The No-Negative Mode Theorem in False Vacuum Decay with Gravity

TL;DR

This paper proves the no-negative mode conjecture in false vacuum decay with gravity, resolving a longstanding problem and establishing the equivalence with the no-supercritical supercurvature mode conjecture in open inflation models.

Contribution

It provides a proof of the no-negative mode conjecture for general models and demonstrates its equivalence to the no-supercritical supercurvature mode conjecture.

Findings

Proof of the no-negative mode conjecture for general models.

Establishment of the equivalence between the two conjectures.

Confirmation of the absence of supercritical supercurvature modes in open inflation.

Abstract

The so-called negative mode problem in the path integral approach to the false vacuum decay with the effect of gravity has been an unsolved problem. Several years ago, we proposed a conjecture which is to be proved in order to give a consistent solution to the negative mode problem. We called it the ``no-negative mode conjecture''. In the present paper, we give a proof of this conjecture for rather general models. Recently, we also proposed the ``no-supercritical supercurvature mode conjecture'' that claims the absence of supercritical supercurvature modes in the one-bubble open inflation model. In the same paper, we clarified the equivalence between the ``no-negative mode conjecture'' and the ``no-supercritical supercurvature mode conjecture''. Hence, the latter is also proved at the same time when the former is proved.