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Modified theories of gravity with non-minimal curvature-matter coupling

In this contribution one examines the generalization of the $f(R)$ theories of gravity where one introduces a non-minimal coupling between curvature and matter. This model has new and interesting features. %, specially concerning the energy exchange between the matter fields and the curvature. However, as any modified gravity theories, these may give origin to anomalies which might turn the theory physically meaningless. In this respect, one undertakes a study on the energy conditions and the Dolgov-Kawasaki criterion specific of this new model.