First principles determination of bubble wall velocity

TL;DR

This paper develops a new, efficient method to calculate the velocity of bubble walls during first-order phase transitions, improving accuracy and categorizing solutions as deflagrations or ultrarelativistic detonations.

Contribution

It rederives fluid equations from fundamental principles without linearization and introduces a spectral method for solving the Boltzmann equation, applied to a scalar extension of the standard model.

Findings

Solutions are categorized as deflagrations or ultrarelativistic detonations.

Out-of-equilibrium effects are often subdominant.

Proposes simplified approximation schemes for bubble wall dynamics.

Abstract

The terminal wall velocity of a first-order phase transition bubble can be calculated from a set of fluid equations describing the scalar fields and the plasma's state. We rederive these equations from the energy-momentum tensor conservation and the Boltzmann equation, without linearizing in the background temperature and fluid velocity. The resulting equations have a finite solution for any wall velocity. We propose a spectral method to integrate the Boltzmann equation, which is simple, efficient and accurate. As an example, we apply this new methodology to the singlet scalar extension of the standard model. We find that all solutions are naturally categorized as deflagrations ($v_w\sim c_s$) or ultrarelativistic detonations ($\gamma_w\gtrsim10$). Furthermore, the contributions from out-of-equilibrium effects are, most of the time, subdominant. Finally, we use these results to propose several approximation schemes with increasing levels of complexity and accuracy. They can be used to considerably simplify the methodology while correctly describing the qualitative behavior of the bubble wall.