Eternal observers and bubble abundances in the landscape

TL;DR

This paper investigates models where eternal inflation leads to endless bubble formation, showing that the frequency of bubble types encountered by an observer aligns with recent theoretical prescriptions for bubble abundance.

Contribution

It demonstrates the equivalence of two definitions of bubble abundance in eternal inflation models with positive energy vacua.

Findings

The bubble abundance matches the recent prescription.

Observers pass through all vacua infinitely often.

The proposed definitions are consistent and equivalent.

Abstract

We study a class of ``landscape'' models in which all vacua have positive energy density, so that inflation never ends and bubbles of different vacua are endlessly ``recycled''. In such models, each geodesic observer passes through an infinite sequence of bubbles, visiting all possible kinds of vacua. The bubble abundance $p_j$ can then be defined as the frequency at which bubbles of type $j$ are visited along the worldline of an observer. We compare this definition with the recently proposed general prescription for $p_j$ and show that they give identical results.