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Bubble wall velocity with out-of-equilibrium corrections

Carlo Branchina*, Angela Conaci†, and Luigi Delle Rose‡

Stefania De Curtis§

  • *Contact author: carlo.branchina@unical.it
  • †Contact author: angela.conaci@unical.it
  • ‡Contact author: luigi.dellerose@unical.it
  • §Contact author: stefania.decurtis@fi.infn.it
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Phys. Rev. D 113, 035024 – Published 23 February, 2026

DOI: https://doi.org/10.1103/nmkw-7kgk

Abstract

We study how out-of-equilibrium effects modify the steady-state propagation of bubble walls during a cosmological first-order electroweak phase transition. Going beyond the local thermal equilibrium approximation, we numerically solve the coupled system of scalar field, hydrodynamic, and Boltzmann equations using a spectral algorithm that allows a first-principle treatment of the collision integral. This approach enables a quantitative assessment of nonequilibrium perturbations in the plasma and their backreaction on the wall motion. Focusing on the singlet extension of the Standard Model as a minimal benchmark scenario, we find that out-of-equilibrium corrections substantially enhance the effective friction on the expanding front, leading to slower wall velocities and broader wall profiles compared to the equilibrium case. These modifications have significant implications for cosmological observables. For instance, they enhance the efficiency of electroweak baryogenesis, thus improving the viability of baryon asymmetry generation within realistic parameter regions that can also be probed by future gravitational wave interferometers.

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Phys. Rev. D 113, 035024– Published 23 February, 2026
  • Received 10 November 2025
  • Accepted 26 January 2026
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