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First-order cosmological phase transitions in the radiation dominated era

We consider first-order phase transitions of the Universe in the radiation-dominated era. We argue that in general the velocity of interfaces is non-relativistic due to the interaction with the plasma and the release of latent heat. We study the general evolution of such slow phase transitions, which comprise essentially a short reheating stage and a longer phase equilibrium stage. We perform a completely analytical description of both stages. Some rough approximations are needed for the first stage, due to the non-trivial relations between the quantities that determine the variation of temperature with time. The second stage, instead, is considerably simplified by the fact that it develops at a constant temperature, close to the critical one. Indeed, in this case the equations can be solved exactly, including back-reaction on the expansion of the Universe. This treatment also applies to phase transitions mediated by impurities. We also investigate the relations between the different parameters that govern the characteristics of the phase transition and its cosmological consequences, and discuss the dependence of these parameters with the particle content of the theory.