Mimicking dark matter through a non-minimal gravitational coupling with matter

In this study one resorts to the phenomenology of models endowed with a non-minimal coupling between matter and geometry, in order to develop a mechanism through which dynamics similar to that due to the presence of dark matter is generated. As a first attempt, one tries to account for the flattening of the galaxy rotation curves as an effect of the non-(covariant) conservation of the energy-momentum tensor of visible matter. Afterwards, one assumes instead that this non-minimal coupling modifies the scalar curvature in a way that can be interpreted as a dark matter component (albeit with negative pressure). It is concluded that it is possible to mimic known dark matter density profiles through an appropriate power-law coupling $f_2 = (R/R0)^n$, with a negative index $n$ -- a fact that reflects the dominance of dark matter at large distances. The properties of the model are extensively discussed, and possible cosmological implications are addressed.