Steady-state bubbles beyond local thermal equilibrium

TL;DR

This paper develops an analytical framework for expanding bubbles in cosmological phase transitions beyond local thermal equilibrium, revealing coexistence of multiple solutions and confirming the dominance of detonation in real-time growth.

Contribution

It introduces a method to incorporate entropy production into hydrodynamic models, enabling analytical computation of fluid profiles and bubble-wall velocities beyond equilibrium assumptions.

Findings

Multiple stable solutions coexist due to entropy production.

Numerical simulations show detonation solutions are typically realized.

The fluid profile may not reach steady-state during bubble acceleration.

Abstract

We investigate the hydrodynamic solutions for expanding bubbles in cosmological first-order phase transitions going beyond local thermal equilibrium approximation. Under the assumption of a tangenosidal field profile, we supplement the matching conditions with the entropy produced due to the interaction of the bubble wall with ambient plasma. This allows us to analytically compute the corresponding fluid profiles and find bubble-wall velocity. We show that due to the entropy production, two stable solutions corresponding to a deflagration or hybrid and a detonation can coexist. Finally, we use numerical real-time simulations of bubble growth to show that in such cases it is typically the faster detonation solution which is realised. This effect can be explained in terms of the fluid profile not being fully formed into the predicted steady-state solution as the wall accelerates past this slower solution.