Non-singular solutions to the Boltzmann equation with a fluid Ansatz

TL;DR

This paper addresses the issue of singularities in Boltzmann equation solutions for cosmological bubble wall velocities by incorporating spatial background dependence, leading to more accurate modeling of phase transition phenomena.

Contribution

It introduces a modified fluid Ansatz that removes unphysical singularities in Boltzmann equations for bubble dynamics during cosmological phase transitions.

Findings

Deflagration solutions are prevalent across various cutoff scales.

Detonation solutions are limited to specific parameter regions.

The modified approach improves the calculation of plasma counter-pressure.

Abstract

Cosmological phase transitions can give rise to intriguing phenomena, such as baryogenesis or a stochastic gravitational wave background, due to nucleation and percolation of vacuum bubbles in the primordial plasma. A key parameter for predicting these relics is the bubble wall velocity, whose computation relies on solving the Boltzmann equations of the various species along the bubble profile. Recently it has been shown that an unphysical singularity emerges if one assumes these local quantities to be described as small fluctuations over a constant equilibrium background. In this work we solve this issue by including the spatial dependence of the background into the fluid Ansatz. This leads to a modification of the Boltzmann equation, and all terms that would give rise to a singularity now vanish. We recalculate the different contributions to the counter-pressure of the plasma on the expanding wall, and discuss their relative importance. The Standard Model with a low cutoff is chosen as benchmark model and the results are shown for different values of the cutoff scale $\Lambda$. In this setup, deflagration solutions are found for almost all the values of $\Lambda$ considered, while detonations are found only for some restricted corner of the parameter space.