Phase transitions with sub-critical bubbles

Abstract

We study the dynamics of cosmological phase transitions initiated from a state of thermal equilibrium. If the effective potential satisfies certain general conditions, a homogeneous phase of false vacuum will form as the Universe expands, and the transition will proceed by well-known bubble nucleation processes. If such conditions do not hold, the Universe may instead be filled with a two-phase emulsion. The evolution of the transition will be determined by the free energy difference between the two phases and by the expansion rate of the Universe. Thermal fluctuations between the phases will determine the final distribution of regions of the Universe in each phase as they freeze out. We develop a method to study the dynamics of such fluctuations, which we call sub-critical bubbles, and apply it to several situations of interest, including the symmetric and asymmetric double-well, and the Coleman-Weinberg scalar potentials. We show that in certain cases it is possible to avoid supercooling, with the transition being completed by sub-critical fluctuations. Possible applications to the electroweak phase transition are briefly discussed.