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We discuss the advantages of using metric theories of gravity withcurvature-matter couplings in order to construct a relativistic generalisationof the simplest version of Modified Newtonian Dynamics (MOND), whereTully-Fisher scalings are valid for a wide variety of astrophysical objects. Weshow that these proposals are valid at the weakest perturbation order fortrajectories of massive and massless particles (photons). These constructionscan be divided into local and non-local metric theories of gravity withcurvature-matter couplings. Using the simplest two local constructions in aFLRW universe for dust, we show that there is no need for the introduction ofdark matter and dark energy components into the Friedmann equation in order toaccount for type Ia supernovae observations of an accelerated universe at thepresent epoch.

international journal of geometric methods in modern physics

Non-vacuum relativistic extensions of MOND using metric theories of  gravity with curvature-matter couplings and their applications to the  accelerated expansion of the Universe without dark components