How many universes are in the multiverse?

TL;DR

This paper estimates the maximum number of distinguishable universes in the multiverse generated by eternal inflation, relating it to entropy and cosmological parameters, and discusses observational and theoretical constraints.

Contribution

It introduces a quantitative bound on the number of distinguishable universes based on entropy and cosmological constants, linking multiverse diversity to observer properties.

Findings

Number of universes limited by e^{e^{3 N}} where N is e-folds of inflation

Bound on distinguishable universes with cosmological constant: e^{|\Lambda|^{-3/4}}

Multiverse diversity exceeds the number of string vacua, constrained by observer properties

Abstract

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.