Sinks in the Landscape, Boltzmann Brains, and the Cosmological Constant Problem

TL;DR

This paper investigates how the string theory landscape's decay channels act as sinks affecting probability measures in eternal inflation, impacting the Boltzmann brain problem and the anthropic solution to the cosmological constant.

Contribution

It analyzes the role of sinks in the landscape, compares different probability measures, and proposes a simplified method for calculating anthropic probabilities.

Findings

Sinks prevent Boltzmann brain dominance in some measures.

Large number of vacua supports measure-independent anthropic solutions.

Certain global measures avoid the BB problem even without sinks.

Abstract

This paper extends the recent investigation of the string theory landscape in hep-th/0605266, where it was found that the decay rate of dS vacua to a collapsing space with a negative vacuum energy can be quite large. The parts of space that experience a decay to a collapsing space, or to a Minkowski vacuum, never return back to dS space. The channels of irreversible vacuum decay serve as sinks for the probability flow. The existence of such sinks is a distinguishing feature of the string theory landscape. We describe relations between several different probability measures for eternal inflation taking into account the existence of the sinks. The local (comoving) description of the inflationary multiverse suffers from the so-called Boltzmann brain (BB) problem unless the probability of the decay to the sinks is sufficiently large. We show that some versions of the global (volume-weighted) description do not have this problem even if one ignores the existence of the sinks. We argue that if the number of different vacua in the landscape is large enough, the anthropic solution of the cosmological constant problem in the string landscape scenario should be valid for a broad class of the probability measures which solve the BB problem. If this is correct, the solution of the cosmological constant problem may be essentially measure-independent. Finally, we describe a simplified approach to the calculations of anthropic probabilities in the landscape, which is less ambitious but also less ambiguous than other methods.