So I'd like to summarize a few of the elements of modern cosmology. And let's begin by saying that this is an incredibly recent story. No more than 100 years ago, our knowledge about the universe was little advanced from the Stone Age. Whereas today, we have a feeling that almost, observational study of the universe is converging in some sense. How is this possible? Well, it's possible by the technology of telescopes. Telescopes have shown us, different lines of sight into the universe. And we know the universe consists primarily of the building blocks of galaxies. Just like the Milky Way, each one, 10 billion stars. Throughout this universe of galaxies, we're able to see how things have changed with time, because the beauty is that light travels at a finite time. So, the further away we're looking, the further back in time we're seeing. So we're able to study the universe as it was then and as it is in different directions. So we learned the universe of galaxies is relatively uniform, so we can be confident that by studying part of the universe, we're learning something that's statistically representative of the whole. And we're able to learn about the entire history of the development of this as well, given a large enough telescope. Now, the most important thing to know about the universe of galaxies is that it's expanding. If that's a set of galaxies at some time, little bit later, the whole distribution is more diffuse. Everything's moving apart, and this expansion obeys Hubble's Law, which we can write the velocity, V, is a constant H times a distance, D. This dates from 1929. How do we know that the galaxies are in motion? The answer is the doppler shift that we can measure through spectroscopy, if I have a galaxy emitting radiation. Now, if I move it away, that radiation is stretched out. It becomes radiation of a longer wavelength, a redder color. So we would say that the wavelength is replaced by the wavelength times the correction, which is roughly the recession of velocity times the speed of light. So if we observe in detail, spectroscopic observations of the galaxies, we can measure this velocity. Many people assume, that this is what was first done by Hubble. But actually, the astronomer that deserves credit for beginning this work was V M Slipher, who worked in Arizona. His first observations were made just over a century ago in 1912, and really, for the next decade, he had the field to himself. So he was the great pioneer who first revealed that all galaxies were moving away from us. Grasping what it means to say the universe is expanding isn't easy. First of all, the distribution of galaxies in this cartoon might go on forever. So there's no way of ever escaping and observing the expansion from the outside. It's not as if material is flowing out to fill a pre-existing empty space. Secondly, there's no centre. That is, although it seems to us that all galaxies are moving away, from the point of view of this one it would be as if the Milky Way was moving away. So, uniform expansion makes the expansion democratic. Everyone sees material moving off in all directions. Finally, you should not think of this, although it's a common analogy. People will say that galaxies aren't moving apart, it's just the space between them getting bigger. The space here is not getting bigger. The universe as a whole gets larger. But that's only on scales where space-time is curved, and that's not an important phenomenon here in this room. So really, you should just imagine the galaxies are moving in flat space, and that's a good description. Now, to follow the evolution of an expanding universe, we've got to deal with gravity. In many ways, we still use Newton's treatment. From the 17th Century, that is, the inverse square law of attraction between two particles. Halve the distance between them, the force goes up by a factor of four. But this is replaced by general relativity in 1915 by Einstein, where he took the view that you should think of this force as arising from a curvature of space and time. Einstein addressed a question which really, Newton was unable to answer, which is what happens in the case of a uniform mass distribution. Newton thought that if you had a lot of particles of mass, that the whole thing would be static. Because the gravitational attraction in this direction would balance, and so there'd be no net motion for any particle. Einstein showed that even within Newton's gravity, that was wrong. You need to modify the law of gravity itself. The change that Einstein made to the law of gravity was to introduce the thing he called the cosmological constant. We use different names today, for the same thing. Although it's still very much a feature of modern cosmology. The most common one would be dark energy, or sometimes vacuum energy. What this means is that you give empty space itself some weight. A sphere of absolutely nothing of volume V, contains a mass, which is the volume times a density of the vacuum. We'll discuss a little bit more later on how that's possible. But if we just accept it for the moment, Einstein proved, a further strange consequence, which is that such a system would exhibit anti-gravity properties. That is, the effective mass inside the empty space would tend, rather than attracting material around it, to push it away. So you could obtain a static universe by balancing this repulsion with the inward attraction due to the matter inside. Whereas today we believe that it was nearly right, but it's just that in the present universe this is out of balance, and the anti-gravity from the vacuum, in fact, dominates. So the expansion of the universe is accelerating.