Vacuum Decay Actions from Tunneling Potentials for General Spacetime Dimension

TL;DR

This paper extends the tunneling potential method to calculate vacuum decay actions in arbitrary spacetime dimensions, providing new insights into gravitational effects, barrier influences, and analytical solutions.

Contribution

It generalizes the tunneling potential formalism to higher dimensions and offers simplified proofs and new results on vacuum decay and gravitational quenching.

Findings

Gravity and higher barriers increase vacuum lifetime.

Derived the thin-wall limit of the action.

Clarified gravitational quenching and detailed balance in the new formalism.

Abstract

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.