Growth of perturbations in an expanding universe with Bose-Einstein condensate dark matter

Abstract: 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.