Multi-Vacuum Initial Conditions and the Arrow of Time

TL;DR

This paper investigates how initial conditions involving multiple vacua affect the emergence of the arrow of time in cosmological models, especially considering vacua that could produce Boltzmann brains, and finds conditions under which the arrow persists.

Contribution

It introduces criteria for initial vacuum distributions that preserve the arrow of time despite the presence of vacua capable of producing Boltzmann brains.

Findings

Including multiple vacua narrows the parameter space for arrow of time predictions.

The dominant eigenvector of the rate equation remains consistent with single-vacuum predictions.

Certain global measures are validated as reliable in the presence of multiple initial vacua.

Abstract

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.