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

TL;DR

This paper explores metric theories of gravity with curvature-matter couplings as a relativistic extension of MOND, demonstrating their ability to explain cosmic acceleration without dark matter or dark energy.

Contribution

It introduces local and non-local metric gravity models with curvature-matter couplings that reproduce MOND behavior and account for accelerated expansion without dark components.

Findings

Valid at the weakest perturbation order for particle trajectories

Can explain supernovae observations without dark matter or dark energy

Provides a relativistic framework for MOND with cosmological applications

Abstract

We discuss the advantages of using metric theories of gravity with curvature-matter couplings in order to construct a relativistic generalisation of the simplest version of Modified Newtonian Dynamics (MOND), where Tully-Fisher scalings are valid for a wide variety of astrophysical objects. We show that these proposals are valid at the weakest perturbation order for trajectories of massive and massless particles (photons). These constructions can be divided into local and non-local metric theories of gravity with curvature-matter couplings. Using the simplest two local constructions in a FLRW universe for dust, we show that there is no need for the introduction of dark matter and dark energy components into the Friedmann equation in order to account for type Ia supernovae observations of an accelerated universe at the present epoch.