To make predictions for an eternally inflating ‘‘multiverse,’’ one must adopt a procedure for regulating ...

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.

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