Evolution of the Order Parameter after Bubble Collisions

If a first-order phase transition is terminated by collisions of new-phase bubbles , there will exist a period of nonequilibrium between the time bubbles collide and the time thermal equilibrium is established. We study the behavior of the order parameter during this phase. We find that large nonthermal fluctuations at this stage tend to restore symmetry, i.e., the order parameter is smaller than its eventual thermal equilibrium value. We comment on possible consequences for electroweak baryogenesis. It has long been known that symmetry may be restored at high temperature in local thermodynamic equilibrium (LTE) [1]. Recently it was realized that certain nonequi-librium (NEQ) conditions can be even more efficient for symmetry restoration [2]. An example of such a nonequilibrium state can arise naturally after inflation in the so-called preheating era [3, 4]. In fact, symmetry may be restored in the NEQ state even if it is not restored in the LTE state formed by thermalization of the NEQ state. Detailed numerical studies [5] confirm that fluctuations of inflaton decay products is large enough for symmetry restoration, as well as for several other important effects, including baryo-genesis [6], and supersymmetry breaking [7], and generation of a background of relic gravitational waves [8]. States with properties similar to those in preheating, namely, anomalously large fluctuations and highly NEQ conditions, can arise in other situations as well. It was suggested in Ref. [9] that if bubble collisions produce large numbers of soft scalar particles carrying quantum numbers associated with a spontaneously broken symmetry, the phenomenon of (or tendency toward) symmetry restoration may occur. The basic point is that bubble collisions create NEQ conditions with a large number of " soft " quanta of average energy smaller than the equivalent LTE temperature corresponding to instantaneous conversion of the bubble energy density into radiation. Since it may require several scattering times for the low-energy quanta to form a thermal distribution, it is rather reasonable to consider the NEQ period as a separate epoch. This is generally referred to as the 'preheating' epoch in a manner similar to the preheating phase of slow-roll inflation [3]. The tendency of symmetry restoration in NEQ conditions after bubble collisions may be readily understood by the following (somewhat oversimplified) reasoning. Let us imagine that particles χ are produced in the bubble wall collisions and are charged under some symmetry group, so that their mass, m χ , depends upon some …