Visible and dark matter profiles in a non-minimally coupled model

A previous work found that a nonminimally coupled theory of gravity can, under appropriate conditions, give rise to an additional contribution to the field equations interpreted as dark matter (Bertolami and Paramos 2010 J. Cosmol. Astropart. Phys. JCAP10(2010)03): in particular, the density of this dark matter component was found to scale as a power of the density of visible matter. However, no explicit solution for the modified field equations was provided, so that a direct computation of the specific density profile followed by visible matter is missing. This question is now addressed: analytical solutions to the modified field equations are derived in the appropriate perturbative regime and characterised, with an emphasis on directly obtaining the visible matter profile in a self-consistent way. We compare with known profiles for visible and dark matter and obtain constraints on the parameters of the model.