Preheating and symmetry restoration in collisions of vacuum bubbles

In first-order inflation a phase transition is completed by the collisions of expanding true-vacuum bubbles. If bubble collisions produce large numbers of soft scalar particles carrying quantum numbers associated with a spontaneously broken symmetry, then symmetry restoration may occur in a ``pre-heating'' phase in a manner similar to symmetry restoration in the pre-heating phase of slow-roll inflation. Since bubble collisions lead to inhomogeneities, there is the possibility of inhomogeneous symmetry restoration where restoration occurs only in the regions of wall collisions.