Collision integrals for cosmological phase transitions

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