discussed the mechanisms and the motivation for inflation itself, I now wish to
move on the main issue that I want to stress in this article - eternal
inflation, the questions that it can answer, and the questions that it raises.
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 speaker, 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.
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.
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.
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.
Contributed by: Dr. Alan Guth