4-volume cutoff measure of the multiverse
  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.
