Tunneling in Stochastic Inflation

TL;DR

This paper analyzes the probability and rates of vacuum decay during inflation using stochastic inflation formalism, applicable to various potential landscapes including multiple minima and maxima.

Contribution

It provides a generalized calculation of decay probabilities and rates in single-field slow-roll inflation, extending previous results to arbitrary potentials.

Findings

Decay probabilities depend on potential shape and initial conditions.

Results align with Hawking and Moss for specific cases.

Applicable to complex potentials with multiple minima and maxima.

Abstract

The relative probability to decay towards different vacua during inflation is studied. The calculation is performed in single-field slow-roll potentials using the stochastic inflation formalism. Various situations are investigated, including falling from a local maximum of the potential and escaping from a local minimum. In the latter case, our result is consistent with that of Hawking and Moss, but is applicable to any potential. The decay rates are also computed, and the case of a generic potential with multiple minima and maxima is discussed.