Okay gang, this is it. We have been on a long voyage through both space and time, which has taken us from our nearby bailiwick of the Milky Way, where most of our cosmic neighbors are merely hundreds to thousands of light years away. Out to the realm of the quasars and the early universe, where light has taken billions of years to reach us here on Earth. I want to conclude our discussions, by giving you a short overview of our current ideas, concerning the history and ultimate fate of the universe as a whole. This is almost a presumptuous undertaking, but astonishingly, there is a lot we can say about this. Which brings our conceptions of cosmology out of the dominion of myth, and into the province of probable scientific fact. Of course, there is the caveat that we live, to borrow a quote from Loren Eiseley, in an unexpected universe, one that is continually full of surprises, and hence changes in our understanding. But lets begin with some phenomena that we can comfortably assume, will not be altered drastically, at least qualitatively. First, Hubble's discovery that the universe is expanding, was the result of almost countless numbers of measurements, of Doppler shifts, of extra galactic objects. Which almost unequivocally showed that the universe was expanding. Note, that this is not just the galaxies are expanding away from us, everything is expanding away from everything else. It doesn't matter where in the universe you do these measurements. Indeed, it is much better to think about this, as if space itself is doing the expanding. Let's look at this carefully. Imagine the universe as the surface of a balloon. And on that balloon, we paste some rigid wire in the shape of galaxies, in order to visualize this. The reason we use rigid wire, is so that we have objects that are held together by strong forces, that don't worry about the possible expansion of the balloon, which represents space itself in our toy model. So this is the picture. At one point early in the universe, our balloon is not very inflated, and we have some galaxies on it. Then it gets larger, and larger, and larger, as time goes on. You can see that if we are on or in the galaxy marked in red, everything seems to be expanding away from us. But does this mean that we're at the center of the universe? Hardly. If we were in any location, for example, the blue galaxy, this same thing would happen. Everything seems to be expanding away from us. Everything appears to move away from everything else. Let's see this more explicitly, using the following simple animation. [BLANK_AUDIO] What we see, is that everything appears to be moving away from us. We appear to be in the center, at the green galaxy. And more over, the distance any galaxy appears to receive from us, seems to be greater in any time interval, if the galaxy is already far away. This is exactly what you would expect if Hubble's Law obtained, V equals Hr. The faster something is moving away, the more it will move in any given time period. You can see that clearly, as the animation repeats over and over, and you focus your attention on various parts of our toy universe. But now, look at this. Here we see what would happen, if we were located on the green galaxy, on the lower left part of the frame. The data for this animation is exactly the same as before. Once again, it appears that everything is moving away from us. V equals Hr again. So, no matter where we are, everything appears the same, at least on a very large scale. There is no preferred direction or place in the universe. It is if the very fabric of space is expanding, and we are just going along for the ride. In fact, this has become what we call, the cosmological principle. We are no longer at the center of the universe. Indeed, the universe has no center. Okay, so far, so good. But what about the shape of the universe? Why should it be in a spherical shape, like our balloon? Why not flat like a rubber sheet? Is there any way we can tell what is happening on that score? Well, it turns out, that the flatness of the universe is related to how much stuff is in it. A flat universe requires an exactly critical density of mass, an energy to maintain its shape. How can we tell if this is the way things are? Well, one thing we can do, is just try to cruise around it. I walk out of the video here, and head to the ends of the universe. I keep going and going and well, maybe I'd better not do that. Suppose the universe is flat, and I just keep on going and going and going? I'll never get back. At least, when I'm on the surface of a balloon, I can just go around and around and come back eventually. It may take a couple a billion years. I'll see some great things out there, and I'll probably get some good exercise. Clearly, this will be impossible to do experimentally, especially if the universe turns out to be flat, and I never get back to finish this video. So what else can we do, to try to determine the shape? We can draw triangles. What, draw triangles? Well, we all know that the angles of a triangle sum to a 180 degrees, right? Any triangle I draw, anywhere on this blackboard, the three angles, when I sum them together, will sum to 180 degrees. However, we have made a crucial assumption. We have assumed that we are in flat space, the surface of our blackboard. Let's try that on a balloon, or the surface of the Earth? So we imagine that we have a Earth, okay? And here's the North Pole, and here's the Equator. And we're just going to march down from the North Pole, until we hit the Equator. That's going to be a pretty long way, but that's one side of our triangle. And then we're going to do a right turn. When we make that right turn, we're going to precede along the Equator. Now, since we made a right turn, that's a right angle. And we're going to proceed along the Equator, one quarter of the way around the circumference of the Earth. Then we're going to make another right turn, and keep on going back up to the North Pole. And you can see that we now, if we have gone a quarter of the way around the Earth, have made a triangle. It's a spherical triangle. But we can define a triangle, in terms of, the shortest distance between two points. Just like we defined a straight line on our blackboard here. And low and behold, the angles are greater than 180 degrees. Huh, look at that. This is what happens if our universe is curved. I've got an idea. Let's call our friends on M31, out there, a few million light years away, and on M87, out there, about 50 million light years away? Okay, [NOISE] No answer? Still dialing? Oh, what a bummer! [SOUND] Is there anything else we can do? Well, we can try to measure all this stuff in the observable part of the universe, and see how it stacks up with what we need for a flat universe? When we do that, we find we come up woefully short. There doesn't seem to be enough stuff in the universe to make it flat. Well, case closed, right? Uh-uh, it turns out we have real problems. We do have data on this, and it comes from the leftover radiation from the Big Bang itself. As the universe cooled, it left its cosmic imprint all over the sky. And we can actually see that leftover radiation from the Big Bang, using the WMAP satellite. What we see here, is the first photograph ever possible of our universe. The black body radiation from when the universe was a mere 350,000 years old, streaming through space for over 13 billion years. The different colors represent tiny, tiny fluctuations in the temperature of the material at that time. The fluctuations are due to gravitational interactions, that cause some over dense regions to be a little bit hotter than others. By examining carefully, the seeming jumble of different sized regions of differing temperatures, we have found out that the universe is indeed, very close to being flat. So what is the matter? We don't see it. Where is the matter? What can it be? Are there clues anywhere else? Well, we can examine the rotation curves of stars going around the centers of their galaxies. When we do this, we find out something quite surprising. To understand this, we first return to our solar system for a moment, and look at the planets as they go around the Sun. We all know about this now. We know that we have an acceleration that is given by v squared over R. That's the centripetal acceleration. And that is a result of the inverse square law of gravity, where M is the mass of the parent object, the Sun or whatever the object is going around. If we solve this for a circular speed, v, we see very clearly that the velocity is proportional to 1 over the square root of R. There are some other numbers in there, but the crucial thing is, is that as R gets bigger, v gets smaller. Okay? Let's see how well v being proportional to 1, over the square root of R, fits the solar system? Look at that. The Sun's mass provides all the gravitational pull necessary, to keep the planets in exquisitely precise agreement with Newton's law of gravity. But look what happens when we look at orbits of stars around a galaxy? It's way off. Even though, the center of the galaxy contains most of the visible mass, the predicted curve is not followed. Instead, the rotation curves stay flat, out to tremendous distances from the galaxy center. And this doesn't happen only once. Look at these. They are screaming at us. We are flat. We are flat. We don't fall off. What are you going to do about it? Well, one thing we can do about it, is say that there's just more stuff out there, that we can't see. The famous dark matter. Just some strange stuff that doesn't interact, except gravitationally. Personally, I just feel this sounds too much like The Emperor's New Clothes, for my taste. I must confess, I am in the minority here in the astronomical community. But I feel, that the problem is not with the inadequate amount of matter. The problem is, or to be fair, might be, that we don't understand gravity at the very small accelerations, such as exists in the far reaches of the galaxies. And it's not like we need just a pinch of the dark matter to do the trick. In the mid 1990s, it was thought that fully 90% of everything in the universe, was mysteriously invisible. So here we have an obvious bone of contention, in the astronomical community. But the most shocking thing was yet to come. Whether or not you imagine a flat universe, a curved universe, or a universe filled with dark matter, one thing should be clear. Gravity ought to slow the expansion down. [MUSIC] Remember our balloon expanding? [MUSIC] Well if the galaxies are interacting, they should all be pulling on one another, trying to slow their expansion speed. How could it be otherwise? So we look deeper and deeper into space, Measuring V, our velocity, via the Doppler shift, and the distance R, from knowing the luminosity of various objects. And the results are shown here. The most distant galaxies, very faint and very tiny appearing, are moving the fastest; as expected. Then the incredible happened. By using type 1a supernovae, which as we have seen, we have good reason to believe are standard candles. Because they're all white dwarf stars of exactly the same mass. Something didn't quite fit. After measuring hundreds of these objects in the far reaches of the observable universe, it became apparent that the universe was not slowing down, it was accelerating instead. Absolutely astonishing. The simple result is summarized here. No doubt about it. Things were further away than one would expect, if just a constant velocity were present. What is going on here? No one knows. The dark matter was lunatic enough, but now we need a source of dark energy, to explain this crazy acceleration. What will be next? Will the universe eventually slow down, and recollapse? Will it expand forever? These are some of the unsolved questions that intrigue us. So these are exciting times in astrophysics, with surprises galore. In just ten years, the 90% of the universe supposedly composed of dark matter, has been reduced to about 25%. In its place, over 70% of the universe is now thought to be dark energy. The only thing that has remained more or less constant, has been us, the ordinary stuff, the stuff of the stars, the stuff of the planets, relegated to a mere 4% of the total mass energy content of the universe. We have to be content with our roles as observers and discoverers. Secure in the knowledge that even though we may be small and somewhat inconsequential, we can still behold the immensity and grandeur of the universe around us.
