A brief Review of the Scalar Field Dark Matter model

In the last time the cold dark matter (CDM) model has suggested more and more that it is not able to describe all the properties of nearby galaxies that can be observed in great detail as well as that it has some problems in the mechanism by which matter is more rapidly gathered into large-scale structure such as galaxies and clusters of galaxies. In this work we revisit an alternative model, the scalar field dark matter (SFDM) model, which proposes that the galactic haloes form by condensation of a scalar field (SF) very early in the Universe, i.e., in this model the haloes of galaxies are astronomical Bose-Einstein Condensate drops of SF. On the other hand, large-scale structures like clusters or superclusters of galaxies form similar to the ACDM model, by hierarchy, thus all the predictions of the ACDM model at cosmological scales are reproduced by SFDM. This model predicts that all galaxy haloes must be very similar and exist for higher redshifts than in the ACDM model. In the first part of this review we revisit the cosmological evolution of SFDM model with a scalar potential m(2)Phi(2)/2 + lambda Phi(4)/4 with two different frameworks: the field and fluid approach. We derive the evolution equations of the SF in the linear regime of perturbations as well. The scalar fluctuations have an oscillating growing mode and therefore, this kind of dark matter could lead to the early formation of gravitational structures in the Universe. We also revisit how BEC dark matter haloes exhibit a natural cut of the mass power spectrum. In the second part, we study the core central density profiles of BEC dark matter haloes and fit high-resolution rotation curves, we show a sample of some low surface brightness galaxies. The mean value of the logarithmic inner density slopes is alpha = -0.27 +/- 0.18. Using a model independent new definition of the core in the BEC density profile, we show that the recent observation of the constant dark matter central surface density can be reproduced. We conclude that in light of the difficulties that the ACDM model is currently facing the SFDM model can be a worthy alternative to keep exploring further.