Nucleation of cosmological phase transitions

A simple model is used to describe the nucleation of bubbles during a first-order relativistic cosmological phase transition. It is shown that if the parameters governing the nucleating action vary as powers of cosmological background quantities (such as temperature), and if the action has a certain general functional form, then the characteristic size of bubbles when the transition ends is smaller than the Hubble length by a factor of at least 1/4 ln [Tsub(P)/Tsub(c)], where Tsub(P) is the Planck temperature and Tsub(c) is the transition temperature. It is therefore unlikely that black holes form if Tsub(P)>Tsub(c), or that perturbations in entropy or pressure caused by the bubbles have any significant direct effect on large-scale cosmological inhomogeneity or nucleosynthesis. (orig.)