A volume-weighted measure for eternal inflation

TL;DR

This paper introduces a new gauge-invariant volume-weighted probability measure for eternal inflation, addressing key paradoxes and providing a method to compute distributions in multiverse scenarios.

Contribution

The paper proposes the reheating-volume (RV) cutoff, a novel measure for eternal inflation that is gauge-invariant, paradox-free, and applicable to landscape models with bubble nucleation.

Findings

The RV measure avoids the youngness paradox.

It can be computed via nonlinear diffusion equations.

Applied to a toy landscape, it yields specific probability predictions.

Abstract

I propose a new volume-weighted probability measure for cosmological "multiverse" scenarios involving eternal inflation. The "reheating-volume (RV) cutoff" calculates the distribution of observable quantities on a portion of the reheating hypersurface that is conditioned to be finite. The RV measure is gauge-invariant, does not suffer from the "youngness paradox," and is independent of initial conditions at the beginning of inflation. In slow-roll inflationary models with a scalar inflaton, the RV-regulated probability distributions can be obtained by solving nonlinear diffusion equations. I discuss possible applications of the new measure to "landscape" scenarios with bubble nucleation. As an illustration, I compute the predictions of the RV measure in a simple toy landscape.