Nuclear Physics B364 (1991) 411-450 North-Holland PHASE TRANSITIONS WITH SUB-CRITICAL BUBBLES Marcel0 GLEISER* Institute for Theoretical Physics, Vniversi& of California, Santa Barbara, CA 93106, USA Edward W. KOLB and Richard WATKINS NASA / Fermilab Astrophysics Center, Fermi National Accelerator Laboratory, Batavia, IL 60510, USA and Department of Astronomy and Astrophysics, Enrico Fermi Institute, The University of Chicago, Chicago, IL 60637, USA Received 26 February 1991 (Revised 6 June 1991) 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 poten- tials. 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. 1. Introduction Since the discovery in the mid-seventies that gauge symmetries are restored at high temperatures, the study of phase transitions in the early Universe has been the object of much interest [I]. Within the context of the big-bang model, as the Universe expanded and cooled from its initially hot and dense state, symmetries were broken in succession until reaching the stage in which particle interactions are well described by the standard model group, SU(3)c 8 SU(2), 0 U(l),. *Present address: Department of Physics and Astronomy, Dartmouth College, Hanover, NH 03755, USA. 0550-3213/91/$03.50 Q 1991 - Elsevier Science Publishers B.V. All rights reserved