Four-volume cutoff measure of the multiverse

Alexander Vilenkin, Masaki Yamada

Research output: Contribution to journalArticlepeer-review

5 Citations (Scopus)


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 avoids 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 four 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.

Original languageEnglish
Article number043520
JournalPhysical Review D
Issue number4
Publication statusPublished - 2020 Feb 15


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