Multi-Vacuum Initial Conditions and the Arrow of Time
  Depending on the type and arrangement of metastable vacua in the theory,
initial conditions in a de Sitter vacuum with arbitrarily large entropy can be
compatible with the observed arrow of time, if the causal patch or related
measures are used to regulate divergences. An important condition, however, is
that the initial vacuum cannot produce observers from rare fluctuations
(Boltzmann brains). Here we consider more general initial conditions where
multiple vacua have nonzero initial probability. We examine whether the
prediction of an arrow of time is destroyed by a small initial admixture of
vacua that can produce Boltzmann brains. We identify general criteria and apply
them to two nontrivial examples of such initial probability distributions. The
Hartle-Hawking state is superexponentially dominated by the vacuum with
smallest positive cosmological constant, so one might expect that other initial
vacua can be neglected; but in fact, their inclusion drastically narrows the
range of theory parameters for which an arrow of time is predicted. The
dominant eigenvector of the global rate equation of eternal inflation is
dominated by the longest-lived metastable vacuum. If an arrow of time emerges
in the single-initial-vacuum approximation, then we find that this conclusion
survives the admixture of other initial vacua. By global-local measure duality,
this result amounts to a successful consistency test of certain global cutoffs,
including light-cone time and scale-factor time.
