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

Andrei Linde

TL;DR

This work analyzes how sinks from decays to Minkowski or collapsing AdS spaces reshape the eternal inflation landscape and tests three probability frameworks—comoving, pseudo-comoving, and standard volume-weighted—for predicting observer distributions. It shows that comoving and pseudo-comoving schemes can suffer Boltzmann-brain problems, whereas the standard volume-weighted measure largely avoids them due to rapid, global volume growth. The paper argues that with a sufficiently large number of vacua, the anthropic solution to the cosmological constant problem can remain robust across a broad class of measures, suggesting a degree of measure-independence for this prediction. A simplified approach to anthropic probabilities in the landscape is also presented, potentially making the calculation of anthropic priors more tractable.

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.

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

TL;DR

This work analyzes how sinks from decays to Minkowski or collapsing AdS spaces reshape the eternal inflation landscape and tests three probability frameworks—comoving, pseudo-comoving, and standard volume-weighted—for predicting observer distributions. It shows that comoving and pseudo-comoving schemes can suffer Boltzmann-brain problems, whereas the standard volume-weighted measure largely avoids them due to rapid, global volume growth. The paper argues that with a sufficiently large number of vacua, the anthropic solution to the cosmological constant problem can remain robust across a broad class of measures, suggesting a degree of measure-independence for this prediction. A simplified approach to anthropic probabilities in the landscape is also presented, potentially making the calculation of anthropic priors more tractable.

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.

Paper Structure

This paper contains 13 sections, 69 equations, 4 figures.

Table of Contents

  1. Introduction
  2. Decay of de Sitter vacua and sinks in the landscape
  3. Tunneling to a collapsing universe with a negative vacuum energy
  4. Currents in the landscape with sinks
  5. Comoving probabilities and incoming currents
  6. Pseudo-comoving volume-weighted measure
  7. 'Standard' volume-weighted distribution: rewarding the leaders
  8. Invasion of Boltzmann brains.
  9. BBs and comoving probabilities
  10. BBs and the pseudo-comoving volume-weighted distribution
  11. BBs and the standard volume-weighted distribution
  12. The standard volume-weighted distribution and the cosmological constant problem
  13. Discussion

Figures (4)

  • Figure 1: Coleman-De Luccia tunneling may go in both directions. A surprising feature of this process is that the tunneling in general occurs not from one minimum of the potential to another minimum, but form one wall of the potential to another wall.
  • Figure 2: A potential with two dS minima and a sink.
  • Figure 3: A potential with three dS minima and two sinks.
  • Figure 4: Boltzman brains populating the landscape