BUBBLE NUCLEATION IN PHI(4) MODELS AT ALL TEMPERATURES

One possible way in which phase transitions in the early universe may have occurred is via nucleation of bubbles of the new phase (true vacu um) in the old phase (false vacuum). The technique most widely used to compute the probability of bubble nucleation is based on instanton me thods in the context of the semiclassical approximation. At zero tempe rature in 3+1 dimensions the nucleation rate is dominated by the O(4) symmetric instanton, a sphere of radius R, while at temperatures T muc h greater than R(-1) the decay is dominated by a ''cylindrical'' (stat ic) instanton with O(3) invariance. There has been discussion in the l iterature as to whether the transition between these two regimens woul d be first order (discontinuity in the first derivative of the nucleat ion rate at the transition temperature T-c), or second order (continui ty of the first derivative, but discontinuity of the second derivative at T-c). In this paper we obtain the finite temperature solutions cor responding to the quantum and the thermal regimes, and compute their a ction as a function of the temperature for different values of the wal l thickness in a (phi(4) potential. Our results indicate that only for the cases of very large wall thickness a second-order transition take s place, while for all the other cases a first-order transition occurs .