MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling

Understand

In this article we construct an extended relativistic f(R) theory of gravity with matter-curvature couplings F(R,L_matt) for which its weak field limit of approximation recovers the simplest version of MOND.

• We do this by (a) performing an order of magnitude approach and (b) by perturbing the resulting field equations of the theory to the weakest field limit of approximation.
• We also compute the geodesic equation of the resulting theory and show that it has an extra force, a fact that commonly appears in general matter-curvature couplings.
• This arxiv version includes a section at the end with an Erratum.