The pocket universes other than our own are believed to be completely unobservable, so one can question whether it makes any scientific sense to talk about them. I would argue that it is valid science, because we are pursuing the consequences of a theory for which we already have other evidence. Of course the theory of inflation has to rest on the evidence that we can observe, but once we are persuaded by these observations, then I think that we should also believe the other implications, even if they involve statements that cannot be directly confirmed.
If one accepts the existence of the other pocket universes, then one can still question whether they have any relevance to the pursuit of science. I will argue that, even though these other universes are unobservable, their existence nonetheless has consequences for the way that we evaluate theories and extract consequences from them.
One question for which eternal inflation has relevance is the question of the ultimate beginning of the universe – what can be learn about it, and how can we learn it? However, if eternal inflation is a valid description of the universe (as I think it is), then I would expect that all such hypotheses about the ultimate beginning of the universe would become totally divorced from any observable consequences. Since our own pocket universe would be equally likely to lie anywhere on the infinite tree of universes produced by eternal inflation, we would expect to find ourselves arbitrarily far from the beginning. The infinite inflating network would presumably approach some kind of a steady state, losing all memory of how it started, so the statistical predictions for our universe would be determined by the properties of this steady state configuration, independent of hypotheses about the ultimate beginning. In my opinion theories of the ultimate origin would remain intellectually interesting, and with an improved understanding of the fundamental laws of physics, such theories might even eventually become compelling. But I expect that any detailed consequences of such a theory would be completely washed out by the eternal evolution of the universe. Thus, there would be no way of relating the properties of the ultimate origin to anything that we might observe in today’s universe.
Although I believe that the inflating network would approach a steady state, I should admit that attempts to pursue this idea quantitatively have run into several technical problems. First, the evolution of eternally inflating universes leads to physics that we do not understand. In particular, quantum fluctuations tend to drive the repulsive-gravity material to higher and higher energy densities, where the poorly understood effects of quantum gravity become more and more important. Second, even if we impose enough assumptions so that the evolution of the eternally inflating universe can be described, we still do not know how to define probabilities on the infinite set of pocket universes that is produced. The problem is akin to asking what fraction of the integers are odd. Most people would presumably say that the answer is 1/2, since the integers alternate between odd and even. However, the ambiguity of the answer can be seen if one imagines other orderings for the integers. One could, if one wished, order the integers as 1,3, 2, 5,7, 4, 9,11, 6 , … , always writing two odd integers followed by one even integer. This list includes each integer exactly once, but from this list one would conclude that 2/3 of the integers are odd. Thus, the answer seems to depend on the ordering. For eternally inflating universes, however, there is no natural ordering to the regions of spacetime that comprise the entire universe. There are well-founded proposals for defining probabilities, but at least in my opinion there is no definitive and compelling argument.
A second implication of eternal inflation is that the probability for inflation to start – the question of how likely it is for an initial speck of repulsive-gravity material to form – becomes essentially irrelevant. Inflation only needs to begin once, in all of eternity. As long as the probability is nonzero, it does not seem relevant, and perhaps it is not even meaningful, to ask if the probability is large or small. If it is possible, then it will eventually happen, and when it does it produces literally an infinite number of universes. Unless one has in mind some competing process, which could also produce an infinite number of universes (or at least an infinite space-time volume), then the probability for inflation to start has no significance.
The third and final implication of eternal inflation that I would like to discuss pertains to the comparison of theories. I would argue that once one accepts eternal inflation as a logical possibility, then there is no contest in comparing an eternally inflating version of inflation with any theory that is not eternal.
Consider the analogy of going into the woods and finding some rare species of rabbit that has never before been seen. You could either assume that the rabbit was created by a unique cosmic event involving the improbable collision of a huge number of molecules, or you could assume that the rabbit was the result of the normal process of rabbit reproduction, even though there are no visible candidates for the rabbit’s parents. I think we would all consider the latter possibility to be far more plausible. Once we become convinced that universes can eternally reproduce, then the situation becomes very similar, and the same logic should apply. It seems far more plausible that our universe was the result of universe reproduction than that it was created by a unique cosmic event