A prescription for probabilities in eternal inflation

TL;DR

This paper extends a gauge-invariant method for calculating probability distributions of variable parameters in eternal inflation, accommodating discontinuous ranges and multiple thermalized regions, and applies it to bubble universe probabilities.

Contribution

It introduces a generalized prescription for probability calculations in eternal inflation scenarios with discontinuous variable ranges and multiple thermalized regions.

Findings

Developed a set of requirements for the generalized method.

Formulated a new prescription satisfying all requirements.

Applied the method to compute probabilities of different bubble universes.

Abstract

Some of the parameters we call ``constants of Nature'' may in fact be variables related to the local values of some dynamical fields. During inflation, these variables are randomized by quantum fluctuations. In cases when the variable in question (call it $\chi$) takes values in a continuous range, all thermalized regions in the universe are statistically equivalent, and a gauge invariant procedure for calculating the probability distribution for $\chi$ is known. This is the so-called ``spherical cutoff method''. In order to find the probability distribution for $\chi$ it suffices to consider a large spherical patch in a single thermalized region. Here, we generalize this method to the case when the range of $\chi$ is discontinuous and there are several different types of thermalized region. We first formulate a set of requirements that any such generalization should satisfy, and then introduce a prescription that meets all the requirements. We finally apply this prescription to calculate the relative probability for different bubble universes in the open inflation scenario.