To understand the stability of galaxies it was necessary to assume that there was a large amount of dark matter in the galaxy — about five or ten times the amount of visible matter — which was needed just to hold the galaxy together. This problem repeats itself when one talks about the motion of galaxies within clusters of galaxies. The motion of galaxies in clusters is much more random and chaotic than the spiral galaxy, but the same issues arise. You can ask how much mass is needed to hold those clusters of galaxies together, and the answer is that you still need significantly more matter than what you assumed was in the galaxies. Adding all of that together, astronomers came up only to about a third of the critical density. They were pretty well able to guarantee that there wasn't any more than that out there; that was all they could detect. That was bad for the inflationary model, but many of us still had faith that inflation had to be right and that sooner or later the astronomers would come up with something.

And they did, although what they came up with was something very different from the kind of matter that we were talking about previously. Starting in 1998, astronomers have been gathering evidence for the remarkable fact that the universe today appears to be accelerating, not slowing down. As I said at the beginning of this talk, the theory of general relativity allows for that. What's needed is a material with a negative pressure. We are now therefore convinced that our universe must be permeated with a material with negative pressure, which is causing the acceleration that we're now seeing. We don't know what this material is, but we're referring to it as "dark energy." Even without knowing what it is, general relativity by itself allows us to calculate how much mass has to be out there to cause the observed acceleration, and it turns out to be almost exactly equal to two-thirds of the critical density. This is exactly what was missing from the previous calculations! So, if we assume that this dark energy is real, we now have complete agreement between what the astronomers are telling us about the mass density of the universe and what inflation predicts.

The other important prediction that comes out of inflation is becoming even more persuasive than the issue of flatness: namely, the issue of density perturbations. Inflation has what in some ways is a wonderful characteristic — that by stretching everything out (and Paul's model takes advantage of the same effect) you can smooth out any non-uniformities that were present prior to this expansion. Inflation does not depend sensitively on what you assume existed before inflation; everything there just gets washed away by the enormous expansion. For a while, in the early days of developing the inflationary model, we were all very worried that this would lead to a universe that would be absolutely, completely smooth. After a while several physicists began to explore the idea that quantum fluctuations could save us. The universe is fundamentally a quantum mechanical system, so perhaps quantum theory was necessary not just to understand atoms, but also to understand galaxies. It is a rather remarkable idea that an aspect of fundamental physics like quantum theory could have such a broad sweep. The point is that a classical version of inflationary theory would predict a completely uniform density of matter at the end of inflation. According to quantum mechanics, however, everything is probabilistic. There are quantum fluctuations everywhere, which means that in some places the mass density would be slightly higher than average, and in other places it would be slightly lower than average. That's exactly the sort of thing you want to explain the structure of the universe. You can even go ahead and calculate the spectrum of these non-uniformities, which is something that Paul and I both worked on in the early days and had great fun with. The answer that we both came up with was that, in fact, quantum mechanics produces just the right spectrum of non-uniformities.

We really can't predict the overall amplitude — that is, the intensity of these ripples — unless we know more about the fundamental theory. At the present time, we have to take the overall factor that multiplies the predicted intensity of these ripples from observation. But we can predict the spectrum — that is, the complicated pattern of ripples can be viewed as ripples of many different wavelengths lying on top of each other, and we can calculate how the intensity of the ripples varies with their wavelengths. We knew how to do this back in 1982, but recently it has actually become possible for astronomers to see these non-uniformities imprinted on the cosmic background radiation. These were first observed back in 1992 by the COBE (Cosmic Background Explorer) satellite, but back then they could only see very broad features, since the angular resolution of the satellite was only about seven degrees. Now, they've gotten down to angular resolutions of about a tenth of a degree. These observations of the cosmic background radiation can be used to produce plots of the spectrum of non-uniformities, which are becoming more and more detailed.