Bubble collisions and measures of the multiverse

TL;DR

This paper examines how the choice of initial hypersurface affects the predicted spectrum of bubble collisions in an eternally inflating multiverse, finding the effect diminishes with certain inflationary parameters.

Contribution

It analyzes the dependence of bubble collision spectra on initial hypersurface placement and shows the effect is generally negligible under realistic conditions.

Findings

Spectrum depends on initial hypersurface orientation

Effect diminishes with higher ratio of inflationary Hubble rates

Placing the observer's bubble near the initial hypersurface does not avoid the dependence

Abstract

To compute the spectrum of bubble collisions seen by an observer in an eternally-inflating multiverse, one must choose a measure over the diverging spacetime volume, including choosing an "initial" hypersurface below which there are no bubble nucleations. Previous calculations focused on the case where the initial hypersurface is pushed arbitrarily deep into the past. Interestingly, the observed spectrum depends on the orientation of the initial hypersurface, however one's ability observe the effect rapidly decreases with the ratio of inflationary Hubble rates inside and outside one's bubble. We investigate whether this conclusion might be avoided under more general circumstances, in particular placing the observer's bubble near the initial hypersurface. We find that it is not. As a point of reference, a substantial appendix reviews relevant aspects of the measure problem of eternal inflation.