Energy budget of cosmological first-order phase transition in FLRW background

We study the hydrodynamics of bubble expansion in cosmological first-order phase transition in the Friedmann-Lema\^{\i}tre-Robertson-Walker (FLRW) background with probe limit. Different from previous studies for fast first-order phase transition in flat background, we find that, for slow first-order phase transition in FLRW background with a given peculiar velocity of the bubble wall, the efficiency factor of energy transfer into bulk motion of thermal fluid is significantly reduced, thus decreasing the previously-thought dominated contribution from sound wave to the stochastic gravitational-wave background.
Comment: v1, 36 pages, 8 figures; v2, 37 pages, 8 figures, major change of conclusion whose application range has shrunk down to the case of slow first-order phase transition, added reference and acknowledgement; v3, 38 pages, 8 figures, version accepted for publication online in Sci.China Phys.Mech.Astron