Bubble collisions and defect formation in a damping environment

Abstract

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. 98.80.Cq

A step beyond the bounce: Bubble dynamics in quantum phase transitions

“…Moreover, we recall that although R is determined variationally in the thin wall approximation-this freedom is exploited by our initial condition-solving the bounce equation directly (under the assumption of O(D) symmetry) determines R uniquely. The coordinate shift transforms (16) so the trajectory of the interface is given by x = ±(x 0 + √ R 2 + t 2 ) in real time, implying that bubbles induced with different sizes will asymptote to different light cones as in Fig. 5.…”

“…We should naturally do first what we can in the classical regime, where we may apply the literature on semiclassical field theory methods in the bubble nucleation problem [2,3] and connect to other numerical studies [16]. The relativistic picture was elegantly framed by Coleman in Ref.…”

Defect formation rates in cosmological first-order phase transitions

“…Ferrera [23] confirmed the hypothesis of [2] by performing a series of simulations of complete global-symmetry phase transitions at different values of the bubble wall terminal velocity. However, quantitative analysis of the defect formation rate in the most realistic scenario cosmologically -a gauge-theory phase transition where the bubbles are slowed significantly by the plasma (as might be expected at the electroweak-or GUT-scales) -has not been studied.…”

“…A damping term of this form has been used by several authors [2], [30], [31], and has also been derived from the stress-energy of the Higgs, assuming a coupling to the plasma [32]. Heckler [30] estimates Γ ∼ g 2 W T c for the electroweak phase transition, by comparing the energy generated by the frictional damping with the pressure on the wall due to the damping.…”

“…The detailed form of the effective potential V (|Φ|) will depend upon the particular particle-physics model being considered, but in order to be able to study the generic features of a first-order phase transition we shall take V , following [2] and [3], to be * Electronic address: lilley@thphys.uni-heidelberg.de † Electronic address: ceefp44@pinar2.csic.es…”