The Growth of Bubbles in Cosmological Phase Transitions

TL;DR

The paper develops a dynamical framework for cosmological first-order phase transitions by coupling a scalar order parameter $φ$ to a relativistic fluid through a dissipative constant $Γ$, solving the nonlinear 1+1D evolution to track bubble growth from nucleation to a steady-front regime. It uncovers how bubbles can propagate as deflagrations or detonations, with shock heating and reheating from bubble collisions playing crucial roles, and derives both numerical results and analytical approximations for the steady-state wall velocities and temperatures in QCD-like and electroweak-like parameter sets. The study shows that the growth velocity is governed by microphysical coupling $Γ$, and that the temperature ahead and behind the front ($T_q$, $T_h$) can cross $T_c$, enabling a range of dynamical outcomes including weak detonations in certain regimes. Overall, the work links microscopic transition parameters to macroscopic hydrodynamic behavior, informing scenarios for baryogenesis and the generation of inhomogeneities in the early universe.

Abstract

We study how bubbles grow after the initial nucleation event in generic first-order cosmological phase transitions characterised by the values of latent heat, interface tension and correlation length, and driven by a scalar order parameter $φ$. Equations coupling $φ$ and the fluid variables $v$ and $T$ and depending on a dissipative constant $Γ$ are derived and solved numerically in the 1+1 dimensional case starting from a slightly deformed critical bubble configuration. Parameters corresponding to QCD and electroweak phase transitions are chosen and the whole history of the bubble with formation of combustion and shock fronts is computed as a function of $Γ$. Both deflagrations and detonations can appear depending on the values of the parameters. Reheating due to collisions of bubbles is also computed.