Bubble Collisions and Defect Formation in a Damping Environment

Within the context of a first-order phase transition in the early Universe, we study the collision process for vacuum bubbles expanding in a plasma. The effects of the plasma are simulated by introducing a damping term in the equations of motion for a $U(1)$ global field. We find that Lorentz-contracted spherically symmetric domain walls adequately describe the overdamped motion of the bubbles in the thin wall approximation, and study the process of collision and phase equilibration both numerically and analytically. With an analytical model for the phase propagation in 1+1 dimensions, we prove that the phase waves generated in the bubble merging are reflected by the walls of the true vacuum cavity, giving rise to a long-lived oscillating state that delays the phase equilibration. The existence of such a state in the 3+1 dimensional model is then confirmed by numerical simulations, and the consequences for the formation of vortices in three-bubble collisions are considered.