Measures on transitions for cosmology from eternal inflation

TL;DR

In eternal inflation, many cosmological observables depend on the inflaton's history rather than solely on the ending vacuum. The paper introduces a transition-based measure by labeling transitions α = NM and modeling $p_i^α$ with branching ratios $μ^α_β$ in a Markov framework, producing asymptotic transition frequencies (and enabling calculation of transition probabilities) without required enumeration of all histories. It demonstrates recovery of one-point vacuum statistics in appropriate limits and extends the formalism to longer histories and spacetime bubble counts via geodesic fractions $f^{NM}$, including higher-order correlations and history-dependent rates. The resulting framework provides a simpler, more natural approach to predicting cosmological observables and performing anthropic conditioning in a multivacua landscape, with practical templates for worldline and spacetime measures and extensions to history-dependent transition dynamics.

Abstract

We argue that in the context of eternal inflation in the landscape, making predictions for cosmological -- and possibly particle physics -- observables requires a measure on the possible cosmological histories as opposed to one on the vacua themselves. If significant slow-roll inflation occurs, the observables are generally determined by the history after the last transition between metastable vacua. Hence we start from several existing measures for counting vacua and develop measures for counting the transitions between vacua.

Figures (1)

• Figure 1: A simple potential landscape. We consider both a positive and negative energy $C$-well, with the zeros in energy density denoted by the solid or dotted line. In the text, we discuss both three-well (composed of $(A,B,C)$) and four-well (composed of $(A,B,C,D)$) landscapes.