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

TL;DR

This paper develops a method to accurately compute the energy transfer efficiency in cosmological first-order phase transitions by considering realistic equations of state beyond simplified models, impacting predictions of gravitational wave backgrounds.

Contribution

It introduces an iterative approach to solve fluid equations with variable sound velocities across bubble walls for realistic EoS, improving upon previous simplified models.

Findings

Efficiency factor is suppressed with sound velocity variation.

Suppression is negligible for strong phase transitions.

Previous bag model estimates remain valid for strong FOPTs.

Abstract

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