Abstract
Scalar fields endowed with a cosh potential behave in the linear regime, exactly as the cold dark matter (CDM) model. Thus, the scalar field dark matter (SFDM) hypothesis predicts the same structure formation as the CDM model. This means that CDM and SFDM are equivalent from the cosmological point of view. The free parameters of the SFDM model are determined by cosmological observations. In previous work we showed that if we use such parameters, the scalar field collapses forming stable objects with a mass around 10^{12} M_⊙. In the present work we use analytical solutions of the flat and weak field limit of the Einstein-Klein-Gordon equations and show that the SFDM density profile corresponds to a halo with an almost flat central density and that it coincides with the CDM model in a broad outer region. This result could solve the problem of the density cusp DM halo in galaxies without any additional hypothesis, thus supporting the viability of the SFDM model.
