Phase transitions in de Sitter: The stochastic formalism
  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.
