Dynamics of metastable vacua in the early universe

We study the question whether a possible metastable vacuum state is actually populated in a phase transition in the early universe, as is usually assumed in the discussion of vacuum stability bounds e.g. for Standard Model parameters. A phenomenological (3+1)-dimensional Langevin equation is solved numerically for a toy model with a potential motivated by the finite temperature 1-loop effective potential of the Standard Model including additional non-renormalizable operators from an effective theory for physics beyond the Standard Model and a time dependent temperature. It turns out that whether the metastable vacuum is populated depends critically on the value of the phenomenological parameter η for small scalar couplings. For large enough scalar couplings and with our specific form of the non-renormalizable operators the system (governed by the Langevin equation) always ends up in the metastable minimum.