Hydrodynamics of ultra-relativistic bubble walls

TL;DR

This paper investigates the hydrodynamics of ultra-relativistic bubble walls during cosmological phase transitions, providing analytical tools to estimate gravitational wave signals from such phenomena.

Contribution

It offers new analytic approximations for energy transfer and back-reaction effects in ultra-relativistic bubble wall dynamics, enhancing predictions of gravitational wave signals.

Findings

Analytic fits for energy injected into fluid and accumulated in walls

Estimates of gravitational wave signals from detonations and runaway walls

Analysis of back-reaction effects on wall motion

Abstract

In cosmological first-order phase transitions, gravitational waves are generated by the collisions of bubble walls and by the bulk motions caused in the fluid. A sizeable signal may result from fast-moving walls. In this work we study the hydrodynamics associated to the fastest propagation modes, namely, ultra-relativistic detonations and runaway solutions. We compute the energy injected by the phase transition into the fluid and the energy which accumulates in the bubble walls. We provide analytic approximations and fits as functions of the net force acting on the wall, which can be readily evaluated for specific models. We also study the back-reaction of hydrodynamics on the wall motion, and we discuss the extrapolation of the friction force away from the ultra-relativistic limit. We use these results to estimate the gravitational wave signal from detonations and runaway walls.