Counting Pockets with World Lines in Eternal Inflation

TL;DR

This work tackles the measure problem in eternal inflation by constructing a finite, gauge-invariant regulator for the distribution of pocket types via world-line sampling and duplicates removal. The full observable probability factorizes as $P(obs_{α_i}|V)=\sum_A P(A|V) P(α_i|A) P(obs|α_i)$, with a dedicated focus on computing $P(A|V)$. They regulate $P(α_i|A)$ through a volume-weighting scheme by taking the volume fraction in a sphere of radius $R$ and sending $R\to\infty$, and demonstrate the method with a concrete three-vacua example to illustrate typicality vs. atypicality of the observed $ρ_{Λ}$. The results yield finite, gauge-independent pocket distributions and offer a way to disfavor some eternally inflating potentials by comparing predicted typicality against our actual cosmological measurements.

Abstract

We consider the long standing puzzle of how to obtain meaningful probabilities in eternal inflation. We demonstrate a new algorithm to compute the probability distribution of pocket universe types, given a multivacua inflationary potential. The computed probability distribution is finite and manifestly gauge-independent. We argue that in some scenarios this technique can be applied to disfavor some eternally inflating potentials.