Speed of sound in cosmological phase transitions and effect on gravitational waves

TL;DR

This paper investigates how higher-order corrections to the sound speed in cosmological phase transitions affect gravitational wave predictions, revealing significant deviations from standard assumptions and implications for dark sector models.

Contribution

It provides the first detailed higher-order computation of sound speed in a specific model and explores its impact on gravitational wave signals and dark sector phase transitions.

Findings

Deviations in sound speed can reach up to 5% from 1/3.

Energy budget of gravitational waves can be suppressed by up to 50%.

Modified field content can lead to order-of-magnitude changes in gravitational wave amplitude.

Abstract

The energy budget for gravitational waves of a cosmological first order phase transitions depends on the speed of sound in the thermal plasma in both phases around the bubble wall. Working in the real-singlet augmented Standard Model, which admits a strong two-step electroweak phase transition, we compute higher order corrections to the pressure and sound speed. We compare our result to lower-order approximations to the sound speed and the energy budget and investigate the impact on the gravitational wave signal. We find that deviations in the speed of sound from $c_s^2 = 1/3$ are enhanced up to $\mathcal O(5\%)$ in our higher-order computation. This results in a suppression in the energy budget of up to $\mathcal O (50\%)$ compared to approximations assuming $c_s^2 = 1/3$. The effect is most significant for hybrid and detonation solutions. We generalise our discussion to the case of multiple inert scalars and the case of a reduced number of fermion families in order to mimic hypothetical dark sector phase transitions. In this sector with modified field content, the sound speed can receive significant suppression, with potential order-of-magnitude impact on the gravitational wave amplitude.