Numerical Analysis of Coleman-de Luccia Tunneling
  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. 
Yuhei Goto, Kazumi Okuyama
hep-ph