No supercritical supercurvature mode conjecture in one-bubble open inflation

TL;DR

This paper investigates the negative mode problem in false vacuum decay with gravity, proposing and supporting a conjecture that supercritical supercurvature modes do not exist in certain inflation models.

Contribution

It establishes the equivalence between supercritical supercurvature modes and negative modes, and provides evidence supporting the conjecture of their non-existence in a broad class of models.

Findings

Supercritical supercurvature modes are linked to negative modes in Euclidean bounce solutions.

The conjecture that no supercritical supercurvature modes exist is validated for various tunneling potentials.

Abstract

In the path integral approach to false vacuum decay with the effect of gravity, there is an unsolved problem, called the negative mode problem. We show that the appearance of a supercritical supercurvature mode in the one-bubble open inflation scenario is equivalent to the existence of a negative mode around the Euclidean bounce solution. Supercritical supercurvature modes are those whose mode functions diverge exponentially for large spatial radius on the time constant hypersurface of the open universe. Then we propose a conjecture that there should be ``no supercritical supercurvature mode''. For a class of models that contains a wide variety of tunneling potentials, this conjecture is shown to be correct.