Collision integrals for cosmological phase transitions

The dynamics of the true-vacuum bubbles nucleated during a first-order phase transition is affected by distribution functions particle species in plasma, driven out-of-equilibrium travelling domain wall. An accurate modelling this phenomenon relevant for quantitative description transitions early universe and determination corresponding cosmic relics, such as, among others, stochastic background gravitational waves. We address problem developing new spectral method devised fast reliable computation collision integral Boltzmann equations. In scalar singlet extension Standard Model chosen as benchmark scenario, we test our algorithm, determining bubble speed profile, asses impact dynamics.