Dark matter as a Bose--Einstein Condensate: the relativistic
  non-minimally coupled case
  Bose--Einstein Condensates have been recently proposed as dark matter
candidates. In order to characterise the phenomenology associated to such
models, we extend previous investigations by studying the most general case of
a relativistic BEC on a curved background including a non-minimal coupling to
curvature. In particular, we discuss the possibility of a two phase
cosmological evolution: a cold dark matter-like phase at the large scales/early
times and a condensed phase inside dark matter halos. During the first phase
dark matter is described by a minimally coupled weakly self-interacting scalar
field, while in the second one dark matter condensates and, we shall argue,
develops as a consequence the non-minimal coupling. Finally, we discuss how
such non-minimal coupling could provide a new mechanism to address cold dark
matter paradigm issues at galactic scales.
