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 eta 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.