  Standard thermodynamical results of ideal Bose gases are used to study the
possible formation of a cosmological Bose-Einstein condensate in Scalar Field
Dark Matter models; the main hypothesis is that the boson particles were in
thermal equilibrium in the early Universe. It is then shown that the only
relevant case needs the presence of both particles and anti-particles, and that
it corresponds to models in which the bosonic particle is very light. Contrary
to common wisdom, the condensate should be a relativistic phenomenon. Some
cosmological implications are discussed in turn.
