Hydrodynamic backreaction force of cosmological bubble expansion

Understand

As a promising probe for the new physics beyond the standard model of particle physics in the early Universe, the predictions for the stochastic gravitational wave background from a cosmological first-order phase transition heavily rely on the bubble wall velocity determined by the bubble expansion dynamics.

• The bubble expansion dynamics is governed by the competition between the driving force from the effective potential difference and the backreaction force from a sum of the thermal force and friction force induced by the temperature jumping and out-of-equilibrium effects across the bubble wall, respectively.
• In this paper, we propose a hydrodynamic evaluation on this total backreaction force for a non-runaway steady-state bubble expansion, which, after evaluated at the wall interface, exactly reproduces the pressure difference $\Delta_\mathrm{wall}[(\bar{\gamma}^2-1)w]$ obtained previously from the junction condition of the total energy-momentum tensor at the wall interface, where $w$ is the enthalpy and $\bar{\gamma}\equiv(1-\bar{v}^2)^{-1/2}$ is the Lorentz factor of the wall-frame fluid velocity $\bar{v}$.