How many universes are in the multiverse?
We argue that the total number of distinguishable locally Friedmann universes generated by eternal inflation is proportional to the exponent of the entropy of inflationary perturbations and is limited by e^{e^{3 N}}, where N is the number of e-folds of slow-roll post-eternal inflation. For simplest models of chaotic inflation, N is approximately equal to de Sitter entropy at the end of eternal inflation; it can be exponentially large. However, not all of these universes can be observed by a local observer. In the presence of a cosmological constant \Lambda the number of distinguishable universes is bounded by e^{|\Lambda|^{-3/4}}. In the context of the string theory landscape, the overall number of different universes is expected to be exponentially greater than the total number of vacua in the landscape. We discuss the possibility that the strongest constraint on the number of distinguishable universes may be related not to the properties of the multiverse but to the properties of observers.
With the invention of inflationary cosmology, the no- tion of a uniform universe was gradually replaced by the notion of a multiverse consisting of many locally uniform exponentially large parts [1, 2]. Each of these parts lo- cally looks like a uniform nearly-Friedmann universe. A collection of all of these universes represents an eternally growing fractal consisting of many such “universes†with different properties [3–5]. This scenario recently became quite popular when a mechanism to stabilize string the- ory vacua was found [6], and string theorists realized [7], in agreement with earlier expectations [8, 9], that the to- tal number of different stringy vacua can be extremely large. The popular estimate of the number of different vacua is ∌ 10500 , but the true number may be much smaller or much greater than that [7]. Because of the transitions from one vacuum state to another, the infla- tionary multiverse becomes divided into an exponentially large number of different exponentially large “universes†with different laws of low-energy physics operating in each of them. This picture, which is now known as the string theory landscape [10], was envisaged in the very first paper on eternal chaotic inflation [4].
http://arxiv.org/abs/0910.1589
