What I'd like to do now, is say a bit more about dark matter and dark energy, and how we infer their existence and properties from observations in cosmology. And this all starts with Friedmann's equation. As I told you, he was the first to understand the full dynamics of the expanding universe. And what he found was that those dynamics are the same as familiar systems. So for example, let me take this pen and throw it up. Initially, it moves quickly, then it moves slowly. Its kinetic energy is reducing but its total energy is conserved. So it transforms kinetic energy into potential energy. Thus. We can say kinetic plus potential is a constant, total energy. Friedmann's equation for the whole universe, has no more content than that. So, if you'll forgive me, because astronomers really love equations. I'm going to write it down just to convince you that it really is quite a simple thing to deal with. And if you're not mathematical then, all I'm doing is writing this in other language. What I need is to symbolize R of t, by which I mean the size of the universe. I won't be specific about precisely what that means. The kinetic term corresponds to how fast the universe is getting bigger. So in calculus notation, that's dR by dt, but it just means a kind of speed for the whole universe. And square it. Then something that involves the gravitational constant. The density. Of the whole universe, times a scale factor squared divided by 3, is equal to a constant. And this constant, according to general relativity comes from the curvature. So, Friedmann's equation involves the rate of expansion of the universe, the density of what's in it and the curvature. So, K would be 0 for a flat universe, as it seems to be. So, what that means, is we can observe how the universe expands over time. This can tell us two great things. It can tell us the density of the universe as a function of time. And it can tell is whether the universe is curved. So that sounds almost too good to be true. The question is how do we figure out how the size of the universe changes with time? So, how do we measure the expansion history of the universe? One way of looking at this is to go back to Hubble's Law. And say that we need the hubble constant as a function of time, because that governs the rate of expansion of the universe, which is what we need. That means, since we can observe spectroscopic red shifts, we just need some means of inferring the distance to objects seen at great light travel times. Measuring distances in cosmology is, is a real challenge, because everything is so far away. The standard technique is known under the strange name of Standard Candles. Imagine you had a very powerful light bulb that you knew was of uniform output. If it's nearby, it's very intense. As you take it further away, this intensity would fade so that the relative intensity that you observe is a direct guide to the distance. In fact, you would say that the, the flux of light, symbolized by F, it's just proportional to 1 over the distance squared, if you can astronomical objects that all emit the same amount of energy. A very good candidate for these emerged during the 1990s, Supernovae, SNE for short. Which are exploding stars around one cell of mass, in the case of type IA. And these all empirically have very nearly the same energy output. So we can use them to measure distances. And therefore empirically one can map out the relationship between distance and red shift in cosmology, normally symbolized 'z', but this just means the small distances ... the recessional velocity in units of the speed of light. Hubble's Law says this is linear. But at large distances, this has some curvature. And it's the curvature of this relation that represents the change of H with t. And this is what lets us measure how the universe has changed its expansion over history. The conclusion is that you can only match the data that we have with Friedmann's equation if the density of the universe consists of a number of different ingredients. There has to be about 70% dark energy. And dark energy remember is something that doesn't change in its density with time, and about 30% matter. But this in itself is broken into about 25% dark matter, and about 5% of ordinary matter, atomic matter. This is the 5% that we got from nuclear reactions. So, strangely, the total adds up to approximately omega equals one. And therefore, the universe is flat. But most of its contents are not the ordinary atomic material that we see. So the expansion history from supernovae is one powerful piece of evidence for an accelerating universe. Another way we can learn about this, and to learn more about the existence of dark matter, comes from studying structure in the universe. And what I mean by this, is looking at the distribution of the building blocks of the universe, that is the galaxies. Which you want to do in three dimensions. We do this very simply just using Hubble's Law. So we measure the velocity, that gives us a radial distance. So we can immediately take a set of galaxies observed on the sky, and figure out how far away each one of them is. So that means take a picture of the sky, take say some, narrow strip on it, and now expand this in the radial direction using Hubble's law. What this allows you to do, is then cut out a kind of pizza slice out of the universe, where this is the radius D and the galaxies are spread out in distance and in direction on the sky. Now what we find is that there are patterns in this distribution. Colossal patterns. The galaxies tend to make up chains, filaments of galaxies, connected together, surrounded by voids, where there's very few galaxies. These patterns are exquisite, and these structures are huge. They might be 100 million light years across. They must be some relic from an early phase of the universe. Which tells us a great deal about how the universe got to be the way it is. But for the moment, what I'm interested in is using these patterns as a way of diagnosing the presence of dark matter. So where does the structure from? In part, the answer is gravity. Wherever there's more matter than average, it will suck further matter in, and computer simulations of this process, give us images that look very like the galaxies surveys. So we know gravity's at work here. Now this is useful, because the operation of gravity has changed over the history of the universe. If I plot density, this is time. In the past, the density of matter was higher, because the universe was smaller. Today, there's radiation, whose energy density is much less than that of matter. The microwave background is almost negligible. But it becomes more important as we go back into the hot, big bang, and there is a cross over time, and this is somewhere around 100,000 years. Before that the energy density in the universe was dominated by radiation. One can see the time that this occurred in the detailed properties of the, the fluctuations that the galaxies obey in space. And also, if we change the amount of matter, make it, less, that transition occurs at a later time. And so the corresponding length scale, the speed of light times the time would be larger. So we find written in the sky some information about the matter density from the so called large scale structure. So by mapping the three dimensional distribution of galaxies, we're able to infer the density of the universe. And this is where the contribution of matter that is not dark energy, because this is only matter that can clump. So, the fact that this is greater than the material, of ordinary atomic material that we infer from say nuclear synthesis, tells us that the majority of the clumpable matter in the universe is of a form that we only see through gravity, we don't see from radiation, so this is dark matter. The large scale structure is probably the most accurate way of measuring the total amount of dark matter, but we can see its influence much more directly. For example, in galaxy rotation curves. So if I have a galaxy, like the Milky Way, stars and gas orbit around the center. And if you plot, this orbital velocity. This is the radius from the center of the galaxy. You might expect to find something like this. Where the velocity declines once you reach the edge of the visible galaxy, and you've run out of matter. Now, you're just further away from what matter there is. But the data actually tend to stay flat, so this is the visible matter, and so the difference is dark. So, apparently the outskirts of galaxies are dominated by dark matter. And that's one of the most direct pieces of evidence that we have for its existence. If a structure in the galaxy distribution grew over time under the action of gravity, we should be able to see that. And this is possible using the microwave background. So, here we are, observing the last scattering surface at the time of 400 thousand years. The seeds for the large scale structure should be in place, already. So, there should be regions that the density that are higher than average. And from these we get more radiation than in between. So fluctuations in the intensity of radiation are expected on the sky. And these were first seen in 1992. And the fluctuations at about 1 part in 100,000. Slightly hotter, slightly colder, all across the sky. And these patches that we see are about 1 degree across. This allows us to learn something about the curvature of the universe, because if I observe the sky in a closed universe, then the light rays would tend to reconverge. And this is just like what would happen on the Earth. Two people set out from the North Pole along great circles. By the time they come to the South Pole, their paths have reconverged. The curved space brings light rays together, positively curved space. Negatively curved space would open them up. Whereas a flat universe is in between, and therefore the size of the spots of the microwave sky can be used to distinguish between the closed case and the open case. And they favour the flat case. So, therefore, we see overall that the total density of the universe is 1. They already had matter contribution of 0.3, and so this tells us that something else that doesn't clump must be the vacuum energy as about 70% of the content. This argument was already made in about 1990. The interesting thing is, very few members of the astronomical community believed it. And it's worth asking why this was. The answer is that to anybody be they a scientist or not, believing that we've proved that the energy density of the vacuum is non-zero, is such a radical step, that you're very reluctant to take it with out further evidence. But then, at the end of the 1990's the evidence from supernova came along and gave us the same conclusion. Now we had two arguments that both call for the existence of dark energy. And so almost overnight this became a new standard model. The burden of evidence was so strong, that a new paradigm was established.
