The Exact Critical Bubble Free Energy and the Effectiveness of Effective Potential Approximations

Abstract

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 $V^{\prime \prime }<0$. We test different effective potential approximations at one loop. The agreement is best if one pulls a factor of ${\mu }^4/T^4$ into the decay rate prefactor [where ${\mu }^2=V^{\prime \prime }({\varphi }_f)$], and takes the real part of the effective potential in the region $V^{\prime \prime }<0$. We perform a similar analysis on the 1-dimensional kink.

Comments: 11 pages plus 3 figures in jyTeX; CALT-68-1881