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. (arXiv:2008.01800v2 [gr-qc] UPDATED)

<a href="http://arxiv.org/find/gr-qc/1/au:+Barrientos_E/0/1/0/all/0/1">E. Barrientos</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Bernal_T/0/1/0/all/0/1">T. Bernal</a>, <a href="http://arxiv.org/find/gr-qc/1/au:+Mendoza_S/0/1/0/all/0/1">S. Mendoza</a>

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.

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.

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