We propose a phenomenological model in which a non-minimal coupling betweengravity and dark matter is present in order to address some of the apparentsmall scales issues of \lcdm model. When described in a frame in which gravitydynamics is given by the standard Einstein-Hilbert action, the non-minimalcoupling translates into an effective pressure for the dark matter component.We consider some phenomenological examples and describe both background andlinear perturbations. We show that the presence of an effective pressure maylead these scenarios to differ from \lcdm at the scales where the non-minimalcoupling (and therefore the pressure) is active. In particular two effects arepresent: a pressure term for the dark matter component that is able to reducethe growth of structures at galactic scales, possibly reconciling simulationsand observations; an effective interaction term between dark matter and baryonsthat could explain observed correlations between the two components of thecosmic fluid within Tully-Fisher analysis.
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