Geodesic measures of the landscape

TL;DR

This paper investigates measures of landscape models in eternal inflation, comparing geodesic-based approaches and proposing that eternal geodesics provide more consistent predictions unaffected by initial conditions.

Contribution

It introduces measure equations for ensembles of geodesics in eternal inflation and highlights the advantages of eternal geodesics over generic time-like geodesics.

Findings

Generic geodesics depend on initial conditions.

Eternal geodesics avoid dependence on initial conditions.

Derived measure equations for geodesic ensembles.

Abstract

We study the landscape models of eternal inflation with an arbitrary number of different vacua states, both recyclable and terminal. We calculate the abundances of bubbles following different geodesics. We show that the results obtained from generic time-like geodesics have undesirable dependence on initial conditions. In contrast, the predictions extracted from ``eternal'' geodesics, which never enter terminal vacua, do not suffer from this problem. We derive measure equations for ensembles of geodesics and discuss possible interpretations of initial conditions in eternal inflation.