Thermal False Vacuum Decay Is More Than It Seems

We study the decay of a thermally excited metastable vacuum in classical field theory using real-time numerical simulations. We find a significantly lower decay rate than predicted by standard thermal theory at moderate temperatures, $E_b/T\sim 10$, where $E_b$ is the critical bubble energy. The discrepancy is due to the violation of thermal equilibrium during the critical bubble nucleation and is reduced if thermalization is enhanced by introduction of dissipation and thermal noise. We formulate a condition for the system to remain in equilibrium during the nucleation process and show that it is generally violated in weakly coupled field theories. Nevertheless, we argue that the violation of thermal equilibrium becomes irrelevant for the false vacuum decay rate at sufficiently low temperatures and the standard thermal rate is recovered.