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

TL;DR

This paper develops an extended f(R) gravity theory with matter-curvature coupling that reproduces Modified Newtonian Dynamics (MOND) in the weak field limit, providing a relativistic framework for alternative gravity models.

Contribution

It introduces a new relativistic f(R) gravity model with matter-curvature coupling that recovers MOND behavior in the weak field limit, expanding the theoretical landscape of modified gravity.

Findings

The theory recovers MOND in the weak field approximation.

The geodesic equation includes an extra force due to matter-curvature coupling.

Perturbation analysis confirms the consistency of the weak field limit.

Abstract

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.