Phase Transitions in de Sitter: Quantum Corrections

TL;DR

This paper compares quantum and stochastic methods for calculating false vacuum decay rates in de Sitter space, showing their agreement at one-loop order and proposing a combined approach for more accurate decay predictions.

Contribution

It demonstrates that the stochastic approach with the constraint effective potential can match quantum decay rates beyond the saddle-point approximation.

Findings

Hawking-Moss decay rate computed at one-loop order

Stochastic approach reproduces quantum results within its validity domain

Proposes combined method for improved vacuum decay analysis

Abstract

We investigate the decay rate of a false vacuum state in de Sitter space at high Hubble rates, using two methods: the Hawking-Moss instanton method which is fully quantum mechanical but relies on the saddle-point approximation, and the Starobinsky-Yokoyama stochastic approach which is non-perturbative but does not include quantum effects. We use the flux-over-population method to compute the Hawking-Moss decay rate at one-loop order, and demonstrate that in its domain of validity, it is reproduced by the stochastic calculation using the one-loop constraint effective potential. This suggests that the stochastic approach together with the constraint effective potential can be used to accurately describe vacuum decay beyond the saddle-point approximation.