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

Andrea De Simone, Alan H. Guth, Andrei Linde, Mahdiyar Noorbala, Michael P. Salem, Alexander Vilenkin

TL;DR

This work analyzes Boltzmann-brain (BB) domination in an eternally inflating multiverse regulated by the scale-factor cutoff measure. It derives a finite BB-to-normal-observer (NO) ratio by relating BB and NO counts to scale-factor volume fractions and vacuum transition rates, and it expresses the ratio in terms of BB nucleation and vacuum decay rates. Through toy landscapes and general arguments, the authors identify sufficient (and quasi-local) conditions to avoid BB domination, notably that BB nucleation in each vacuum be outpaced by its decay, and that BB production along any chain leading to an anthropic vacuum be suppressed by suppressed transition factors. They bound BB nucleation rates using entropy-based limits in Schwarzschild–de Sitter space and compare them to vacuum-decay rates from string-inspired landscapes, arguing that, under plausible assumptions, the scale-factor cutoff remains viable but remains sensitive to unknown high-energy physics. The results bind the BB problem to landscape dynamics and provide concrete criteria for the viability of this measure in predicting our observations.

Abstract

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.

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

TL;DR

This work analyzes Boltzmann-brain (BB) domination in an eternally inflating multiverse regulated by the scale-factor cutoff measure. It derives a finite BB-to-normal-observer (NO) ratio by relating BB and NO counts to scale-factor volume fractions and vacuum transition rates, and it expresses the ratio in terms of BB nucleation and vacuum decay rates. Through toy landscapes and general arguments, the authors identify sufficient (and quasi-local) conditions to avoid BB domination, notably that BB nucleation in each vacuum be outpaced by its decay, and that BB production along any chain leading to an anthropic vacuum be suppressed by suppressed transition factors. They bound BB nucleation rates using entropy-based limits in Schwarzschild–de Sitter space and compare them to vacuum-decay rates from string-inspired landscapes, arguing that, under plausible assumptions, the scale-factor cutoff remains viable but remains sensitive to unknown high-energy physics. The results bind the BB problem to landscape dynamics and provide concrete criteria for the viability of this measure in predicting our observations.

Abstract

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.

Paper Structure

This paper contains 15 sections, 159 equations, 2 figures.

Table of Contents

  1. Introduction
  2. The Scale Factor Cutoff
  3. The Abundance of Normal Observers and Boltzmann Brains
  4. Mini-landscapes and the General Conditions to Avoid Boltzmann Brain Domination
  5. The FIB Landscape
  6. The FIB Landscape with Recycling
  7. A More Realistic Landscape
  8. A Further Generalization
  9. A Dominant Vacuum System
  10. General Conditions to Avoid Boltzmann Brain Domination
  11. Boltzmann Brain Nucleation and Vacuum Decay Rates
  12. Boltzmann Brain Nucleation Rate
  13. Vacuum Decay Rates
  14. Conclusions
  15. Boltzmann Brains in Schwarzschild--de Sitter Space

Figures (2)

  • Figure 1: Graph shows the holographic bound, the D-bound, and the m-bound for the entropy of an object that fills de Sitter space out to the horizon. The holographic and D-- bounds are each shown as broken lines in the region where they are superseded by the other. Although the m-bound looks very much like a straight line, it is not.
  • Figure 2: Graph shows the ratio of $\Delta S$ to $I_{\rm BB}$, where the nucleation rate for Boltzmann brains is proportional to $e^{- \Delta S}$. All curves are based on the $I$-bound, as discussed in the text, but they differ by their assumptions about the size $R$ of the Boltzmann brain.