Cosmological Vacuum Decays from Schwinger-Keldysh Formalism

In this work, we establish a systematic framework to describe the vacuum decays in a radiation-dominated FLRW universe from the Schwinger-Keldysh formalism. By splitting the phase transition field $\Phi$ into the mean field $\phi$ and the short-wavelength modes $\sigma$ and tracing over the latter as the environment, we obtain a classical Langevin-type equation-of-motion for the mean field $\phi$, where the quantum effects are encoded in a non-Markov memory kernel and a non-Gaussian noise. As a phenomenological example, we consider a polynomial potential and study the structure of the memory kernel as well as the correlation functions of the noise term. With a less restrictive scale split by allowing $\phi$ to carry spatial dependence, further extensions remain possible to describe the whole dynamics of cosmological first-order phase transitions via numerical simulations.