Hydrodynamic backreaction force of cosmological bubble expansion

As a promising probe for the new physics beyond standard model of particle in early Universe, predictions stochastic gravitational wave background from cosmological first-order phase transition heavily rely on bubble wall velocity determined by expansion dynamics. The dynamics is governed competition between driving force effective potential difference and backreaction sum thermal friction induced temperature jumping out-of-equilibrium effects across wall, respectively. In this paper, we propose hydrodynamic evaluation total nonrunaway steady-state expansion, which, after evaluated at interface, exactly reproduces pressure ${\mathrm{\ensuremath{\Delta}}}_{\text{wall}}[({\overline{\ensuremath{\gamma}}}^{2}\ensuremath{-}1)w]$ obtained previously junction condition energy-momentum tensor where $w$ enthalpy $\overline{\ensuremath{\gamma}}\ensuremath{\equiv}(1\ensuremath{-}{\overline{v}}^{2}{)}^{\ensuremath{-}1/2}$ Lorentz factor wall-frame fluid $\overline{v}$.