Vacuum decay actions from tunneling potentials for general spacetime dimension

The tunneling potential method to calculate the action for vacuum decay is an alternative to the Euclidean bounce method that has a number of attractive features. In this paper we extend the formalism to general spacetime dimension d > 2 and use it to give simple proofs of several results. For Minkowski or Anti de Sitter false vacua, we show that gravity or higher barriers increase vacuum lifetime and describe a very clean picture of gravitational quenching of vacuum decay. We also derive the thin-wall limit of the action, show how detailed balance for dS to dS transitions works in the new formalism and how to obtain potentials for which the vacuum decay solution can be obtained analytically.

Automated summary

The tunneling potential method is an attractive alternative to the Euclidean bounce method for calculating the action of vacuum decay. This paper extends the formalism to general spacetime dimension d > 2 and uses it to provide simple proofs of several results. It shows that gravity or higher barriers increase the lifetime of Minkowski or Anti de Sitter false vacua and presents a clear picture of the gravitational quenching of vacuum decay. The paper also derives the thin-wall limit of the action, demonstrates how detailed balance for dS to dS transitions works in the new formalism, and outlines a method for obtaining analytical solutions for vacuum decay potentials.