So what is the way to test this idea? This really, nearly crazy idea. That this macroscopic structure we see today in the universe actually came up from this tiny, tiny quantum noise at a 10th of minus 26 centimeters or less. So one thing we know about this quantum noise. When we actually looked at this experiment of shooting the guns through the walls- holes in the wall to a screen. Everything was, indeed, random, right? So randomness means that probability should follow a simple bell curve. And this is the bell curve. And when you, and when people talk about, say, population growth, and many other statistics. Large statistics always means that you have this kind of Bell curve. And that represents the total randomness. So can we test that? And, indeed, we can. So what you can do is look at this map of temperature. Looking at all possible directions you can measure the temperature of from our- coming from the big bang. And then just count the numbers of okay, how many of them have say- temperature 10 to minus 5 higher, 10 to minus 5 lower. And you keep plotting the numbers as a function of the temperature. So this horizontal axis here tells you how much temperature is different from the average. So here, is- is twice as big, compared to the typical variation. Here, it's twice as less than the typical variation you have among the temperatures. And indeed you see a beautiful bell curve. So what this is telling you is that this idea that the variation of temperature in cosmic microwave background really does come from the quantum noise when universe was incredibly tiny. When the microscopic laws of physics, namely, quantum mechanics, was at work. So it looks like we have, have a group, very good evidence now that inflation produced this quantum noise. And quantum noise eventually led to the vari- temperature variation in the cosmic microwave background. And that temperature variation eventually led to the formation of stars and galaxies, so everything is now tied together. So we are born out of that quantum noise, it seems. But of course, we would like to test that further. Now the recent test coming from the Planck satellite I mentioned the first day, is really the beginning of that kind of test. And that case is getting stronger and stronger. Now, you would like to understand yet another question though. So how could it possibly be true that energy density was constant for a while? And the idea is this, and again these slides are slightly technical, so if you don't want to follow through it, that's okay. So it's like the ball just falling down this hill. So let me show this once again. So, if you have a ball sitting on a hill, slightly rolling down from up here, Then it starts doing this, but the same time, the universe actually expands exponentially. Now, why is that? Well, if the ball is falling down very, very slowly. Then for a while, we have this energy sitting there without changing very much, assuming it's very slow. So that's the situation. You have more or less constant energy density. Not exactly constant. Because the ball keeps going down the hill. Energy keeps getting smaller and smaller. But only very slowly. So to a good approximation, the energy density is actually constant when the ball is slowly rolling down the hill. And indeed that's actually what happens. So if you assume this potential is shallowing up. So it's nearly flat. The slope is more less flat. Then the ball wouldn't be pulled down very quickly, so it rolls down the hill very slowly. And if you put that into an equation. You’ll find this equation here which shows that the expansion of the universe itself actually acts like a molasses. And it doesn't actually let the ball fall down quickly. It sort of tries to stop it on the way. It acts like a friction. So when the ball keeps going down the hill because of friction, it can't go very fast. It doesn't get accelerated. So it just keeps going downhill very, very slowly. So energy density remains small as constant. And if you put those equations together, this equation and the Friedmann equation we talked about a few minutes ago, then you find this result. That energy density is just given by this height of the potential and then and, and the universe expands exponentially. And to make sure that we understand why the entire universe looks so smooth and flat these days. Then you need to have this exponential expansion more than a 60 in exponent. Well once you achieve that, then you get this the explanation of everything we talked about today. Namely how come different parts of the universe seem to have almost exactly the same temperature. How come the universe is so smooth and flat. But also at the same time the universe seems to have these wrinkles. And all of these things can be tied together with this very slowly rolling downhill of a single ball. And that ball, or particle, is named inflaton, and that's the particle that caused inflation of the universe. But there are still many mysteries, so what exactly is this inflaton? Who caused inflation? When did it happen? How much did it inflate? Can we come up with a definitive proof of this idea? So we'd like to solve these mysteries too. And one clue it turns out, is that when the inflation happened, not only that it caused these fluctuations of the vacuum. It also created the wrinkles and ripples in space time itself. So that is the, what a property called the gravitational waves. Space and time itself has a wrinkles and that propagates like a wave. And so that wave is something we can still detect today if we try hard enough. So when you have this cosmic microwave background, it's just a form of light as you remember. It's a radio wave but the same thing as light. And one thing we benefit from is the kind of sunglasses with the polarized lenses. And that shuts out the glare from the surface very efficiently, because the glare has the polarization. Meaning that electric field oscillates only sideways. So if you block the sideways motion, and only let only the vertical motion get through. That's a particular kind of sunglasses you can buy, then you've shut off the glare almost completely. But you can see everything else, because most of them have both horizontal and vertical polarizations. And you use these polarizations to separate different kinds of modes of light, or radio waves. One of them is called E-mode. It looks like something is sort of emerging from a point. The other one is called B-mode. It looks like something is sort of curling around. And it turns out that this E-mode can be generated without having these ripples in space-time. But B-mode cannot. So if you manage to detect this mode of polarization, that would be a very good proof, that indeed inflation produced ripples. Not only on overall energies, but also on the space and time itself. And that would be a definitive proof that inflation indeed happened. And you can even measure at what time in- inflation has happened at the same time. And there are many experiments that try to do so and here is a partial list of those experiments. So just to repeat everything gets this quantum noise including gravitons which is the fluctuation of space and time. And that will lead into this B-mode polarization of Cosmic microwave background. And how big that fluctuation is, how big this B-mode is, is directly tied to the energy scale when inflation happens. Which is the same as saying when it happened. And these experiments are gearing up to do so. So I'm going to tell you, just one experiment called LiteBIRD, with the Japanese community trying to launch sometime in the next few years. And this will be a satellite onboard, and this is really dedicated to study this B-node polarization of cosmic microwave background. And that may have a sensitivity to really see the definite approval of inflation. So this is again the angular scale we talked about before And so, if you go this way, you're looking at sort of a globally on the entire space time. If you look at this way then you're looking at the different spots at a smaller angular scales. And many inflation theories predict the size the B-mode in this range and the LiteBird experiment can go down to this part. So if the prediction of these theories are right, then the LiteBIRD experiment should be able to show that B-mode prioritization indeed exists. And that would be a very good and strong proof that inflation indeed happened, not only produce these ripples in energies, but also ripples in space and time itself. So that's the way we try to understand this period of inflation much better, and we can now go back- all the way back to the point when the universe was incredibly tiny. And the time scale is something like 10 to minus 334 seconds. We don't know exactly what it is. As I told you, we'd like to measure that now, but it happened very, very early on in the history of the universe. Where the individual stretched by an incredible amount in a very short period of time. And planting this quantum noise on space and time and energies throughout the stars and galaxies and us. Could have gone much, much later, 13.8 billion years later. So that's what we think is what happened at the beginning of the universe. Now we switch our gear to think about what may happen in the future. And you might notice that here is expanding, but now sort of picking up speed. So something is going on here, rather recently in the big story of the universe that universe is actually speeding up. So what's causing this speedup of the universe is called dark energy and that's the subject next.
