Growth of perturbations in an expanding universe with Bose-Einstein
  condensate dark matter
  We study the growth of perturbations in an expanding Newtonian universe with
Bose-Einstein condensate dark matter. We first ignore special relativistic
effects and derive a differential equation governing the evolution of the
density contrast in the linear regime taking into account quantum pressure and
self-interaction. This equation can be solved analytically in several cases. We
argue that an attractive self-interaction can enhance the Jeans instability and
fasten the formation of structures. Then, we take into account pressure effects
(coming from special relativity) in the evolution of the cosmic fluid and add
the contribution of radiation, baryons and dark energy (cosmological constant).
For a BEC dark matter with repulsive self-interaction (positive pressure) the
scale factor increases more rapidly than in the standard \Lambda CDM model
where dark matter is pressureless while for a BEC dark matter with attractive
self-interaction (negative pressure) it increases less rapidly. We study the
linear development of the perturbations in these two cases and show that the
perturbations grow faster in a BEC dark matter than in a pressureless dark
matter. This confirms a recent result of Harko (2011). Finally, we consider a
"dark fluid" with a generalized equation of state p=(\alpha \rho + k \rho
^2)c^2 having a component p=k \rho ^2 c^2 similar to a BEC dark matter and a
component p=\alpha \rho c^2 mimicking the effect of the cosmological constant
(dark energy). We find optimal parameters that give a good agreement with the
standard \Lambda CDM model assuming a finite cosmological constant.
