Reheating-volume measure for random-walk inflation

TL;DR

The paper introduces the reheating-volume measure as a new way to obtain probabilistic predictions in eternal inflation scenarios, demonstrating its gauge invariance and independence from initial conditions, and showing it avoids the youngness paradox.

Contribution

It provides a detailed description of the RV measure, derives a general formula for its application to random-walk models, and demonstrates its advantages over previous measures.

Findings

RV measure is gauge-invariant.

Results are independent of initial conditions.

RV measure avoids the youngness paradox.

Abstract

The recently proposed "reheating-volume" (RV) measure promises to solve the long-standing problem of extracting probabilistic predictions from cosmological "multiverse" scenarios involving eternal inflation. I give a detailed description of the new measure and its applications to generic models of eternal inflation of random-walk type. For those models I derive a general formula for RV-regulated probability distributions that is suitable for numerical computations. I show that the results of the RV cutoff in random-walk type models are always gauge-invariant and independent of the initial conditions at the beginning of inflation. In a toy model where equal-time cutoffs lead to the "youngness paradox," the RV cutoff yields unbiased results that are distinct from previously proposed measures.