Bubble nucleation and growth in slow cosmological phase transitions

TL;DR

This paper analyzes slow bubble wall dynamics in cosmological phase transitions, providing analytical solutions and improved models for bubble growth, nucleation rates, and reheating effects, with implications for cosmic relics.

Contribution

It introduces refined analytical models for slow bubble wall velocities, incorporating temperature-dependent velocities and various nucleation rate approximations, improving understanding of phase transition dynamics.

Findings

Delta-function nucleation rate with temperature-dependent velocity accurately describes dynamics

Gaussian nucleation rate yields precise bubble size distribution

Reheating effects significantly influence bubble growth and transition completion

Abstract

We study the dynamics of cosmological phase transitions in the case of small velocities of bubble walls, $v_w<0.1$. We discuss the conditions in which this scenario arises in a physical model, and we compute the development of the phase transition. We consider different kinds of approximations and refinements for relevant aspects of the dynamics, such as the dependence of the wall velocity on hydrodynamics, the distribution of the latent heat, and the variation of the nucleation rate. Although in this case the common simplifications of a constant wall velocity and an exponential nucleation rate break down due to reheating, we show that a delta-function rate and a velocity which depends linearly on the temperature give a good description of the dynamics and allow to solve the evolution analytically. We also consider a Gaussian nucleation rate, which gives a more precise result for the bubble size distribution. We discuss the implications for the computation of cosmic remnants.