Probabilities in the inflationary multiverse

TL;DR

This paper analyzes the distribution of physical constants in the multiverse resulting from inflationary cosmology, proposing methods to estimate their volume distribution and relative abundances across different pocket universes.

Contribution

It introduces an analytic estimate for the volume distribution of constants in pocket universes based on an ergodic conjecture and proposes a method to determine their relative abundances.

Findings

Derived an approximate volume distribution formula for constants in pocket universes.

Proposed a method to compute the relative abundances of different pocket universe types.

Combined these approaches into a comprehensive distribution expression.

Abstract

Inflationary cosmology leads to the picture of a "multiverse," involving an infinite number of (spatially infinite) post-inflationary thermalized regions, called pocket universes. In the context of theories with many vacua, such as the landscape of string theory, the effective constants of Nature are randomized by quantum processes during inflation. We discuss an analytic estimate for the volume distribution of the constants within each pocket universe. This is based on the conjecture that the field distribution is approximately ergodic in the diffusion regime, when the dynamics of the fields is dominated by quantum fluctuations (rather than by the classical drift). We then propose a method for determining the relative abundances of different types of pocket universes. Both ingredients are combined into an expression for the distribution of the constants in pocket universes of all types.