Let's take a look now at the cosmic inflation which is now the dominant theoretical paradigm of what happened in the very, very early universe. And the basic idea was mostly credited to Alan Guth, but a couple of people before him, including Alexei Starobinsky in Soviet Union, came up with the same idea, but did not really follow it or interpret it in correct way. And then it was developed by many others, including Andrei Linde. And so three of them, Guth, Starobinsky and Linde shared the Kavli Fundamental Physics prize for 2014 for their work on inflation. And they got prize now because CalTech experimental cosmologists found pretty good signature confirmed inflation was right. This is a page from Guth's notebook, where he figured out what's going on and wrote spectacular realization. And the theory was so compelling, that almost instantly people started believing it, even though there was no clear experimental prediction or proof yet. People believed it because it explains some long nagging problems, and two of them in particular are very striking. The first one is, universe today is close to flat, even back in 1980, it was so close to one but it somewhere between 0.1 or 2 or something like that. Anyway, it's very close to unit. The second problem was simple horizon problem. Tell you this in a moment. The third one is monopole problem. Early theories predicted there'll be large abundance of magnetic monopoles, which were so massive that they would completely dominate and close the universe, and yet here we are. And there were no detections of monopoles, so somehow they had to be diluted away. It also explains the power spectrum of large-scale structure. And it predicts spectrum of primordial gravitational waves. So let me tell you a little bit more what these problems are. Flatness problem is that if you look at three-dimensional models, omega total evolves in time. And it always evolves away from 1. If it's a little less than 1, it's going to be ever less so as time goes on. If it's a little more than 1, it's going to get stronger and stronger. And so in order for it to be so close to 1 now, it had to start with an extremely close to 1. Now this is a vivid illustration of it, and this is from Ned Wright. If you look at the behavior of the scale factor of the universe, over say, 12 billion years. And ask, what was density one nanosecond after the Big Bang, and so we have this number of 400 odd 6 trillion or whatever grounds be cubic centimeter. If you add 1 gram per cubic centimeter to this number, the universe would have collapsed into big crunch by now. And if you subtract 1, would have been twice as big. It's that sensitive. Right, and so obviously had to be just amazingly well tuned not to blow itself apart exponentially, or to collapse back into big crunch. I'll tell you quantitatively exactly how much. The horizon problem is this. At any given time, you can see particles that are as far as it took time for light to come to you. And so the longer time goes on deeper into the past, you can see, right? And the question is, how far could you see at the time of the cosmic recombination, when the universe was 380,000 years old? It wasn't 380,000 light years. Expansion slope. But it was about a few hundred million light years, or 120 some mega parsecs. So you ask the question then, what was the angular diameter of the observable universe at that time projected in the sky now? And the answer is of the order of one or two degrees. So there's tens of thousands of patches on sky today. Each of which was not in a causal contact with any others at the time micro background was produced. And yet they all have the same temperature to a few parts in a million. How do they know that regions that were causally disconnected from them had the exact same temperature? And the inflation explained why this happened. Essentially that they were thermal contact earlier, then just got carried apart by the inflation. So how does this work? The idea here is that, modern view of physical vacuum is that it's not vacuum empty, but it's filled with virtual particle pairs that [INAUDIBLE] and so on. And in any quantum mechanical system, there is uncertainty principle which is if you know exactly what some energy level is, you don't know is it the, which one it is. Is it the lowest or not? So you cannot at the same time know that this is something truly ground level and measure it. This can happen to physical vacuum too. And so supposedly for whatever reason, physical vacuum wasn't one energy level up. It's just like exciting atom of hydrogen by one orbit [INAUDIBLE]. And then for reasons the theories worry about, at some point that fill the case and physical vacuum drops to a lower energy state. Which means a great deal of energy has to be released everywhere at once. And this turns out to be also equivalent to a phase transition. Let's say boiling liquid into steam, at some point things are unstable or in this case will be like freezing going from liquid to frozen, into a solid state. And it starts in different places, but very quickly spreads out. And just like there is latent heat for evaporatiob, latent heat for freezing or melting, same thing happens here. So this amount of energy then drives exponential expansion, and also through some processes, is responsible for all of the matter energy density content of the universe since then. So these bubbles of, through vacuum then forming false vacuum. And it could be many of them. Those will be independent universes. And that is where the idea of multiverse comes in. Problem is that they're not a priori, not testable. But it could have happened, we just don't know. So this is called chaotic inflation. Now let's look at this quantitive right? Remember, cosmological constant, a form of dark energy, corresponds to energy density to the physical vacuum. This is what we're talking about here. But we're talking now about something that's many, many orders of magnitude higher than the cosmological constant today. And that vastly dominates everything else. It could have been no other matter at all, all right? Friedmann equation for just constant vacuum density, eliminate all of the terms, the matter, the radiation, the sun, just has cosmological constant term, right, which is energy density physical vacuum then, is very simple differential equation. Take square root, it's D X over X. And solution of that is an exponential, and that tells you that in the situation, where there is a constant energy density, the universe is going to expand exponentially. And then some point, something else happened that stops that expansion. But according to the theoretical estimates, this happens over about 100 e folding times. 100 e folding times is 43 orders of magnitude, powers of ten. This is how you can have size of the universe, maybe size of sub atomic particle suddenly inflate, carry the part regions that were previously in quasal contact. And now they're distributed over much larger volume, but they used to be in thermal contact at one point. And this is why we all have same temperature. Now in terms of what happens with density parameter. Evolution of the density parameter as it deviates from unity, there's this negative exponential. And to exactly to the -200 power. And that tells you that if you want to have omega as observed today, you have to tune it to 87 orders of magnitude, roughly speaking, in order not to mess it up later. So the universe becomes asymptotically flat. This is the expansion history except this is flipped. Remember, 1 + red shift is inverse of the scale factor, so this should have been flipped vertically as a function of time in the logarithmic axis. And sometime around Planck era, universe did something, maybe it was expanding. Then suddenly, this inflation period happens. It was a very rapid period of expansion and inflation ends, and then resumes as normal Friedmann model. And so this extra period of size inflation is what produces interesting things. So how does this solve flatness problem? Well, if you take surface of sphere, some region on it, you can see there is a curvature. If you keep the region the same size, but make the sphere much bigger, eventually it becomes hard to tell that it's not flat. It is just like people used to think that Earth is flat because it looks flat, but when you look from a spacecraft, you see it's a sphere. And it's the ratio of the region you look at to the curvature radius that determines just how close locally it is to flatness. So this is exactly what happened. Universe got inflated by so much, that size of the observable universe is tiny in comparison. And therefore, it looks flat no matter how much curvature there was originally. Right? How about horizon problem. What? It's what I told you already. You can have regions in a thermal equilibrium, and then different pieces of it get carried apart faster than speed of light, because space can expand faster than speed of light and become reconnected causally only later, like today. And yet they started with same temperature and follow the same physics, so therefore they're all going to look same way and combination. So this is such a beautiful explanation for these two very fundamental problems which are otherwise completely mysterious, that people said, this must be right somehow. Moreover, as a benefit, inflation said that, in early universe, their quantum fluctuations as particles get annihilated and formed and so on. And there's gonna be density and fluctuations. And when you compute this correctly and expand them to large scales, you expect to see mass density spectrum, power spectrum, that is a power law. And that's exactly what's observed, as you may recall, so is another spectrum. So inflation explained several fundamental observations. It did not predict them, because we already knew the answer, we just didn't know why. This is pretty good, but it's really nice if you can make a prediction. And it did have one important prediction. And that is that universe would be filled with primordial gravitational wave background, which is sort of like gravitational equivalent of the cosmic microwave background, but from the Planck era. Because that was sort of the equivalent of recombination epoch, but for gravity, with a particular spectrum. Now the energy density in the background is so low that there is just no chance at all of observing it in any form or fashion, here and now. However, back at the recombination era, it had very, very slight effect on the polarization of electromagnetic radiation from the plasma. And that effect is part in 100 million of the signal. All right? So the microwave background signal itself is part in the hundred million of thermal background in this room or in Antarctica. And this is one hundred millionth of that one hundred millionth. This is a really precise experimental physics. And in fact, they did that, and this is a plot of piece of sky. There, blue and red are density fluctuations, they're measured, and these little lines are indicating the polarization vectors, that's exactly what inflation predicted. And this is why there was this big hoopla about BICEP2 result. And now people are scrutinizing it. Could it be polluted by something else? But if it holds, this would be a direct experimental verification of what was the sole prediction of inflation theory. Something that we didn't know before. Explaining important stuff is already pretty good, but this was actually prediction. Theorists have to live dangerous lives, stick their neck out, and this one did. And this is why Linde, Starobinsky and Guth just won the Kavli Prize.