Reheating-volume measure in the landscape

TL;DR

This paper extends the reheating-volume measure to bubble nucleation scenarios in the multiverse, providing a way to calculate observable distributions and showing Boltzmann brains are negligible compared to ordinary observers.

Contribution

It generalizes the RV measure to landscapes with bubble nucleation, deriving a formula for bubble distributions and demonstrating its independence from initial conditions.

Findings

RV measure is well-defined and initial-condition independent.

Boltzmann brains are negligible compared to ordinary observers.

Explicit results for toy landscapes with multiple vacua.

Abstract

I recently proposed the "reheating-volume" (RV) prescription as a possible solution to the measure problem in "multiverse" cosmology. The goal of this work is to extend the RV measure to scenarios involving bubble nucleation, such as the string theory landscape. In the spirit of the RV prescription, I propose to calculate the distribution of observable quantities in a landscape that is conditioned in probability to nucleate a finite total number of bubbles to the future of an initial bubble. A general formula for the relative number of bubbles of different types can be derived. I show that the RV measure is well-defined and independent of the choice of the initial bubble type, as long as that type supports further bubble nucleation. Applying the RV measure to a generic landscape, I find that the abundance of Boltzmann brains is always negligibly small compared with the abundance of ordinary observers in the bubbles of the same type. As an illustration, I present explicit results for a toy landscape containing four vacuum states and for landscapes with a single high-energy vacuum and a large number of low-energy vacua.