A criterion for bubble formation in de Sitter universe

TL;DR

This paper investigates the conditions under which vacuum decay via bubble formation occurs in a de Sitter universe, providing criteria based on the scalar potential's curvature and analyzing their implications for different potential shapes.

Contribution

It derives necessary and sufficient conditions for bubble formation in de Sitter space, clarifying the role of potential curvature and identifying a parameter space 'grey zone' for decay.

Findings

Necessary and sufficient conditions depend on potential curvature at different points.

The 'grey zone' in parameter space is likely forbidden for certain potentials.

Conditions are related to the curvature being greater than 4 times the Hubble constant squared.

Abstract

The influence of the shape of scalar field potential on the outcome of vacuum decay in de Sitter universe is studied. Sufficient condition for vacuum decay via bubble formation, described by Coleman - de Luccia instanton, is revisited and necessary condition is found. Both conditions require that the curvature of the potential is greater than 4 $\times$ (Hubble constant)$^2$, but while the sufficient condition states that this inequality is to be valid at the top of the barrier, the necessary condition requires that it holds at least somewhere throughout the barrier. The conditions leave a 'grey zone' in parameter space, which however seems to be forbidden for quartic potential as well as for quadratic potential with a narrow peak proposed by Linde in the context of open inflation.