Numerical Analysis of Coleman-de Luccia Tunneling

TL;DR

This paper numerically analyzes false vacuum decay via Coleman-de Luccia instantons, demonstrating calculations beyond the thin-wall approximation for specific potentials, with implications for cosmology and axion physics.

Contribution

It introduces a numerical method to compute the bounce factor for CdL tunneling without thin-wall approximation, applied to cosine and hyperbolic potentials.

Findings

Numerical calculation of tunneling rate without thin-wall approximation.

Restriction on axion decay constant range due to tunneling.

Application to cosmologically relevant potentials.

Abstract

We study the false vacuum decay of a single scalar field $\phi$ coupled to gravity described by the Coleman-de Luccia (CdL) instanton. We show that it is possible to numerically calculate the bounce factor, which is related to the CdL tunneling rate, without using the thin-wall approximation. In this paper, we consider $1/\cosh(\phi)$- and $\cos(\phi)$-type potential as examples, which have cosmological and phenomenological applications. Especially, in the $\cos(\phi)$-type potential we show that the range of values in which axion decay constant can take is restricted by the form of the periodic potential if the CdL tunneling occurs.