Escaping the crunch: gravitational effects in classical transitions

TL;DR

This paper explores how gravitational effects influence classical transitions between vacua during eternal inflation, revealing conditions under which higher-energy vacua can be accessed and implications for eternal inflation measures.

Contribution

It introduces a detailed analysis of gravitational effects on classical transitions, including explicit solutions and conditions for allowed geometries in eternal inflation.

Findings

Gravitational effects enable transitions to higher-energy vacua.

Transitions from negative or zero energy vacua to de Sitter phases are possible.

Transitions cannot produce vacua with energy exceeding the parent vacuum.

Abstract

During eternal inflation, a landscape of vacua can be populated by the nucleation of bubbles. These bubbles inevitably collide, and collisions sometimes displace the field into a new minimum in a process known as a classical transition. In this paper, we examine some new features of classical transitions that arise when gravitational effects are included. Using the junction condition formalism, we study the conditions for energy conservation in detail, and solve explicitly for the types of allowed classical transition geometries. We show that the repulsive nature of domain walls, and the de Sitter expansion associated with a positive energy minimum, can allow for classical transitions to vacua of higher energy than that of the colliding bubbles. Transitions can be made out of negative or zero energy (terminal) vacua to a de Sitter phase, re-starting eternal inflation, and populating new vacua. However, the classical transition cannot produce vacua with energy higher than the original parent vacuum, which agrees with previous results on the construction of pockets of false vacuum. We briefly comment on the possible implications of these results for various measure proposals in eternal inflation.