Four-volume cutoff measure of the multiverse

• Main Authors: Vilenkin, Alexander (Author), Yamada, Masaki (Author)
• Other Authors: Massachusetts Institute of Technology. Center for Theoretical Physics (Contributor), Massachusetts Institute of Technology. Department of Physics (Contributor), Massachusetts Institute of Technology. Department of Nuclear Science and Engineering (Contributor)
• Format: Article
• Language: English
• Published: American Physical Society (APS), 2020-05-07T20:18:04Z.
• Subjects: Article
• Online Access: Get fulltext

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.
U.S. Department of Energy, Office of Science, Office of High Energy Physics (Grant DE-SC0012567)