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PHYSICAL REVIEW D 82, 063520 (2010)

Boltzmann brains and the scale-factor cutoff measure of the multiverse

Andrea De Simone,1 Alan H. Guth,1 Andrei Linde,2,3 Mahdiyar Noorbala,2 Michael P. Salem,4 and Alexander Vilenkin4 1Center for Theoretical Physics, Laboratory for Nuclear Science, and Department of Physics, Massachusetts Institute of Technology, Cambridge, Massachusetts 02139, USA 2Department of Physics, Stanford University, Stanford, California 94305, USA 3Yukawa Institute of Theoretical Physics, Kyoto University, Kyoto, Japan 4Institute of Cosmology, Department of Physics and Astronomy, Tufts University, Medford, Massachusetts 02155, USA (Received 25 July 2010; published 14 September 2010)

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.