KINETICS OF SUBCRITICAL BUBBLES AND THE ELECTROWEAK TRANSITION

We investigate the role of large-amplitude sub-critical thermal fluctu ations in the dynamics of first-order phase transitions. In particular , we obtain a kinetic equation for the number density of sub-critical fluctuations of the broken-symmetric phase within the symmetric phase, modeled as spherical bubbles, and solve it analytically for temperatu res above the critical temperature. We study the approach to equilibri um and obtain the equilibrium distribution of sub-critical bubbles of the unstable phase by examining three possible mechanisms responsible for their removal; their shrinking, their coupling to thermal noise, a nd by thermal fluctuations of the true vacuum inside them. We show tha t for sufficiently strong transitions, either the shrinking or the cou pling to thermal noise dominates the dynamics. As the strength of the transition weakens we show that sub-critical fluctuations become progr essively more important, as a larger fraction of the total volume is o ccupied by the broken-symmetric phase, until the point where our analy tical approach breaks down. Our investigation suggests that pre-transi tional phenomena may considerably change the dynamics of sufficiently weak first-order transitions. We apply our results to the standard ele ctroweak transition.