4-volume cutoff measure of the multiverse

TL;DR

This paper introduces a new 4-volume cutoff measure for the multiverse that is well-defined everywhere and aligns with observations, improving upon the scale-factor cutoff measure.

Contribution

A novel 4-volume cutoff measure is proposed, addressing limitations of the scale-factor cutoff in contracting regions of the multiverse.

Findings

The measure avoids problems like the youngness paradox and Boltzmann brains.

Probability distributions match observational data.

The measure is well-defined in all regions, including contracting ones.

Abstract

Predictions in an eternally inflating multiverse are meaningless unless we specify the probability measure. The scale-factor cutoff is perhaps the simplest and most successful measure which avoid catastrophic problems such as the youngness paradox, runaway problem, and Boltzmann brain problem, but it is not well defined in contracting regions with a negative cosmological constant. In this paper, we propose a new measure with properties similar to the scale-factor cutoff which is well defined everywhere. The measure is defined by a cutoff in the 4-volume spanned by infinitesimal comoving neighborhoods in a congruence of timelike geodesics. The probability distributions for the cosmological constant and for the curvature parameter in this measure are similar to those for the scale factor cutoff and are in a good agreement with observations.