EXACT CRITICAL BUBBLE FREE-ENERGY AND THE EFFECTIVENESS OF EFFECTIVE POTENTIAL APPROXIMATIONS

To calculate the temperature at which a first-order cosmological phase transition occurs, one must calculate F(c)(T), the free energy of a critical bubble configuration. F(c)(T) is often approximated by the classical energy plus an integral over the bubble of the effective potential; one must choose a method for calculating the effective potential when V'' < 0. We test different effective potential approximations at one loop. The agreement is best if one pulls a factor mu4/T4 into the decay rate prefactor [where mu2 = V''(phi(f))], and takes the real part of the effective potential in the region V'' < 0. We perform a similar analysis on the one-dimensional kink.