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 (BEC) dark matter. We first ignore special relativistic effects and derive a differential equation that governs the evolution of the density contrast in the linear regime. This equation, which takes quantum pressure and self-interaction into account, 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 pressure effects (coming from special relativity) into account in the evolution of the cosmic fluid and add the contribution of radiation, baryons, and dark energy (cosmological constant). For 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 it increases less rapidly for BEC dark matter with attractive self-interaction (negative pressure). We study the linear development of the perturbations in these two cases and show that the perturbations grow faster in BEC dark matter than in pressureless dark matter. 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 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 good agreement with the standard Lambda CDM model that assumes a finite cosmological constant.