Time to moves toward the most interesting inflationary model and the one with the infinities.
Having discussed the mechanisms and the motivation for inflation itself, I now wish to move on to eternal inflation, the questions that it can answer, and the questions that it raises.
Before going on, I should clarify that the different topics that I am discussing have various levels of certainty. The standard big bang theory, as far as cosmologists are concerned, appears to be essentially certain to all but a few of us. Inflation seems to be by far the most plausible way that the big bang could have started, but it is not so well established as the big bang itself. I should also admit that inflation is vague. It is not really a theory, but a class of theories, so there is a significant amount of flexibility in describing its predictions. Eternal inflation, which I am about to describe, seems to me to be an almost unavoidable consequence of inflation. This point, however, is somewhat controversial. In particular, I believe that the following scientist, Neil Turok, will argue either that eternal inflation does not happen, or that it is in any case not relevant to understanding the properties of the observable universe. I, however, will argue that eternal inflation does happen, and is relevant.
Figure 1. Spectrum of the cosmic background radiation anisotropies, as measured by the Boomerang experiment. The intensity of fluctuations is shown as a function of the angular size parameter ℓ, where the angular size of a fluctuation is roughly 180o/ℓ. The black line is a theoretical curve corresponding to a standard inflationary model with Ω = 1. The mass density in the model is composed of 5% baryons, 25% cold dark matter, and 70% cosmological constant. The data and theoretical curve were taken from Ref. 5.
By eternal inflation, I mean simply that once inflation starts, it never ends. The term future-eternal would be more precise, because I am not claiming that it is eternal into the past – I will discuss that issue at the end of the talk.
The mechanism that leads to eternal inflation is rather straightforward to understand. Recall that we expect inflation to end because the repulsive-gravity material is unstable, so it decays like a radioactive substance. As with familiar radioactive materials, the decay of the repulsive-gravity material is generally exponential: during any period of one half-life, on average half of it will decay. This case is nonetheless very different from familiar radioactive decays, however, because the repulsive-gravity material is also expanding exponentially. That’s what inflation is all about. Furthermore, it turns out that in essentially all models, the expansion is much faster than the decay. The doubling-time for the inflation is much shorter than the half-life of the decay. Thus, if one waits for one half-life of the decay, half of the material would on average convert to ordinary matter. But meanwhile the part that remains would have undergone many doublings, so it would be much larger than the region was at the start. Even though the material is decaying, the volume of the repulsive-gravity material would actually grow with time, rather than decrease. The volume of the repulsive-gravity material would continue to grow, without limit and without end. Meanwhile pieces of the repulsive-gravity material decay, producing a never-ending succession of what I call pocket universes.
In Fig. 2 I show a schematic illustration of how this works. The top row shows a region of repulsive-gravity material, shown very schematically as a horizontal bar. After a certain length of time, a little less than a half-life, the situation looks like the second bar, in which about a third of the region has decayed. The energy released by that decay produces a pocket universe. The pocket universe will inflate to become huge, so to its residents the pocket universe would look like a complete universe. But I will call it a pocket universe because there is not just one, but an infinite number of them.
Figure 2. A schematic diagram to illustrate the fractal structure of the universe created by eternal inflation. The four horizontal bars represent a patch of the universe at four evenly spaced successive times. The expansion of the universe is not shown, but each horizontal bar is actually a factor of three larger than the preceding bar, so each region of repulsive-gravity material is actually the same size as the others. During the time interval between bars, 1/3 of each region of repulsive-gravity material decays to form a pocket universe. The process repeats ad infinitum, producing an infinite number of pocket universes.
On the second bar, in addition to the pocket universe, we have two regions of repulsive-gravity material. On the diagram I have not tried to show the expansion, because if I did I would quickly run out of room on the page. So you are expected to remember on your own that each bar is actually bigger than the previous bar, but is drawn on a different scale so that it looks like it is the same size. To discuss a definite example, let us assume that each bar represents three times the volume of the previous bar. In that case, each region of repulsive-gravity material on the second bar is just as big as the entire bar on the top line.
The process can then repeat. If we wait the same length of time again, the situation will be as illustrated on the third bar of the diagram, which represents a region that is 3 times larger than the second bar, and 9 times larger than the top bar. For each region of repulsive-gravity material on the second bar, about a third of the region decays and becomes a pocket universe, leaving regions of repulsive-gravity material in between. Those regions of repulsive-gravity material are again just as big as the one we started with on the top bar. The process goes on literally forever, producing pocket universes and regions of repulsive-gravity material between them, ad infinitum. The universe on the very large scale acquires a fractal structure.
The illustration of Fig. 2 is of course oversimplified in a number of ways: it is one-dimensional instead of three-dimensional, and the decays are shown as if they were very systematic, while in fact they are random. But the qualitative nature of the evolution is nonetheless accurate: eternal inflation really leads to a fractal structure of the universe, and once inflation begins, an infinite number of pocket universes are produced.