Phase transitions in de Sitter: The stochastic formalism

TL;DR

This paper extends the stochastic spectral expansion method to analyze metastable vacuum states in de Sitter spacetimes, providing a way to compute decay rates and observables even when no stable vacuum exists.

Contribution

It introduces a novel extension of the stochastic formalism to unbounded potentials, enabling decay rate calculations for metastable vacua in de Sitter space.

Findings

Decay rate given by the lowest non-zero eigenvalue of the Fokker-Planck equation

Eigenfunction determines the field probability distribution

Method applicable to both bounded and unbounded potentials

Abstract

The stochastic spectral expansion method offers a simple framework for calculations in de Sitter spacetimes. We show how to extend its reach to metastable vacuum states, both in the case when the potential is bounded from below, and when it is unbounded from below and therefore no stable vacuum state exists. In both cases, the decay rate of the metastable vacuum is given by the lowest non-zero eigenvalue associated to the Fokker-Planck equation. We show how the corresponding eigenfunction determines the field probability distribution which can be used to compute correlation functions and other observables in the metastable vacuum state.