The energy budget of cosmological first-order phase transitions beyond the bag equation of state

The stochastic gravitational-wave backgrounds (SGWBs) from the cosmological first-order phase transitions (FOPTs) serve as a promising probe for new physics beyond standard model of particle physics. When most bubble walls collide with each other long after they had reached terminal wall velocity, dominated contribution to SGWBs comes sound waves characterized by efficiency factor inserting released vacuum energy into bulk fluid motions. However, previous works estimating this have only considered simplified case constant velocities in both symmetric and broken phases, either bag equal or $\nu$-model different which is unrealistic viewpoint In paper, we propose solve EoM an iteration method when taking account sound-velocity variation across general realistic equation state (EoS) simple $\nu$-model. We found suppression effect motions, though such could be negligible strong FOPT, estimation EoS on motions still good approximation.