower power if they were left-right symmetric. I don't have an intuition as to why that is the case. But it's good to think about. Yes. AUDIENCE: Why is parity an almost perfect symmetry? Why is it a symmetry at all? I'm curious. If physics is just a whole bunch of these near-symmetries, which are symmetries that are slightly broken, but [INAUDIBLE]. Parity is one of these things. Why does it exist at all? STEPHON ALEXANDER: I think what you mean by that is in the weak interaction, parity of course is maximally violated. We never see the other thing. But that's right. In terms of all the forces combined, the weak is the odd man out. OK. It's the one that violates parity. And the other is, if it violates parity, it's just like very weakly or not at all. And so to be honest with you, there is no good answer to that question. We don't know the answer to that. Part of why I pursued this line of research was to understand-- to use gravity as a diagnostic theoretically to understand that question. Because in this case parity is just weakly violated. It's in between. The talk I was really going to give you guys was a partial answer to your question, which was to show that actually gravity and the weak interaction are really the same theory. And the parity violation is a consequence of parity symmetric theory that includes gravity in the weak interaction. But that talk had-- a friend of mine warned me to not give that talk here because, well, there were no words in the talk. [LAUGHTER] Or very little words in the talk. AUDIENCE: [INAUDIBLE] the weak interaction can be unified into the [INAUDIBLE] weak theory. STEPHON ALEXANDER: That's right. AUDIENCE: [INAUDIBLE]. STEPHON ALEXANDER: That's right. So it's a very good point. I notice your question. So the electroweak interaction-- that's a very good point. The electroweak force actually includes both electromagnetism and the weak interaction. OK. But what happens is that the Higgs field breaks that symmetry. That's what the Higgs does, right? It's like a magnet. It points in a given direction. That's what the Higgs field is, like a magnet pointing in a given direction. And that aligns the weak field now to actually disassociate itself from the electromagnetic field and the weak field. And actually the way that it's done is quite artificial, if you look at the details. And this is called a Weinberg angle. So what sets the Weinberg angle to be what it is, is kind of an input that you-- you kind of put that answer into the dynamics. What we would like is to actually-- see, the answer to your question is related to the origin of the parity violation. AUDIENCE: What are your views on the existence of firewalls around black holes? STEPHON ALEXANDER: You guys know what a firewall is? Put a wall of fire, you fall into it. So there's this idea that the Hawking radiation actually organizes itself-- when a black hole emits Hawking radiation into a wall of fire for an observer falling into the black hole. I would say that even if firewalls exist or it doesn't exist, there's still a more fundamental question of information loss. And so I don't lose sleep over firewalls, unless I find myself near one. Why did you ask that question? AUDIENCE: Just curious what your stance on it is? I guess you don't think either way? STEPHON ALEXANDER: No, it's a good question. I think it's a really good question of, do holes only emit Hawking radiation, or does it absorb Hawking radiation?