Making Predictions in Eternally Inflating Universe

TL;DR

This paper introduces a volume comparison method in eternally inflating universes that minimizes dependence on the choice of time variable, enabling more reliable probability estimates of different physical constants and fluctuation spectra.

Contribution

The paper proposes a new volume comparison approach in eternal inflation that reduces sensitivity to time variable choices, improving probability assessments of universe properties.

Findings

Method reduces dependence on time variable t

Applied to evaluate probabilities of inflaton potential minima

Derived distribution for density fluctuation spectra

Abstract

Eternally inflating universes can contain large thermalized regions with different values of the constants of Nature and with different density fluctuation spectra. To find the probability for a `typical' observer to detect a certain set of constants, or a certain fluctuation spectrum, one needs to compare the volumes occupied by different types of regions. If the volumes are taken on an equal-time hypersurface, the results of such a comparison are extremely sensitive to the choice of the time variable t. Here, I propose a method of comparing the volumes which is rather insensitive to the choice of t. The method is then applied to evaluate the relative probability of different minima of the inflaton potential and the probability distribution for the density fluctuation spectra.