Numerical Analysis of Coleman-de Luccia Tunneling

We study the false vacuum decay of a single scalar field $ϕ$ 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 $1/\cosh(ϕ)$- and $\cos(ϕ)$-type potential as examples, which have cosmological and phenomenological applications. Especially, in the $\cos(ϕ)$-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.

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