First order phase transition in cosmology and monopole production

The purpose of the present work is to investigate whether the overproduction of monopoles is suppressed without conflicting with cosmological observation or not. The cosmic scale factor of the universe with vacuum energy density and radiation energy density was defined. The phase transition is triggered by the nucleation of bubbles. The volume fraction of false vacuum U(t) is described. The number density of black holes and wormholes (BWHs) is the number density of the false vacuum regions trapped by bubbles. The fraction of magnetized BWHs is given by the group theoretic factor p as shown by Kibble. When the phase transition finishes, the energy density difference between two vacua is released, and the universe is strongly heated up. The temperature and the entropy after the phase transition were calculated. The phase transition is discussed. In summary, if the nucleation rates are sufficiently small, the overproduction of monopoles is suppressed, and the baryon/entropy ratio is not diluted by the entropy production of BWHs. (Kato, T.)