Phase transitions in de Sitter spacetimes: 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 metastable vacuum states, both the case when potential is bounded from below, and it unbounded below therefore no stable state exists. In cases, decay rate of given by lowest nonzero eigenvalue associated Fokker--Planck equation. corresponding eigenfunction determines field probability distribution which can be used compute correlation functions other observables state.