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We consider alternative theories of gravity with a direct coupling betweenmatter and the Ricci scalar We study the relation between these theories andordinary scalar-tensor gravity, or scalar-tensor theories which includenon-standard couplings between the scalar and matter. We then analyze themotion of matter in such theories, its implications for the EquivalencePrinciple, and the recent claim that they can alleviate the dark matter problemin galaxies.

Modified gravity with R-matter couplings and (non-)geodesic motion