Bubble Free Energy in Cosmological Phase Transitions

Free energy as a function of temperature and the bubble radius is determined for spherical bubbles created in cosmological first order phase transitions. The phase transition is assumed to be driven by an order parameter (e.g. a Higgs field) with quartic potential. The definition of the bubble radius and the corresponding generalized, curvature-dependent surface tensions are discussed. In the free energy expansion in powers of the inverse radius, the coefficients of the curvature term and the constant term are also calculated.