[SOUND] Welcome back to my course, From the Big Bang to Dark Energy. So as we discussed in the previous two classes, we would like to address these fundamental questions about the universe. And here's the Outline. We finished the first lecture, From daily life to the Big Bang, and second lecture, Birth of elements and Higgs boson. So in, in this lecture, we'd like to talk about Dark matter and Anti-Matter. So both are sort of mysterious components o- of the current composition of the universe. To get started with these questions I'd like to introduce the idea called power spectrum. you may not be familiar with the term. So I'd like to give you a little bit of an idea on what it is. So we talked about the cosmic micro background. That's the way we can still observe the Big Bang happening. 13.8 billion light years away, which means we are looking at the Universe when it was 13.8 billion years ago. That's the when the time the Universe was so hot, and was radiating like, a lot of light. And what we observing today is the light emitted from the Big Bang stretched by the expansion of the Universe, to much longer wave length That we observed that as a microwave or a radio wave we can detect using satellites for example. So you have seen this picture before so what's going on here is that early on, in the very early stage of the Universe it was so hot that even atoms couldn't exist. They'd sort of melt, into some, something called plasma. It's a kind of soup, made up of electrons and atomic nuclei. So back then, Universe was so dense, the light could not penetrate into it, really, so that we could not see through it. So that's why that part of the Universe looks kind of foggy and, and, and, obscure. But at one point the old electrons got bound together with atomic nuclei and became neutral atoms. At that point, the Universe all of a sudden became transparent, and so the light can now travel through it without any problems. And that's the stage that is called recombination. And I do know why it’s called recombination, it's a combination of electrons to the atomic nuclei. And so that they became unusual atoms. And what we see today is the light that was emitted at this stage of recombination, traveling through the Universe, over 13.8 billion years. And finally reaching us in terms of the telescopes. So that's the information we can get out of this era, when the Universe was only 380,000 years old. And, so what we can observe then, is by studying what the temperature was at this stage, by looking at all different kinds of directions we can observe today. And what we've, have found though, is that the temperature was pretty much the same anywhere with a very good accuracy. One part in about every 100,000. But it turns out that there is a tiny, tiny differences in temperatures depending on where you look. And that is actually a consequence of the sound that was propagating through this plasma of the soup of electrons and nuclei when Universe was very hot and dense. So these, sound waves are sometimes also called acoustic waves, and those acous- acoustic waves can still be seen in what is called the power spectrum. And if this doesn't slide make sense to you, that's Okay. We're not going to actually much of technical information for later discussions. But, just those of you who would like to understand the definition of the power spectrum, here it is. So, what do you do is observe the temperature over the entire sky. And we can't picture the sky in a, in a flat map, so we just open it up in a sort of egg shaped way to try to show the entire directions of the Universe you can observe. And what you see is some hot spots and some cold spots. And, and as I said, they only differ by 10 to the minus 5 or so, very little difference. But nonetheless you can observe this temperature variation depending on which direction you look at. And if you're versed with mathematics what you are supposed to do, is to decompose this temperature variation which is delta T in this equation in terms of something called spherical harmonic function. And then compute this quantity that gives you the definition of the power. For a given angular scale. And this number L, refers to the angular scale. And let me tell you what that is. So if you change the angular resolution of the map of the temperatures, what you see here is that you can actually go from very large scales where looking at sort of The rather the broad brush pictures of what's going on. to a very fine scale, where looking at these tiny spots. So what you can do is that, by starting from this map of the entire sky, you separate out the features on a broader brush scale, and features of the tiny spot scale. And that's the difference of these angular resolutions. So depending on which resolution you're looking at, you may see a rather big variation in temperature, and focus on this moment. This is when the contrast is the biggest. If you go down there, contrast is rather dim. So that's the definition of this angular power spectrum, depending on angular resolution you use, you may see a bigger contrast or a smaller contrast, and that is plotted in this power spectrum. So that's the idea of the angular power spectrum. And the most important thing about this is that, because the entire Universe is now lit up by the background of this light coming from th- 13.8 billion light years away, everything in front of it, that's the en- entire Universe content, is shown through this light. So if you study this light coming from the Big Bang very carefully, you get information about what's inside. So that's the idea, how you can get information on what's going on about the composition of the Universe today. So, one information you get, is actually the shape of the Universe. That might sound very strange to you. But what's going on is that you can view the sides of the Big Bang going on over there. And there's some typical size of space that is relevant for the sound waves that propagated through the, plasma, in early days. And what you can do is measure how big that would look to you. That is called the angular size. How wide that size of the sound horizon Looks like to you and that actually tells you what the shape of the Universe actually is. You're looking at an object of some fixed size here, or here, and if the Universe is flat then this angle here is proportional directly to the size here. But if the Universe is curved in a certain way, then your apparent angular size may look smaller or bigger. So that's the way you can tell the shape of the Universe apart. And here we go, if you change the shape of the Universe, you're angular power spectrum should look different. And when the what you'd expect and what the data agree with each other is when the Universe has this completely flat shape, it's not curved at all. So as a result of this data and, and compare that to what you'd expect theoretically, you can actually understand the shape of the Universe. Then the answer turns out to be that Universe seems totally flat like this one. You can also look at what is inside the Universe. So depending on the composition of the Universe in terms of the ordinary atoms, that is usually called baryons due to some history reason in this community. The amount of atoms in the Universe also ends up changing the shape of this angular spectrum. So looking back again at the data, you can try to decide what is the composition of the Universe in terms of ordinary atoms. And that's a number you can extract from the data. See how much it varies as you vary the amount of atoms in our Universe. So, by looking at this data, you can extract what is making up the entire Universe today. And that is called energy budget of the Universe. So, when we admire the Universe by looking at these bright Stars and galaxies, they look so beautiful. But they, together, make up only about, like, a half percent of the Energy Budget of the Universe. If you put together, sort of ghost-like particles called Neutrinos, which we briefly talked about in previous lectures, you know, it's amazing that these tiny particles make up pretty much about the same amount as the, all the stars and galaxies combined. So these tiny things can make up a lot of energy budget because they're so many of them. But still, this is clear that's it's a far cry from 100% of the energy budget of the Universe. And now come the Rest of ordinary matter, that is made up of electrons, protons and neutrons. And they give up about 4.4%. So, again, it's a far cry from 100%. Then comes the component called Dark Matter. Again, we talked about this in previous lectures. And, roughly speaking, they make up about a quarter of the Universe, but that still leaves quite a bit. The rest is called Dark Energy that makes up about 70% of the Universe. And as we will discuss in this lecture and the next lecture, we don't know what is Dark Matter, we don't know what is Dark Energy. So, 95% of the Universe is still unknown to us. We know they exist, but we don't know what they are. So that was a huge surprise to us when we discovered this situation only as recently as 2003. So, we now have to change our view of the Universe completely. We used to think the entire Universe is made of the kind of matter we are made of. But that's actually not true at all. It's only less than 5%. The rest, 95%, is still a big mystery. In addition to the fact that we have discovered something unknown to us, there's another mystery. That there is supposed to be something we know in the Universe, but it isn't. So that is something called Anti-Matter. Because we can actually make Anti-Matter in the laboratory, Big Bang must have made Anti Matter too. But as far as we can look, there's no Anti-Matter in the Universe, which actually turns out to be a good thing, we will talk about that later in this picture. So, putting that together this is the current Energy Budget of the Universe. And what we make, or made of, is actually less than 5%. And the remaining 95% is still a big mystery. Okay, now the questions to you, is that okay, so given this amount of ordinary atoms that make up the Universe. And if you remember what we talked about in the previous lecture, what is the amount of helium, in the energy budget, think about that.
