4-volume cutoff measure of the multiverse. (arXiv:1912.02187v1 [hep-th])

<a href="http://arxiv.org/find/hep-th/1/au:+Vilenkin_A/0/1/0/all/0/1">Alexander Vilenkin</a>, <a href="http://arxiv.org/find/hep-th/1/au:+Yamada_M/0/1/0/all/0/1">Masaki Yamada</a>

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.

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.

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