Hydrodynamic backreaction force of cosmological bubble expansion
  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 and friction forces induced by the temperature
jumping and out-of-equilibrium effects across the bubble wall, respectively.
Recently, a thermodynamic evaluation for the difference
$\Delta[(\bar{\gamma}^2-1)w]$ in the vicinity of the bubble wall is proposed to
account for this backreaction force in a local thermal equilibrium from the
enthalpy $w$ and the Lorentz factor $\bar{\gamma}\equiv(1-\bar{v}^2)^{-1/2}$ of
the wall-frame fluid velocity $\bar{v}$. However, this proposal has neglected
the hydrodynamic contribution from the sound shell with a non-vanishing fluid
velocity profile. In this paper, we propose a complete hydrodynamic evaluation
on the backreaction force for a non-runaway bubble expansion, whose wall
contribution exactly matches the previous thermodynamic evaluation.
