  We study the back-reaction effects of the finite-temperature scalar field and
the photon field in the background of an Einstein universe. In each case we
find a relation between the temperature of the universe and its radius. These
relations exhibit a minimum radius below which no self-consistent solution for
the Einstein field equation can be found. A maximum temperature marks the
transition from the vacuum dominated era to the radiation dominated era. An
interpretation to this behavior in terms of Bose-Einstein condensation in the
case of the scalar field is given.
