So armed with general relativity, theorists were able to explore cosmology. The first to do so was De Sitter in 1917. He produced a universe that contained only vacuum energy. But it was realized after a few years, that this predicted Hubble's law, and in fact, this prediction was very influential. A number of astronomers before Hubble, leading up to Hubble's paper, which was the most comprehensive of these analyses, in 1929, discovered, or tested, this prediction. So, although Hubble's Law is often presented as an unexpected surprise, in fact the theoretical context led people to look for a result of this form. It's interesting to speculate how long its discovery might have taken otherwise. But of course, the most general universe contains more than just vacuum. And this was solved by the Soviet physicist, Friedmann, in 1922 to 24. Friedmann reached a number of remarkable conclusions, the most important of which, was what we today call the Big Bang. What this means is that you can make a plot. This is time at the size of the universe. I don't need to say exactly what I mean by that. Just pick some piece of the universe, plot how big it is versus time. Here it is. It's getting bigger now, we know that. Solving the equations given him by Einstein, Friedmann showed that in the past this would've emerged from a singularity. And the time between the singularity and today is about one over Hubble's constant, which today is 14 billion years. So, Einstein's dynamics have given us this strange conclusion that the universe was only a finite time. The other remarkable conclusion of Friedmann's work was that the matter content of the universe affected its curvature. Think about the Earth. This is what would be called a closed surface. By which I mean that it's finite. You can walk around it forever. You never come to a boundary. But you come back to your starting point. So the universe can be closed and have what's called positive curvature. Three dimensional space can be curved in exactly the same sense. But what Friedmann also showed was that you could have negative curvature. Now, I can't draw you a picture of what that means. But, curvature means that straightforward geometry doesn't apply. For example, we know that the sum of these three angles adds up to 180 degrees. That's not true in curved space. But the negative curved universe, is what's called an open universe. And it would be infinite. So unlike a closed universe which is finite, the universe with negative curvature would go on forever, and it's the density of the universe that turns one of these into another. There's a critical density which is minute, it's about one atom per cubic metre. It's a better vacuum than we can make anywhere on Earth. But that's enough material to turn an open universe into one that closes back in on itself. And, every now and then, you might see the symbol omega, which is the density divided by this critical value. And so we would say that omega equals 1, tells us to join the universe at the boundary between open and closed, which is flat. And strangely enough for modern observations, this is where we seem to be. One of the ways that we learn about the early stages of the expanding universe is the fact that it was hot. So anybody who owns a bike appreciates this. As you pump up your tires, you compress the air, it becomes hot. So the temperature of material in the expanding universe is actually proportional just to one over the size of the universe. The smaller it is, the higher the temperature. This means at early times, the temperatures can be really extreme. So, when the universe is about one minute old, the temperature is about a billion degrees. This means that nuclear reactions can happen. So atomic, so nuclei can be assembled. So, the higher temperatures, they couldn't survive, so you have individual protons and neutrons. But as the universe cools below this threshold, these can come together to make a deuterium nucleus, and two deuterium nuclei can come together to make helium. Now what we see in the universe today is that all the stars contain roughly 25%, by mass, of helium. When this was first discovered early in the 20th century, it was unexplained, but it was then realized that this was an inevitable prediction of nuclear reactions in the early universe. Furthermore, by looking at the relic abundance of deuterium, you can measure the density of all ordinary material that participates in nuclear reactions today. And the answer is, it's something like 5% of the critical density. Remember omega equals one was a universe that was flat. So ordinary atomic material, we can be sure was being synthesized at the time when the universe was about one minute old. And we know today it's far short of closing the universe. Now, a more direct way of probing the early hot universe is the fact that we can see it. If we look far enough away, we can see directly back to a time when the universe had that temperature. So, there's radiation left over in the universe that comes from great distances. That's from a, a shell known as the last scattering shell, and that's because at great distances, corresponding to early times, as we look at it, material is ionized so that light can't propagate freely. Temperatures thousands of kelvin. It's just like the surface of the sun. But eventually, the universe cools to the point where atoms form. That is, say for example with hydrogen, you have a proton and an electron come together to make a single atom of hydrogen. That doesn't scatter light so effectively and then the radiation can propagate to see us. So over here, it's say, 3,000 kelvin, but it's at great distances and the expansion of the universe red shifts it by the time it reaches us, it's a mere 2.7 kelvin. So radiation of such a low temperature is characterized by radio waves, as a wavelength of something like one millimetre. This is the so-called CMB, stands for cosmic microwave background, and this was found in 1960, well 1964, published in 1965 by Penzias and Wilson who received a Nobel Prize for this work, even though it was a complete accident. And it's a strange irony that, elsewhere in the world, groups who understood this cosmological transition had predicted the existence of radiation and were preparing to search for it. In any case, it is there and we can see back, therefore, to this era, where the time is something like 400,000 years after the big bang. So, we can get this close to the initial singularity with direct observations, and that's extremely powerful.