From friction scaling to an efficient method for estimating bubble wall velocity

TL;DR

This paper develops an efficient method to estimate bubble wall velocities in cosmological phase transitions by linking phenomenological models with microscopic Boltzmann equation analysis, providing accurate and scalable predictions.

Contribution

It introduces a simplified analytical expression for friction based on microscopic theory, enabling quick and reliable estimation of bubble wall velocities in cosmological models.

Findings

Derived a power-law scaling of friction parameter with transition strength.

Validated the phenomenological model against microscopic analysis results.

Provided an efficient computational method for bubble wall velocity estimation.

Abstract

We present a unified description of first-order cosmological phase transition dynamics that links the phenomenological friction model employed in hydrodynamic simulations to the microscopic treatment based on Boltzmann equations. We derive an approximate analytical expression for the chemical potential and demonstrate that the resulting friction parameter $\tilde{\eta}$ follows a simple power-law dependence on the transition strength ($\propto v_n^4/T_n^4$). Incorporating this scaling into a phenomenological framework accurately reproduces the terminal wall velocities obtained from the full microscopic analysis performed using \texttt{WallGo}. This approach offers an efficient method to quantify out-of-equilibrium contributions to friction and reliably estimate bubble-wall velocities.