 Okay, let's start. Welcome back to all of you. It's a pleasure to have this second lecture of Alanguth, which are the salam distinguished lectures for 2018. As I mentioned yesterday founded by KFAS and the topics inflationary cosmology is our universe part of a multiverse. And today Alanguth will tell us about internal inflation and its implications. I have a short time memory problem. Okay, so let's welcome Alanguth again, please. Okay, so today's talk will be more or less a continuation of yesterday's talk. Tomorrow's talk will be about a topic that's more or less separate. It will be some overlap, but tomorrow's talk about the hour of time will sort of change gears and talk about different things. So for today's talk, I want to first of all point out something I forgot to point out yesterday. This picture that appears on the bottom left-hand corner of my slides, of my title slide, is an artist's rendition of the Planck satellite. The satellite that brought back that beautiful curve that I showed you yesterday. I'll show it to you again today because I like it so much. The curve of the spectrum of the fluctuations in the cosmic microwave background. So I'll give you, begin with an outline of what I want to say today. Today's talk is also divided into more or less three parts. The first I'd like to expound upon something which I told you last time, which is that almost all, and what's meant by almost all is very subjective, but from my point of view, almost all inflationary models lead to eternal inflation. And I'll tell you about how that works in more detail than I did yesterday. Secondly, I'd like to talk about some of the good things about eternal inflation. Inflation, which has the property that once it starts, it never stops, that goes on forever producing an infinite number of pocket universes. For a theoretical point of view, there are some attractive features of that scenario. First of which is something which I mentioned yesterday, but we'll go into more detail today. The possible explanation for the very small vacuum energy density that we observe in our universe, which as I told you yesterday is about 120 orders of magnitude smaller than what particle physicists would expect it ought to be if it were obedient, but it's not. Second, a good feature about eternal inflation is that in most of its versions, again these things, different versions people have considered, but in most of its versions and the ones that I consider attractive, eternal inflation completely frees us from any dependence on the initial conditions. Once this process of eternal inflation sets in, in most scenarios, it approaches an equilibrium state, which is completely independent of the details of the initial conditions. And that means that we can make predictions in principle from these theories without knowing how the universe actually started. And that's a good thing because we don't know how the universe actually started. Third, and this I'll need to explain in more detail when we get there, eternal inflation allows us to avoid a thermal equilibrium phase and what I will explain when we get there is what is meant by a thermal equilibrium phase. And I'll also try to explain what's bad about getting into a thermal equilibrium phase and then I'll also explain, this part will be fairly obvious, how eternal inflation avoids that. So that to me is also an important attractive feature of eternal inflation that I'll be telling you about. But then finally I'll also point out that eternal inflation does lead to what is still an outstanding problem conceptually, which is that in an eternally inflating universe, any kind of event that's allowed by the laws of physics will happen again and again and again, an infinite number of times literally as the system goes on evolving through an infinite number of pocket universes. It turns out that that makes it hard to define probabilities. If all events happen an infinite number of times, it's hard to know what you mean if you want to say that some events are more common than others. And I'll talk about the status of that problem when we get to the third part of today's talk. So that's the outline. Let's proceed. Except first I want to remind you of this wonderful curve and it's important because it's the success of this curve that motivates these much more abstract ideas about what the implications of inflation are for the creation of other universes, for example. There'd be no reason to take that at all seriously if we didn't start out by thinking that inflation really does give us a very good description of our observable universe. And it's because that description is so good that it seems to be worthwhile to explore all the implications of inflation, including what I'll be talking about, the implications for a multiverse. Okay, so this is the part where I want to explain why almost all inflationary models lead to eternal inflation. So I want to begin by just describing a little bit more of the details of how exactly inflationary models work. They hinge on the existence of things called scalar fields. So I have to describe scalar fields for those of you who don't already know it. I'm sure many of you do, but for those who don't know what a scalar field is about, I want to begin by pointing out that in current particle physics, short of string theory, which has a more elaborate description, but in the context of quantum field theory, the standard model of particle physics, for example, we associate a field with each of the elementary particles of the theory. You're probably all more or less familiar with hearing about photons and electromagnetic waves. The photon is a quantized lump of energy of an electromagnetic field. It turns out that that's the way we describe all relativistic particles. So we attach a field to each of these particles, that is, we hypothesize that a field exists for each elementary particle, each fundamental particle, and then the particle becomes just the quantized excitation of that field, the lump of energy in which the energy of those fields is concentrated. Now a scalar field might be a new word for many of you. You should think of it just like the way you think of an electric or a magnetic field. We don't try to explain it in terms of something else, except maybe string theorists do, but I'm not going to. In the context of quantum field theory, we just accept these fields as being fundamental ingredients. The electric field is the fundamental ingredient, and so is a field associated with the electron, fields associated with each kind of quark. And we write down equations for how these fields evolve, and we promote these fields to quantum objects, to a quantum description. And in the quantum description, the energy of these fields becomes quantized. One quantum, one lump of energy is a particle. So the electron is simply a quantized excitation of the electron field, just as the photon is a quantized excitation of the electromagnetic field. What makes a scalar field a scalar field is that unlike electric or magnetic fields, which are vectors, they point in a definite direction, a scalar field, as the word scalar suggests, is just a number defined at each point in space. It has no directionality. It's simply a number defined at all points in space. In terms of where scalar fields are believed to turn up in physics, there's only one that we've actually seen direct evidence of, and that is the Higgs field of the standard model of particle physics, where the associated particle was finally discovered after 50 years at CERN at the Large Hydrogen Collider in 2012. And the Higgs field is an example of a scalar field, and it really gives us the prototype for everything that we think about scalar fields. And certainly the Higgs field was a strongly motivating factor in the development of inflation, even though the Higgs field had not been found yet when inflation was first invented. Everybody believed in the Higgs field, and certainly I did. Almost everybody did, maybe I should say. But it was people already calling it the standard model at that point, even though we admitted that there was a link in the standard model that had not yet been found. In addition, particle physicists play with theories called grand unified theories, which are an attempt to unite the weak, strong, and electromagnetic interactions into one unified interaction. Those require a large number of scalar fields, which are closely analogous to the Higgs field of the standard model. And finally, at the highest energies, string theory is an attempt to unify not only the weak, strong, and electromagnetic interactions, but also gravity into one unified theory. And string theory involves fundamentally different ingredients than field theory. But nonetheless, for energies well below the plonk scale, the scale where quantum gravity really becomes important. For energies well below that, string theory is itself well approximated as a field theory, and it has many scalar fields. So the bottom line here is that although we only know for sure of one scalar field, physicists have pretty much faith that there's actually a large number of scalar fields in nature. What can we do with the scalar field? The important properties of a scalar field are characterized by its potential energy function. And what I've shown here is an example of a system with two scalar fields, which I very, with great originality, I decided to call scalar field A and scalar field B. So those are the two scalar fields. And this is an energy density diagram. Scalar field A is plotted on this axis, scalar field B is plotted on that axis. And then for any point, characterizing the value of scalar field A and scalar field B, above it is a surface which tells you the energy density associated with that combination of fields. So this is energy density as a function of the two fields that's being displayed here. And notice that it's completely symmetric under rotations in the A, B plane. And that's intentional. Scalar fields often come with symmetries. And in fact, the Higgs field of the standard model of particle physics is really four fields that are connected by a symmetry. So we talk about them as if they were one field. And what is also true for the Higgs field of the standard model and what is shown here is that the potential energy function has a peculiar form. Instead of the potential energy vanishing when the fields vanish, the potential energy actually has a large value where the fields vanish. It's shown here at the local maximum. And the minimum potential energy occurs on a circle as some non-zero value of scalar field A squared plus scalar field B squared. In other words, for a non-zero, for a particular value of the radius from the center in this diagram. And that means that the vacuum, the state of lowest possible energy is degenerate. There's not a unique vacuum. Any point along this circle, shown as the vacuum circle, will have zero energy even though there are different combinations of the fields. And when the fields vanish, we have a high energy as shown. And this is characteristic of the actual Higgs field of the standard model and it's characteristic of the kind of fields that we assume are relevant for driving inflation. Which, by the way, might be the Higgs field of the standard model, but it also might be a totally different scalar field. Both possibilities are open. What's important for driving inflation is that if the scalar field represented as this ball, which is someplace on this surface, if that scalar field is perched right at the top, which means that both fields A and B vanish, then you have a quasi-stable state. If the field is right at the top, it doesn't really know which way to roll down. And it will be stable sitting on the top of the hill for some period of time. In this case, we really are thinking of this as a quantum system. And as a quantum system, even if it's right at the top at the beginning, it will not stay there forever. Quantum fluctuations will randomly push it in one direction or another and it will fall off the hill and roll down to the minimum of the energy density. I should maybe add that the evolution of a scalar field is very similar to the evolution of a ball rolling on a surface like this. Qualitatively, it's just the same. So if you start with the ball right at the top and imagine that quantum fluctuations give it a small knowledge, it will roll in one direction or the other, then start to oscillate about the bottom of the hill and then settle into someplace at the bottom of the hill. The state in which the scalar field is perched right at the top of the hill is called a false vacuum. The word false is used here in the sense of temporary and vacuum is being used in the sense that particle physicists use it. It doesn't just mean emptiness. A vacuum is the state of lowest possible energy density. In this case, the point at the top of the hill is certainly not the point of lowest energy density, but temporarily it acts that way because it takes some period of time for the scalar field to fall off the top of the hill and by early universe standards that can be a long time. So for some, quote, long time the scalar field is stuck at the top of the hill and that's the state that we call the false vacuum, temporary vacuum. Now what does this have to do with inflation? There are two important links here to link this to exponential expansion. The first is to understand the pressure of the system like this. I told you yesterday that negative pressures drive repulsive gravity. What I want to tell you now is that the false vacuum that we just described necessarily has a negative pressure. And the way to see that or at least one way to see that is a thought experiment. Let's imagine that we had a piston chamber that we could tell what we wanted to do and it would do it. And what I tell it to do is to be filled on the inside with this false vacuum state that is with scalar fields which both vanish, A and B both vanish inside the piston, producing a high energy density. The energy density is the height of that hill in the middle of the diagram. And outside of the piston chamber we're just going to put ordinary vacuum, vacuum that has zero energy and zero pressure. And now we're going to ask ourselves what happens if we pull out on the piston. Now I want to assume that the interior is designed in a way that it maintains this false vacuum content. So inside it will still be filled with false vacuum but the region of false vacuum will expand. Because the region of false vacuum has expanded and the false vacuum has a positive energy density, that means that the total energy inside the piston expands if I pull outward. Now since energy is conserved, that means that work has to be done by somebody if the total energy inside is going to go up. And the only somebody involved in this little thought experiment is the person who's pulling out on the piston. So that guarantees that the person who's pulling out on the piston has to pull with force to make it go out. He has to exert a positive force pulling it outward. And that means that the piston itself is sucking backwards. It has a suction inside pushing against the person pulling out on the piston. And that means that the substance inside here has a negative pressure. If you had a positive pressure it would push outward on the piston and help the person pulling outward. So we know it can't do that by conservation of energy. It has to make it hard for the person pulling outward and that means it has to have a negative pressure. And you could even use this argument to calculate exactly what the negative pressure is. And it turns out that the negative pressure has to be exactly equal to the energy density in magnitude. It's negative, the energy density is positive, but they're equal to each other in magnitude. So this guarantees that the pressure of our false vacuum state is negative. And now I'll just more or less repeat what I told you yesterday. I won't really give you a better derivation. But according to general relativity, pressures can also create gravitational fields. Positive pressures create attractive gravity, which I can't really explain very well except that certainly what the equations give. And it's also I think what you would intuitively expect, a positive pressure is in some sense a normal pressure. It's the kind that we're accustomed to seeing. And attractive gravity is the kind of gravity that we're accustomed to seeing. So it's not too surprising that they come together. So positive pressure creates attractive gravity, but then a negative pressure creates a gravitational repulsion. And we've just convinced ourselves, I hope, that this false vacuum state necessarily has a negative pressure and therefore creates gravitational repulsion. In the example I showed you, we have a plateau in the potential energy diagram. And that's one way inflation can happen. And that was the earliest way that was talked about. But it's not the only way. Even if we just have a potential energy function, now I just have one scalar field called phi here. And v means the energy density being plotted as a function of the value of the field on the horizontal axis. Even if the potential energy function looks more normal, vanishing where the field vanishes and getting larger where the field gets large, you could still have inflation. What Linda showed in 1983, I guess, is that if the scalar field starts out high enough on this hill, you will still have a state which is dominated by the potential energy of the scalar field. And that's really what matters in the end. And if you put it high enough, as the scalar field rolls down, there will still be enough inflation that happens so that we can have a successful inflationary model with a potential that looks as simple as what's shown on this slide without the fancy double well or a Mexican hat. And this was called chaotic inflation by Linda. Okay, I wanted to also fill in one other gap from yesterday's talk, a gap that's essential to the workings of inflation. I told you yesterday that the energy density of a gravitational field was negative, and that's crucial for inflation to be able to build a huge universe starting from almost nothing. It's essential that that huge universe, even though it looks like it has a lot of stuff in it, really has a total energy that's incredibly small, and might even be zero, where the huge energy and the matter that fills the universe is being canceled by a huge negative energy in the gravitational field that fills the universe. You might recall that yesterday, I told you that if you know how to derive the energy density of an electrostatic field from Coulomb's law, you can just repeat that calculation for Newton's law of gravity, and it's the same calculation really. If we compare Newton's law with Coulomb's law, we notice that they actually are exactly the same in form, they're inverse square laws, but they have opposite signs, two positive charges repel each other, two positive masses attract each other, so when you do this calculation of getting the energy density from the force law, you start out with a different sign and you end up with a different sign, so you end up showing that the energy density of a gravitational field according to Newtonian physics is negative, and that's fine if you remember how to derive the conservation of the energy density from the force law, but for those who don't remember that, and there might be one or two in the audience, I don't know, if you don't remember how to derive the energy density from the force law, I have here a different argument which uses I think less underlying physics to show that the energy of a gravitational field has to be negative, so what I want to do here is again a thought experiment similar to my piston, I want to imagine a shell of matter completely hollow inside, it's a spherical shell, and I will ask you to read your Newton and understand what the gravitational field of a shell of matter is, this is fairly well known, what Newton showed way back in the 1600s I guess, is that the gravitational field outside the shell is exactly what it would be if the same mass were just concentrated at the center, but the gravitational field inside the shell is exactly zero, always being canceled by the gravitational fields pulling in different directions from the sphere around any point inside the sphere, it cancels exactly, so that's a picture of what's shown here, these lines represent the gravitational field, this is my hollow shell, that's how we start our thought experiment. Now what I want to do is to imagine that this spherical shell material is somehow flexible, clay like, so that it can allow it to collapse under its own weight, there is a gravitational force on the outside of the shell, that's the self force of the sphere, so we can imagine tying little ropes at lots of places around the outside and as the shell implodes we can have the shell pull on those ropes and I have little generators there, that's supposed to be a generator in case you can't tell, looks kind of like my old bicycle generator, we have a lot of generators tied around the outside and as the ropes are pulled they can generate electricity producing power that leaves the system and lights a light bulb somehow off to the side, the light bulb over here you can't see it but it's really there and it's being lit by the energy being released by the shell collapsing under its own weight. Now we can look at the final situation where the shell ends up being this big and ask what's the gravitational field now and we can divide it up into three regions, I kept a dotted line where the original shell was, outside of that dotted line, the gravitational field is still exactly what it would be for the total mass at the center, so no change outside the dotted line, we can also look inside the final shell, it's zero there and started out zero, so no change inside the shell but in the region that the shell crossed which is shown as a shaded region in this diagram we now have a gravitational field well at the beginning there was no gravitational field there whatever, it was just zero so the net effect of this whole process is to extract energy, the light bulb over here that I told you was there and you believe me and it was lit up and we created the gravitational field so by creating a gravitational field we were able to extract energy and there were no other changes that's the whole thing and that implies that the energy of that gravitational field had better be negative if energy is going to be conserved, so I think this is a very simple argument that guarantees anybody who knows the basics about gravitational fields of spheres that Newtonian gravity does indeed imply that the energy of a gravitational field is negative when you create a gravitational field you actually can extract energy, okay so those are the basic physics items I wanted to talk about now let me talk in a little more detail about how inflation actually works and what causes it to become eternal so one kind of inflation is inflation essentially in the first kind of potential energy function that I showed you I do it in with two fields and it looks like a Mexican hat it's often called a Mexican hat potential this is just a one-dimensional version of that same picture where the field strength goes this way total energy density goes up the false vacuum is when the field is perched right at the top of the hill way inflation ends in a model like this is as I said earlier it ends when quantum fluctuations push the scalar field off the top of the hill and it rolls down to the bottom and that makes this false vacuum state metastable it only exists for some length of time when one describes these fluctuations of the scalar field quantum mechanically one can show at least in the approximate version of this that the field rolls off the hill with an exponential probability that is the probability that the field remains at the top of the hill falls off exponentially with time so the volume of the false vacuum okay that's the first statement it decays exponentially and that means that it has some half life and if you wait a certain amount of time there's probably over half that the scalar field is still at the top like the same one at the time again probably that's still at the top is a quarter and then an eighth and so on but meanwhile the whole volume is inflating exponentially that is it's doubling and redoubling and redoubling with a certain doubling time and the important point is that for any successful version of inflation the rate of inflation that is the exponential rate of growth greatly exceeds the rate of decay otherwise you would not have a successful inflationary model well can I imagine a particle theory where that works either way but if we're talking about a model of inflation it has to obey this inequality inflation has to be faster than the decay because you need a hundred and about a hundred doublings of inflation we said yesterday and that implies therefore that if we look at what happens to the volume of false vacuum it's evolving by the product of two factors it's growing exponentially because of the inflation it's decaying exponentially because of the decay but that product of two factors is totally dominated by the exponential expansion which is much faster so if you wait for a length of time the total volume that's inflating the total volume where the scalar field is at the top of the hill will be growing exponentially with time even while the scalar field is sometimes rolling off the hill and that's all that's needed to guarantee eternal inflation in this for this model the total volume that's inflating does not go to zero because the scalar field rolls off the top of the hill everywhere but rather the total volume that's inflating grows exponentially because the exponential expansion outruns by a large margin the exponential decay I told you earlier that inflation doesn't require a plateau in the potential energy diagram like I just showed you another version of inflation has a simple minimum in the scalar field the potential energy function going upward on both sides and if the scalar field starts off high enough I told you you could still get enough inflation as the scalar field rolls down however this model also has the possibility of becoming eternal if the scalar field starts off high enough on the hill and it's much less obvious it took several more years before this was noticed but this was also noticed originally by Andrei Linde in 1986 and what he introduced was an approximate way of describing the evolution of this scalar field rolling down the hill the important thing that's being added here is a description of the quantum fluctuations of the scalar field as it rolls down the hill it is a quantum field and not a classical field so one has to understand its evolution allowing for the probabilistic uncertainties of quantum theory and what Andrei did was to start with a more fundamental description of how quantum fields behave and show actually this part was more or less shown earlier but other people that there's a simple description that does that accurately describes how the scalar field will behave in this case what we're going to do is we're going to first of all decide on a time step instead of trying to follow it continuously we'll ask what happens after one step in time and the natural time to use for this time step is what's called the Hubble time it's just the inverse of the Hubble expansion rate h here is the Hubble expansion rate it says that if you look out at a distance point the velocity of that point will be equal to h times the distance and as the units h itself has the units of an inverse time and h inverse then is a time and that's the time that we want to talk about so we're going to use a time interval equal to h inverse the other thing that's per show whenever you talk about the quantum behavior of the field and this is really true for electric and magnetic fields as well as scalar fields it turns out that if you try to measure a quantum field at a point at an exact location the fluctuations are always infinite it's just really completely undefined to talk about a measurable value for a quantum field you have to specify some resolution some volume they're going to measure the scalar field as an average over so we get to choose what volume we're going to average over and in this problem the only relevant scale is the Hubble scale the Hubble expansion rate so we're going to use that to also determine the size of region we're going to average over we're going to average over a Hubble length and the Hubble length is just a Hubble time times the speed of light as you might guess we think of the speed of light as being kind of one it's just a universal constant so there's such a thing as a Hubble length and we're going to be averaging the scalar field of a region of size h inverse Hubble length and ask then how it behaves and what then they showed is that it really has a very simple model during one Hubble time if you want to know what the scalar field is going to be Hubble time later you start by writing down the classical answer that's the first term in your equation but then you add to it a random jump where the root mean square value of that random jump is the Hubble expansion rate divided by 2 pi so it's this is something you might just get by dimensional analysis the only scale in the town is this Hubble expansion rate so the answer had to be proportional to h in order to do the dimensional analysis you have to know the dimensions of things but scalar fields in fact have dimensions of the same as h which means inverse time so the jump in the scalar field has to be of the same order of magnitude as h and you can really calculate it for a particular definition of exactly how you do the averaging and it's h over 2 pi for that definition important thing is really just that's order h so we have the scalar field which is rolling down the hill but for each Hubble time it's given a random kick where that random kick has a well-defined magnitude and because of the random kick at the end of the Hubble time it can either go down or up it's more likely to go down because the classical evolution is always downward and this random kick is equally likely to be up or down because it is just a purely random random kick it's taken from the Gaussian distribution if you know what that means but it doesn't matter so now let's think a little more about what's going on let's imagine that the scalar field starts out I'm now talking about the average value in the Hubble region let's suppose it starts out at some value which I'll call phi sub zero and then we wait a Hubble time delta t equals h inverse during that time we said it will be given this random kick but also during that time the volume is going to expand during one Hubble time the radius will expand by exactly a factor of little e that's the base of the natural algorithms the volume then will increase by e cubed one of the deep mathematical facts that one learns when one does inflationary cosmology is that e cubed is about equal to 20 which is useful to know so that means that during this Hubble time our one region is essentially turning into 20 regions and they are pretty much 20 independent regions because the Hubble length the size of these regions is about the maximum distance of communication that's this system undergoes because again the Hubble scale is the scale that determines everything and therefore it also determines the range of communication so we have one region turning into 20 regions and then we can ask ourselves what happens to the scalar field in each of these regions and we can calculate that if we know how big this kick is and we know the probability distribution of the kick and we do and then if the probability that the scalar field goes up instead of down is let's say first suppose it's exactly equal to 120th then the situation will be at the end of the one Hubble time that one of these 20 regions will have a scalar field as large as what we started with and the other 19 will have fallen to lower values of the scalar field that's kind of breakeven as far as eternal inflation is concerned but if the probability is more than more than 120th then at the end of one Hubble time you'll have more than one region out of the 20 with the scalar field will be as large as phi naught and if that's the case every time you repeat this by looking at the next Hubble time and the next Hubble time the number of regions where the scalar field is above phi naught will be larger than it was the previous time and that will just go on forever and you have eternal inflation so the requirement of eternal inflation boils down to the question of under what circumstances does the probability of the scalar field going up instead of down due to the quantum fluctuations under what circumstances is that probability more than a 20th and what you always find is that if you go high enough on the hill that probably will always exceed 120th so most any shape potential here will tell you that eternal inflation will set in if the scalar field gets high enough on the hill and that's how these kind of models become eternal might mention that you can have the value with the scale where eternal inflation sets in is in fact always higher than the value needed for inflation itself to work so if you believed that there's some mechanism that just put the scalar field at some low value and let it roll down you could you could have inflation without it being eternal so how to decide whether that means it's really eternal or really not depends a little bit on what underlying assumptions one makes about how all this fits into a bigger picture my own prejudice has always been that whatever mechanism started the universe and we don't really know what that mechanism is but my own prejudice has always been that whatever that mechanism is it's something that comes out of the ultimate laws of physics and therefore it's not going to happen only once anything that we could describe by the laws of physics happens again and again and again so if there are many many trials here if there's any probability of eternal inflation happening the way I view it we should expect eternal inflation to happen and therefore for a system like this I do expect eternal inflation to happen if this is the right description that is sooner or later when the universe has made the scalar field will end up high enough on that hill to set off the eternal inflation and then if you have some cases where eternal inflation happens in some cases where it doesn't the ones where it's eternal will obviously dominate over everything else just because being eternal you get an extra factor of infinity for the number of pocket universes that would be created under those circumstances okay so this explains how eternal inflation sets in for really both sorts of the ways in which inflation can happen and that completes the first part of my talk I think the explanation of why why we say that almost all models become eternal actually it doesn't quite complete it I forgot that I added this slide this slide talks about our own pocket universe and what we might infer from it and the point is that we may not fully understand what's going on under the hood for our pocket universe but it sure looks like our pocket universe is headed for eternal inflation regardless which allows one to ignore all the details of the previous explanations and just say that if their physics correctly describes if there is physics that correctly describes our pocket universe it looks like it leads to eternal inflation the idea is that our own universe today does appear to have a positive cosmological constant or said in another way a positive vacuum energy density the dark energy that drives the exponential expansion fits best as being described as simply vacuum energy which is synonymous with Einstein's cosmological constant and that means that our universe is headed for a period of exponential expansion we're just starting that period of exponential expansion now if our vacuum is absolutely stable then our visible universe will just become eternal it will approach a purely exponentially expanding space that will exponentially expand forever life as we know it will die out but in the infinite exponentially expanding region that will follow there will be quantum mechanical tunneling that will create new pocket universes in an exponentially expanding space it's possible to tunnel even to an exponentially expanding space that expands faster and if we have an infinite amount of time for such things to happen all kinds of pocket universes would be expected to materialize just out of our own pocket universe another possibility is that a vacuum might be metastable it itself might decay if that were the case though the only way to prevent eternal inflation would be for that decay to be rather fast if the decay was slow even when decays happen here there and there when a decay happens it happens locally and spreads at the speed of light because of the exponential expansion if the rate is slow even while it decays the total volume that's still in the state of our universe will continue to exponentially expand the only way to stop that is to have it decay and decay quickly and by quickly I mean that the probability is that will decay more or less tomorrow not with certainty but should decay on the time scale same time scale as the current age of the universe and that's possible but requires a pretty delicate balancing so our universe I claim is well almost certainly by by its own lonesome producing eternally inflating multiverse okay onward next I promise to talk about the theoretical benefits the good things that theorists like about eternal inflation and the first of those I want to talk about is the possible explanation of this very small vacuum energy density that we've been talking about the energy density that's 120 or is the magnitude lower than what theorists might expect and I'll just tell the story in more detail it's basically the story of dark energy this energy that drives the expansion of the universe is called dark energy in 1998 as I've said before the astronomers discovered that the universe has in fact been accelerating rather than slowing down for about the last five billion years out of its 14 billion year history an implication is that it really means that inflation is happening today we are going into a period of accelerated expansion at a much slower rate than we were talking about for the early universe but it is essentially the same phenomenon of accelerated expansion which is projected to become exponential in cosmological time and within general relativity this requires some material that has a negative pressure the only way it can happen and this repulsive gravity material the negative pressure stuff is called the dark energy and if you ask what is the dark energy the answer is we don't really know but by far the simplest explanation is that the dark energy is just equal to vacuum energy and cosmology observational cosmologists have been making more and more sensitive measurements of tracking this expansion history of the universe and everything still fits perfectly with exactly what would be expected as the dark energy was vacuum energy so I'm going to assume that that's the case here for the subsequent discussion and in any case it was certainly the dark energy that changed the previous measurements of omega the mass density parameter from point two or point three as people thought in 1998 to the current value which is something like 0.999 now this turns out to be a theoretical nightmare for particle physicists and I'll try to explain why an important point is that the quantum vacuum is far from empty so the idea that we have a non-zero vacuum energy is not by itself at all surprising it's in fact what we should expect but we have tremendous trouble understanding why the answer we the observers get is so incredibly small one contribution to this vacuum energy is the energy density of the quantum fluctuations of fields in particular say the electromagnetic field as a familiar example uh physicists know how to calculate the contribution to the vacuum energy for any given range of wavelengths and that's some finite number that's even small in most cases but when we try to apply it to the electromagnetic field uh in empty space uh we have a serious problem uh because there is no shortest wavelength uh and that means as we include shorter and shorter and shorter wavelengths the energy density of these quantum fluctuations just grows and grows and grows without bound that diverges is the word that physicists use becomes infinite essentially so infinity is not really a meaningful answer here so we believe there has to be something that cuts off this ever-increasing sum as we go to shorter and shorter wavelengths uh and that's a reasonable hypothesis because we certainly don't have any good reason to believe that the quantum field theory that we understand can be extrapolated to arbitrarily small wavelengths so it's reasonable that something might change that makes the calculation no longer valid for wavelengths below that scale but when particle physicists scratch their heads and ask where is that likely to happen uh the most plausible answer uh is that it is expected to happen at the scale where quantum gravity becomes important uh because we know we have not included the effects of quantum gravity in these quantum field theories that we're using for the calculations uh so this is what the reasonable guess is that i've been talking about the reasonable guess is that a plausible cutoff for these fluctuations is what's called the Planck length uh which is the scale at which we expect quantum fluctuations uh to become quantum fluctuations of gravity uh to become dominant uh it's about 10 to the minus 33 centimeters so a natural scale is to cut it off there and ask how big is it and the problem is that it's whopping big uh using that cutoff we find that the vacuum energy that we predict is too large larger than what's observed by this fantastic number of 120 orders of magnitude uh so that's the problem that we're trying to get out of uh whoops not a good success um so the the method that i'm going to be talking about is a possible resolution for this problem uh involves some elements of string theory uh string theory has some interesting properties here uh since the inception of string theory uh theorists have worked hard to try to figure out what the vacuum of string theory is and they can never find anything that looked like a sensible vacuum to string theory uh but since about 2000 uh the trend has changed completely and now almost all string theorists have come to believe that there is no unique vacuum to string theory but rather a huge number of people talk about 10 to the 500 or more and the number might very well be infinite actually of different types of vacuum that are allowed by string theory and each of these could serve as a substrate for a pocket universe it could be the type of vacuum that fills a given pocket universe and as these different pocket universes form I should add their quantum jumps involved in the formation of these pocket universes so each pocket universe will essentially be making a random choice of what kind of vacuum is going to be insided as that pocket universe nucleates the choice will not be necessarily be independent of the previous vacuum but it doesn't have to be the same vacuum you can have jumps from one vacuum to another and the expectation is then that over time eternal inflation will populate the landscape that is it will produce pockets of every type of vacuum we use the word landscape to refer to the set of possible vacua having nothing to do with cosmology landscape is really just a string theory particle physics phrase and multiverse refers to an alleged system in physical space but there are many different pocket universes of cosmology theory okay so eternal inflation as I said can presumably produce an infinite number of pocket universes populating the landscape pocket universes of every type and the key theme is summed by this last comment the kind of multiverse we're talking about here is one where the ultimate laws of physics are the same everywhere they would be the ultimate laws of string theory itself but in any given pocket universe with a given type of pop of a vacuum the physics in that pocket universe will really be the physics of what kinds of fluctuations you can have about that type of vacuum and that means that the low energy physics in each of these pocket universes will be completely different even the kinds of particles that can exist in the different pocket universes can be completely different because particles are really just quantum fluctuations of fields where fields really are just variations of the structure of the vacuum so different vacuums means different fields means different particles and also the vacuum energy will be different for each of these vacuums and we think a typical vacuum energy will be of the order of the plonk scale and could be positive or negative extending from more or less plus the plonk scale to minus the plonk scale but all values in between are possible as far as we know they're more or less equally likely although we don't really know okay so how does this solve our vacuum energy problem well if we imagine that these vacuums are evenly spaced we don't know that but that's a reasonable hypothesis to make some crude estimates then if the landscape has a bare minimum of 10 to the 500 vacuums that appears to be the bare minimum that string theorists tell me and suppose a fraction of those of only 10 to the minus 120 have a small vacuum energy is what we observe and this just comes from the fact that i'm going to assume that the typical value is the plonk scale and what we see is 10 to the minus one hundred and twentieth of the plonk scale so if things are evenly spread the probability of finding a vacuum that small is about 10 to the minus 120 then if we ask how many vacuums will there be with vacuum energy densities as low as what we see we have to multiply 10 to the minus 120 times 10 to the 500 and as you probably know and just add the exponents we get 10 to the 380 so there'll be a huge number roughly 10 to the 380 vacuums whose energies would be as low as what we observe as a crude estimate but it would still be an incredibly small fraction 10 to the minus 120 of all vacuums so if we could explain why we would be living in one of these 10 to the 380 then we would have solved the problem because these 10 to the 380 vacua have vacuum energies like what we observe but how can we explain why we might be living in such an unusual kind of vacuum and that's where selection effects come in how can we explain why we'll be living in such a fantastically unusual type of vacuum possible answer maybe it is a selection effect that is maybe life only forms where the vacuum energy is unusually small and if that were the case then we would explain why we happen to be living in one of these very rare kinds of vacuum and we'll be thereby explaining why we see such a small vacuum energy density um oops skipped a slide here going back in history a little bit as early as 1987 Steve Weinberg is actually one of the original people to talk about this pointed out that the vacuum energy density might be explained whoops i think i skipped a slide vacuum energy density might be explained by this selection effect and selection effect you had in mind is that the vacuum energy controls the acceleration of the universe if the universe accelerates very quickly outward galaxies will not have time to form but the universe has a negative cosmological constant it would rapidly implode and galaxies would not have time to form so galaxies and presumably life would only form in those universes uh where the vacuum energy is incredibly small it's possible therefore that life can arise only if the vacuum energy density is very near zero and then in 1998 a few years later Weinberg teamed with two real astrophysicists to try to actually estimate uh what the effect of vacuum energy density would be on galaxy formation uh and they found that roughly to within a factor of five or so uh the vacuum energy would have to be as small as what we observe in order for galaxies to form at all uh and they were assuming that galaxies are a proxy for life if there are no galaxies uh they're presumably will not be any life so this is the argument uh has been controversial i'll admit it's controversial although it does seem to me that the controversy is getting less intense with time that is more and more people are considering this as a at least a possible explanation for why the vacuum energy we see is so small um in my own opinion uh this selection effect argument is both logical and scientific uh i don't think there's any grounds for thinking that it's not a valid form of science um and i point out that i think we all accept selection effect arguments in other contexts which i think are really equivalent except that we're more familiar with them so we don't worry about it much uh and the example i want to give here is the simple fact that we live on the surface of a planet um if you look around the universe and ask yourself are most places like surfaces of planets and the answer is a resounding no surfaces of planets are very rare places uh most of the universe isn't a planet at all and if it's a if you find a planet the surface i'm defining surface here roughly as plus or minus one kilometer of the surface so i'll allow for birds and fish and creatures like that to fit within where i would call the surface of a planet um but surfaces of planets are still very rare places i try to estimate about what fraction of the volume of the universe is within a surface of a planet and uh i assumed it was roughly maybe one planet per star or something like that uh and i got about 10 to the minus 35 so i'm claiming if you just put down a dot at a random place in our visible universe uh probability that would be within one kilometer of the surface of a planet is only about 10 to the minus 35 so it's incredibly improbable that we should find ourselves on the surface of a planet uh perhaps uh so how do we explain this uh you might think it's just chance uh you might think it requires divine providence to put us here on the surface of the planet but i think really almost everybody would accept the idea that this is a selection effect uh we are on the surface of a planet precisely because it's only on the surfaces of planets that life has a high probability of forming uh and that's exactly what this selection effect argument is all about that we don't expect life to be uniformly distributed through whatever physical system we're talking about uh but that life picks out very special places uh that are conducive to life uh so we're not surprised that we're living on the surface of a planet precisely because we think that's where life is expected to form and similarly uh in this vacuum energy argument we should not be surprised that we're living in a place where the vacuum energy is very very low precisely because that's where life is most likely to form so however i would advocate that selection effect explanations should i think be thought of as explanations of last resort uh that is the main thing that makes it convincing is that we don't have a better argument uh and therefore we have to always be on the lookout for better arguments if we had some dynamical mechanism that would somehow automatically make the vacuum energy small i think everybody would agree that that would be the natural explanation to accept and these anthropic arguments or selection effect arguments uh would probably not be nearly so often spoken about um that leads to the question of whether or not it's time to accept uh this explanation of last resort and uh i would say that your guess is as good as mine it's hard to tell uh i think we don't have to make any kind of a definite decision now but for the vacuum energy density um because we really have not found any other explanation in the 20 or so years that people have been thinking hard about this uh i would say that uh it's uh apparently strongly motivated that we consider this vacuum selection the selection effect explanation and i would say that it's hard to deny that as of the present time uh the selection effect explanation seems by far the most plausible uh of any explanation we know uh but that still allows the possibility of some other explanations to be found in the future okay that was the first uh of the three uh theoretical advantages i wanted to talk about in terms of uh the uh multiverse um and eternal inflation uh number two is very short the whole this is it the whole slide all in one slide in just a few sentences uh one of the nice features about eternal inflation is that it frees us uh from having to know anything about the ultimate initial conditions in in most of its forms uh eternal inflation starts with something small perhaps and then starts to exponentially expand and continues to exponentially expand uh and in the course of all this exponential expansion it approaches an equilibrium uh probability distribution uh which completely forgets how it started uh so it allows you in principle to be able to make predictions about what's probable and what's improbable uh in the eternally inflating universe uh that do not require you to know anything about the initial conditions and that from the point of view of a theorist is a very attractive feature uh it's something that really is only true in principle at this point we don't know enough about the dynamics to to make much in the way of real predictions but in principle we can make predictions uh without knowing the initial conditions okay finally I wanted to talk about this avoidance of a thermal equilibrium phase which I think does require some explanation before you even know what it is that I want to be talking about uh so first I want to explain why we need to avoid uh thermal equilibrium uh so let me suppose the universe did reach thermal equilibrium and I'll describe what the problems are uh suppose for example that reality is described by some quantum system with a maximum possible entropy uh then the system will reach this entropy as the entropy grows uh and it will then be in thermal equilibrium uh in thermal equilibrium the system uh will be undergoing what are called Poincare cycles uh that is in thermal equilibrium the actual microstate goes around a big big loop and comes back to where it started from and then does it again and again and again so every microstate that's allowed that has the right to conserve quantities will occur with equal probability because all just happened one after the other in a big chain that then recycles and that's called a Poincare recurrence and this will go on forever and then you can ask about life uh you might think that life would just not exist in thermal equilibrium uh and that's a natural thought but most cosmologists including me would argue that that's not really the case at all uh in thermal equilibrium you have the peculiar property that essentially anything that can anything can happen uh the probability of some particular thing materializing as a thermal fluctuation uh is just proportional to the famous Boltzmann factor of e to the minus the energy of that fluctuation divided by k t t being the temperature uh so in thermal equilibrium assuming the temperature is non-zero um and it would be for uh an eternally inflating universe uh in thermal equilibrium um it's not true that nothing happens rather everything happens but rarely um so in particular uh one of the things that can happen very very rarely but we don't care uh is the materialization of a brain uh b r a i n not the string theory kind the biological kind uh one of the things that can happen is the materialization of a brain just like mine with exactly every neuron in exactly the same state as my brain is currently so that all of my memories would happen to be encoded just by chance in this brain that materialized from nowhere uh just as a thermal fluctuation and the probability of that is very small it's proportional to e to the minus the total energy of my brain divided by k t but the probability is non-zero uh and the amount of space time we have for these brains to materialize is infinite uh if the system reaches thermal equilibrium because once in thermal equilibrium will stay there forever they have an infinite amount of time for these brains uh to materialize these are called Boltzmann brains um and how does that affect anything uh the point is that if we think of the kind of quote experiments we do um what seems to really be the right way to look at it is to admit that we don't really know what the actual past is of our existence all we really know is what's in our brain what our memories are of all of our experiences and everything that we've read and everything that we've learned from people who've said they've looked in telescopes and things like that um but these Boltzmann brains will have exactly those same characteristics exactly those same set of memories uh so if I imagine discussing the experiment of suppose I know that I have a brain that has exactly these memories what do I expect to happen next uh then uh most of us think that the right way to answer that question in a system that reaches thermal equilibrium is to average over all these Boltzmann brains as well as the possible real me that's in front of the room here in front of you uh and there's only one of the so-called real me and there's an infinite number of these Boltzmann brains uh who have all the same memories and all the same thoughts uh and that means that really with probability one the brain that's thinking these thoughts is not the so-called real me that's in front of this room but one of these Boltzmann brains way out there uh and then if you ask what should that Boltzmann brain expect to happen next uh the answer is that the Boltzmann brain should expect to see the whole world just dissolve almost instantly because through the Boltzmann brain that world's never existed the Boltzmann brain is really just surrounded by a thermal equilibrium gas uh and that should become apparent shortly uh even though it's not apparent to the Boltzmann brain at the time we're discussing it so we don't see that we don't see the world dissolve every second we see tremendous continuity uh and uh I interpret that and I think many cosmologists interpret that as meaning uh that we do not live in a universe that's dominated by Boltzmann brains and if Boltzmann brains could exist at all they would dominate and therefore we do not live in a universe that approaches thermal equilibrium and stays there forever uh so that's the problem that I'm talking about uh of concerning the thermal equilibrium phase and why we think we have to avoid it uh we in fact think uh that our world is very non-thermal not described at all by thermal equilibrium and a particular argument was made in a well-known paper by Dyson Klebin and Suskind in 2002 uh and what they pointed out was that we view and successfully view the history both political history historical geographical history everything uh in terms of history that is we try to explain the world that we see in terms of what we think the past of the world that we see was uh and in particular for example if we talk about the cosmic microwave background uh we can essentially predict that the temperature should be 2.7 degrees Kelvin based on other things that we measure of course it changes with time it's not an absolute number uh but given features of the universe that we could see uh we could imagine predicting before the cosmic microwave background was ever measured what its temperature ought to be based on the history that we think the universe underwent however if we were just talking about a system that was a fluctuation from thermal equilibrium and didn't really have a history the important thing about in thermal equilibrium there is no history uh the probability of seeing something is really just a measure of the number of microstates uh that correspond to the macro state that we're describing uh so if our world uh were governed by counting microstates uh then you could imagine an alternative universe uh that would look just like ours uh but would have a temperature of the cmb of 10 degrees for example instead of 2.7 uh if state counting is what governed as it would in thermal equilibrium that would be vastly more likely than saying the 2.7 degrees that we actually do say uh so the key point here is that everything we know about our lives uh is based on the idea that we view the world historically and that would not be possible if the world reached thermal equilibrium okay um so uh let's say yeah now I want to talk about uh eternal inflation in this context if instead of having a finite system that reaches thermal equilibrium and stays there forever if instead we have an eternally inflating universe uh and it looks like the way I described now I should admit that my description was really a semi-classical description we don't really have a full quantum mechanical spacetime uh description of what eternal inflation might be and things could change someday when we develop such a description but if we believe the semi-classical picture of pocket universes forming and more and more pocket universes forming then uh this uh thermal equilibrium death is avoided uh more and more pocket universes are created which means that all the time the system is exploring totally new region of the phase space that it never saw before and these Poincare recurrences that I mentioned uh would not ever happen uh and then eternally inflating universe it would avoid all the effects associated with thermal equilibrium uh which from my point of view is a strong advantage uh now in order for this to happen uh it is essential uh that the available phase space or the quantum mechanical Hilbert space has to be infinite uh if the total available phase space were finite eventually you would spread and fill it all up and reach thermal equilibrium and be in the problems that I was talking about and no matter how long that takes because the thermal equilibrium will survive for an infinite length of time uh the Boltzmann range would still dominate and we'd be in trouble um so uh it only works with uh infinite phase spaces uh okay uh now I want to that actually completes my discussion of the advantages of uh eternal inflation uh now I want to talk about the one problem of eternal inflation uh which is this measure problem that I mentioned the problem of how to define probabilities uh in an eternally inflating universe now just to illustrate what the problem is I want to start with kind of a toy example uh you might think that it should always be obvious what fractions things have even if you have an infinite set uh so let's consider a particular infinite set uh the set of integers um now normally uh we could ask ourselves for example what fraction of the positive integers we'll just deal with positive ones uh what fraction of the positive integers are odd and I'll bet if any of you venture to answer to that question you would say a half uh and that's can be true if one takes into account the ordering of the integers and there are ways of defining probabilities that take into account the ordering which do give the answer of a half uh but if you really think of this as just the set of integers rather than the ordered set of integers and that by the way is the status of our pocket universes uh the pocket universes are mostly uh situated with respect to each other by a what's called the space like separation which means that some observers will think that this came first and some observers will think that that came first so there is no universal ordering of our pocket universes but the set of pocket universes would be defined uh so we think of the set of integers uh we should notice that we could put that set uh in a different order still including every element once and only once uh we can start by writing one and then three the first two odd numbers then we can write two the first even number then we can write five and seven the next two odd numbers then we can write four the next even number uh and then nine and eleven the next two odd numbers then the next one even number we can go on doing this forever and if you think about it every integer will appear once and only once on this list so it really is a faithful list of the set of integers uh but if you looked at the integers in this order you would say that two-thirds of them were odd uh it really depends on what order you write it in uh so there is no automatically well-defined answer uh to the question of what fraction of the integers are odd and it's the same situation in the multiverse if we ask what fraction of the pocket universes have any given problem and even property excuse me or if we just imagine any experiment it could be pi on nucleon scattering and ask what fraction of the time is it elastic uh that's also an event that will happen an incident number of times in the multiverse and talking about what fraction happens different ways uh is a matter of uh comparing the infinities of the multiverse now a natural thing to do when one has a system like this uh is to uh introduce some kind of a cut-off so that one is temporarily discussing a finite region of spacetime uh and then one can define in that finite region of spacetime the relative occurrences of different kinds of events uh and then take the limit as that region of spacetime becomes infinite uh and that is in fact exactly what cosmologists attempt to do here uh but what we find uh is that the answers we get can in some cases depend rather strongly uh on the nature of the cut-off that is the nature of how you choose an initial spacetime volume uh and how you let it enlarge I think uh I had some details of possible measures but I think I'm gonna skip it that's uh I'll include some of this uh I think we're far running a little late and we don't need to know specific proposals for measures uh but uh I'll discuss some qualitative issues here um one one issue which is important is whether this measure problem is a showstopper doesn't mean that the idea of a multiverse really doesn't make any sense at all and we should be talking about this nonsense uh this showstopper point of view is the point of view taken by for example by Paul Steinhardt uh who wrote the Scientific American article that I maligned yesterday um he's certainly right that this is an unsolved problem and I think it really is a judgment call whether it means that we're on the wrong track because we can't solve it or whether it just means we haven't solved it yet uh I take the position that it means we just haven't solved it yet and I point out uh that the description of the multiverse itself uh is not a problem just as for example the description of the integers is not a problem piano told us exactly how to describe the integers uh centuries ago uh it only becomes a problem when you want to ask what fraction of those integers is odd uh so it's only when you try to ask statistical questions about the multiverse that one runs into problems that we don't know how to solve uh in more detail we can imagine modeling the multiverse on a lattice because it's like to put systems that are continuous onto a lattice so it has a finite number of variables instead of a continuous set of variables uh and then the lattice uh can be finite but growing there's a definite update rule that would be implied by the laws of physics uh we don't claim to know all the laws of physics but someday we might uh and we can certainly build toy models that use the update rules to the best of our current knowledge uh and this infinite system that would follow by setting things up this way on a lattice and using the update rules coming from the laws of physics uh that infinite system would be perfectly mathematically well defined uh that is we'd have a perfect perfectly solid mathematical description of the multiverse what we're lacking is a way of defining probabilities on this space uh but it seems to me that that's our problem and not it's uh okay the multiverse itself is mathematically well defined as I said the major problem arises only when we try to count events in the multiverse and I would argue although as I said Paul Steinhardt would argue the exact opposite but I would argue that the fact that we don't understand the measure problem is no reason to think that eternal inflation is off track uh nature is not required to behave in a way uh that we find easy to understand uh and I think a relevant example here is Arthur Ettingen in black holes uh historically Arthur Ettingen argued strenuously against the existence of black holes because he said that if a black hole formed we have no way of knowing what's going to happen uh we lose control uh and it's similar here uh if a multiverse happens we have questions that we don't know how to answer uh but I I at least don't think that that should in any way mean uh that the multiverse cannot happen okay let me summarize uh by just pointing out that in the course of this uh what I think I did uh was to indicate three trends in modern physics uh all of which are pointing towards the existence of a multiverse uh and in fact a diverse multiverse uh in which election effects can play an important role in explaining what we see uh first of all from theoretical cosmology uh we have the development of inflation and the fact that I tried to persuade you of that most inflationary models uh lead automatically to eternal inflation uh secondly from observational cosmology we have this bombshell from 1998 uh the fact that the universe appears to have a non-zero cosmological constant uh the most plausible explanation I claim uh for why the vacuum energy is so small uh is this anthropic or selection effect explanation uh that I've been describing to you uh the way it works basically is eternal inflation can populate the landscape producing poppy universes of all different vacuum energies and then there are good arguments not completely solid arguments but good arguments that life only forms where the cosmological constant uh is incredibly small and finally an important development that's also part of the story comes out of string theory uh it was only fairly recently that string theorists uh realized that the vacuum of string theory is not unique but in fact string theory probably offers us a plethora of vacuum with a wide range and a high density of vacuum energy densities allowing for this selection effect argument to be completely within the realm of physics we're not hypothesizing uh any kind of a deity that's designing the world to make it suitable for life string theory allows many vacuums that are suitable for life uh and eternal inflation allows uh you the multiverse to evolve in a way so that life uh will have the opportunity to form exactly those poppy universes uh where the vacuum energy is incredibly small and I'll stop there thank you thank you very much Alan that's a very thought provoking talks so I'm sure there will be some questions real yes recently Sean Carroll has been working uh on the idea describing the quantum evolution of the of the universe as some through its Hilbert space structure but he uses quite strongly the assumption that the Hilbert space is finite dimensional is could this run into trouble with the idea of having a finite an infinite phase space or how are those two things related right no very good question uh I've uh tried to uh pin Sean Carroll down on that if you look at what he says very carefully he says that the Hilbert space is locally finite and by that he means that every finite region of classical space uh involves only a finite number of quantum variables inside it uh but he in fact does advocate that the total total phase space of the universe is infinite just like me persons let me warm up well over there yes so your picture of uh um multiplicity of uh metastable state is essentially the picture of uh working on this metaphysics is known as structural glass of spring glass uh and uh once one um first of all this is a very complex problem numerically analytically in any case um but also uh if you start to consider tunneling between different uh metastable states which I think is uh the next generation of development of this theory then there will be fantastic effects like uh aging memory all all these effects which are known in in the structural glass and spring glass theory so as far as I understand the um tunneling is so far beyond reach of the of the theories so or I'm wrong um the answer is you might be right or you might be wrong uh we certainly talk about tunneling whether or not we describe it accurately is something that maybe needs to be thought about more uh but tunneling and this kind of a quantum system that I'm describing uh was in fact first just studied in detail in the late 1970s by sydney colman and frank dilution and so we do have a detailed theory of semi classical tunneling tunneling uh in the limit where the barrier is almost arbitrarily high so that the tunneling is extremely rare and the way the tunneling works in our in our picture uh is that the tunneling starts locally uh in a tiny region uh which can be described in detail by the configuration calculated by colman and dilution uh and then once we have tunneling in a tiny region from one vacuum to another uh this region of new vacuum assuming it has a lower energy density starts to grow at the speed of light uh and exactly how that happens is also described in this colman dilution picture uh the key assumption is uh I guess semi classical tunneling one looks for the tunneling solution that minimizes the action of the euclidean instanton that takes you from one vacuum to another so we talk about tunneling all the time and we think we know what we're doing uh but uh to be honest I don't know anything about spin glasses it might be uh very helpful for cosmologists to get together with spin glass people and uh see what we have in common can you comment on the possibility of having a multiverse which is eternal in the past and in particular on the validity of the bgv theorem in a full quantum theory of gravity didn't quite hear what you said sorry sorry I didn't quite hear what you said okay can you comment on the possibility of having a multiverse which is eternal in the past and in particular on the validity of the bgv theorem in a full theory of quantum gravity okay right you mentioned the btv theorem um yeah uh well this btv theorem uh bgv what's the name the g there is me um there is a theorem that makes it very difficult to talk about a universe that's eternally inflating into the past um and it's a theorem that I proved some years ago with um it's it's board of dooth and belincoln that's those the authors um and what we looked at was what happens if you trace light rays backwards uh through the spacetime that you think may have been eternally inflating uh and the key element is that in an expanding universe uh photon's red shift and particles move slower and slower they're retarded by the expansion but that means as you project things backwards the photon's blue shift uh and the particles accelerate up to the speed of light uh and what we found is that if you believed there was an eternal period where the expansion rate exceeded some minimum as you might this was sort of our definition of an eternal inflation into the past was mean if you believe there was a infinite region going down to the past where the expansion rate was always above some minimum uh then we found that these whirl lines traced backwards uh would reach the speed of light uh the photon whirl lines would reach infinite momentum uh the particle whirl lines would reach the speed of light uh before you reached some finite distance into the past uh which seemed to mean that uh an eternally inflating region in the past was not possible um if you ask is there any chance that somehow this will change uh in a full theory of quantum gravity um i guess i could imagine that the whole question changes in a full theory of quantum gravity in that in a full theory of quantum gravity you don't have a classical spacetime and asking whether that classical spacetime could be inflating all the way into the past doesn't even sound like a meaningful question anymore so i guess i'd be willing to admit that everything is up for grabs uh if we imagine changing the description completely into a full quantum theory of spacetime uh but within the semi-classical picture i think there is very good reason to believe that inflation cannot be eternal into the past although it has a very high chance of being eternal into the future no question here the time direction that is valid for our universe because time increases the temperature decrease is valid for every for all the universe or uh okay is the time that we perceive valid throughout the entire universe or maybe multiverse um i actually be talking about exactly that tomorrow uh and i'll tell you that i think the answer is no uh but i'll give you the details tomorrow more questions well let me ask you something that i usually get asked so i i can have the advantage to see what you think so well you have mentioned the benefits of the multiverse and all that and uh can you see any way that eventually this can be tested in the future experimentally eventually people can see well there's something that can put to test that there are many universes okay um what do you answer when you ask that my answer is please ask allen good okay i'll give it a try uh what i i i've i've i've figured out three possible answers i can give when people ask me that question of course all of them are hypothetical future observations i think nobody's gonna expect the idea of a multiverse to be confirmed anytime soon but sometime in the distant future and i don't know if we're talking 25 years 50 years or maybe a hundred years one could imagine i could imagine at least that the multiverse might become standard science uh and i can imagine three kinds of ways that can happen um number one eternal inflation really is a consequence of certain detailed types of inflation it's not just an extra assumption that's being made uh we are all the time uh better constraining through mainly observations of the cosmic microwave background radiation the details of how exactly inflation happened what kinds of fields were involved what kinds of interactions those fields had and if we could really pin down the details of the field theory interactions that led to inflation uh that could tell us uh that that particular kind of inflation leads to eternal inflation no doubt about it uh so by learning enough details about inflation one can imagine uh that eternal inflation could simply be a consequence that's method number one probably the most likely of the three i'll mention here um method number two has to do with these fine tuning problems like the cosmological constant or vacuum energy density um i've tried to argue to you folks that uh although we don't know for sure what the right explanation is the best explanation we have so far for why the vacuum energy is so incredibly small is the selection effect argument uh and the vacuum energy is not the only thing that people talk about in terms of selection effects uh i focused on it because i think it's the most clear cut by far it doesn't involve any assumptions about what life requires whether life has to be carbon based or whether carbon has to exist for life to exist it just requires basic elements of of times uh it requires you to assume that life can't form if the universe only exists for 10 to the minus 43 seconds and that's about all you need to assume about life so so the vacuum energy is i think the most clear cut of these fine tuning problems but there are in fact many fine tuning problems and no doubt more that might be discovered and uh if we keep finding that the only way we can understand why the laws of physics that we observe are what they are is the selection effect argument uh that can make this selection effect argument all the more persuasive as time goes on so that's number two of my selection number three is the most direct but i think the least probable uh in in a multiverse model where pocket universes are nucleating here there and everywhere uh if pocket universes nucleate more than a certain distance apart uh they'll never see each other because the space in between will be expanding fast enough so that even though the two pockets expand at the speed of light the space in between will expand fast enough to shield them from ever touching each other and that will be the normal case but uh if two pocket universes nucleate close enough to each other then as they evolve they will actually collide uh and that leads to the outside possibility that we could perhaps observe the effects that indicate that our pocket universe underwent a collision sometime in the past and uh this would have a chance of showing up uh as a distortion of the cosmic microwave background radiation uh it would be a circular pattern on the cosmic microwave background sky uh circular because the collision of two bubble universes is where the collision of two spheres and when two spheres intersect they intersect on the circle and that would produce these circles on the sky uh cosmologists have looked for them in the in the w map in plonk data so far nobody's found anything or you wouldn't have heard about it uh but uh the data's getting better all the time there is still a possibility that something like this could be found sometime in the future I have to admit that I think we have no idea really how to calculate the probability that our universe would have undergone a collision in the past even if this whole multiverse picture is correct there are still too many parameters describing the multiverse that we don't really know um my own hunch is that it's incredibly improbable that we will find a collision of our universe with another in the past uh but I don't really know so it is a conceivable avenue and if we did find such a collision uh presumably it would take a while to really pin down the details of what this what it looked like and whether it really agrees with what you'd expect uh from a collision of two bubble universes uh but it could be very definitive well actually we have seen collisions of two black holes 1.2 billion years ago that's also highly improbable so what about the getting an open universe after Kolemander Luce sorry getting an open universe after Kolemander Luce the cake will you think that this is something that can be stated as a potential prediction that uh you know whatever you get after after Kolemander Luce bubble nucleation that would naturally give you an open universe rather than the yes okay I mean that's I don't think that will ever confirm the multiverse but these Kolemander Luce tunlings as you said always give you universes that are slightly open and if we observed that our universe was not so far up universes consistent with flat but if we observed that our universe was actually slightly closed and not slightly open that would make this multiverse picture that I'm describing very difficult to keep and probably it would rule it out completely so that's a way of showing that we don't have a multiverse but it's not a good way of showing that we do very good and since today's your last talk on inflation you mentioned the problem of inflation regarding the the measure problem can you mention other problems that people could be eventually solved in the next few years about inflation or what which questions do you think are are are potential good questions to ask about inflation that haven't been solved yet in the next few years okay I do think that the measure problem is the most salient because I think in order to have a quantitative picture of this multiverse we we definitely need to solve the measure problem you're asking me are there other problems that I might talk about and I well I guess the other key problem is how to describe inflation completely in the context of string theory that's certainly something that is an important goal I think most inflationary enthusiasts are also string theory enthusiasts and inflation would be a much more solid footing if we could describe it fully in the context of string theory that's the answer I was hoping you would say well I think it's sort of clear that the experiment that would cause all of our jaws to drop would be if the if the experimental group could succeed in doing what bicep two thought they did two years ago three years ago now three years ago a group of microwave background experimenters called bicep two as many of you know announced that they had seen in the polarization of the cosmic microwave background patterns that are called b modes the letter b and such patterns of the polarization would be indicative of gravitational waves in the very early universe gravitational waves that it was assumed would have been produced directly by inflation itself in the very early universe initially this discovery looks fantastically exciting and the initial announcement made it sound like the result was absolutely rock solid no chance of anything going wrong the significance of the experiment was quoted at seven sigma if you know what that means it means the experiment is really certain but it turns out that dust in the galaxy can also produce these b modes the bicep two group was aware of that statement but when they tried to estimate how much b modes could be produced by the dust they came up with a very low number much lower than what they were observing and they were satisfied with that but in the next few months other groups started looking in more detail at these dust estimates and at first it became an object of doubt whether or not maybe there was enough dust to account for the signal then the definitive study was a joint paper by the bicep two team and the plonk satellite team to analyze this data in the asking whether or not dust could explain it the collaboration between those two groups was very important because the bicep two experiment only observed at one wavelength so they could see the b modes but when you only measure them at one wavelength you have very little clue about what's causing those b modes the plonk satellite had I think seven or eight detectors at different wavelengths so they had much broader coverage and much better information therefore to figure out what's dust and what's primordial signal anyway the bottom line is that when it was all put together they came up with the definitive answer that it could all be dust after all and that's where we currently stand but there's still a possibility that these b modes exist at levels that can be detected theoretically different models of inflation produce b modes of very different amplitudes so it's possible that the b modes are just around the corner and as these experiments become a little bit more sensitive they'll find them that would be very exciting it's also possible that the actual level of the b modes is far below anything that will ever detect so the non-observation of b modes is by no means a problem for inflationary models but the observation of b modes would be very very exciting I might mention that one of the reasons it's so exciting is not just that we have an extra piece of evidence for inflation but we'll also answer a question that we're really totally clueless about right now I think I probably mentioned maybe even near the beginning of my talks that we don't know at what energy scale inflation happened and another way of saying that is that we don't know exactly what time in the early history of the early universe inflation happened so far everything we've observed is consistent with a broad range of possible times at which inflation might have happened if we could see these b modes that would be the observation that would tell us at what what the energy density of the universe was at the time of inflation or what time inflation happened and that would be incredibly important in terms of trying to understand in detail what the actual field theory physics was that drove the inflation my last question could you comment on alternatives to inflation no the the alternatives to inflation I guess the principal ones are the ecoporotic model of Paul Steinhardt and Neil Turrock there are variable speeds of light so-called alternatives to inflation my feeling is that none of these have the same underlying physics appeal that inflation has one of the beauties of inflation is that it really does not involve assuming anything new about physics it does involve extrapolating what we know the very high energies but it really only needs the straightforward extrapolation of what we know and one doesn't necessarily even need a new scalar field the ordinary Higgs field of the of the standard model seems to be a possible candidate for the field that drove inflation so that makes it I think far more plausible than for example variable speed of light theories because we don't have any theory that suggests that the speed of light should be variable the ecoporotic model is very similar to inflation actually one can argue about whether or not it's really a different model at all but it's a model that includes a bounce so it's basically a bounce a bouncing universe followed I'm sorry inflation happens before the bounce rather than after the bounce so we have inflation bounce and then universe to me the biggest implausibility of that theory is that even if if God asked Paul Steinhard how he wanted him to start the universe and God accepted Paul's suggestion and started the universe in this ecoporotic pattern if the physics of the universe included anything more complicated than what Paul puts in which is one scalar field that has just the right potential energy function to make these bounces work if the physics is any more complicated than that then sooner or later this ecoporotic bouncing universe well as far as I can tell undergo a tunneling exciting the other fields and I think it will very quickly lead to eternal inflation of exactly the type that I've been describing so I don't view the ecoporotic model as being stable against tunnelings to a more generic kind of inflation okay so before we finish again so everybody's welcome to some refreshments and we have the students to come down and ask more questions to to Alan and we promised today would be even more food for the students that will stop here just like Alan again