2 research outputs found
Boltzmann brains and the scale-factor cutoff measure of the multiverse
To make predictions for an eternally inflating "multiverse", one must adopt a
procedure for regulating its divergent spacetime volume. Recently, a new test
of such spacetime measures has emerged: normal observers - who evolve in pocket
universes cooling from hot big bang conditions - must not be vastly outnumbered
by "Boltzmann brains" - freak observers that pop in and out of existence as a
result of rare quantum fluctuations. If the Boltzmann brains prevail, then a
randomly chosen observer would be overwhelmingly likely to be surrounded by an
empty world, where all but vacuum energy has redshifted away, rather than the
rich structure that we observe. Using the scale-factor cutoff measure, we
calculate the ratio of Boltzmann brains to normal observers. We find the ratio
to be finite, and give an expression for it in terms of Boltzmann brain
nucleation rates and vacuum decay rates. We discuss the conditions that these
rates must obey for the ratio to be acceptable, and we discuss estimates of the
rates under a variety of assumptions.Comment: 32 pp, 2 figs. Modified to conform to the version accepted by Phys.
Rev. D. The last paragraph of Sec. V-A, about Boltzmann brains in Minkowski
space, has been significantly enlarged. Two sentences were added to the
introduction concerning the classical approximation and the hope of finding a
motivating principle for the measure. Several references were adde
Cosmological Measures without Volume Weighting
Many cosmologists (myself included) have advocated volume weighting for the
cosmological measure problem, weighting spatial hypersurfaces by their volume.
However, this often leads to the Boltzmann brain problem, that almost all
observations would be by momentary Boltzmann brains that arise very briefly as
quantum fluctuations in the late universe when it has expanded to a huge size,
so that our observations (too ordered for Boltzmann brains) would be highly
atypical and unlikely. Here it is suggested that volume weighting may be a
mistake. Volume averaging is advocated as an alternative. One consequence may
be a loss of the argument that eternal inflation gives a nonzero probability
that our universe now has infinite volume.Comment: 15 pages, LaTeX, added references for constant-H hypersurfaces and
also an idea for minimal-flux hypersurface