  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.
