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

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.

Presence of a Fundamental Acceleration Scale in Galaxy Clusters

“…Various models that modify gravity have been considered in Refs. [70][71][72][73][74][75][76][77][78][79][80][81]. However, in the case of f (R) modified gravity models, it can be shown [70,71,82] that the models are equivalent to usual gravity coupled in a non-standard way to some scalar field.…”

Extending Friedmann Equations Using Fractional Derivatives Using a Last Step Modification Technique: The Case of a Matter Dominated Accelerated Expanding Universe

“…and substitute this together with the definitions of the fractional deceleration (34) and Hubble parameter (22) into Equation (38) to obtain:…”

“…The model independent relation between the luminosity distance d L (z) as a function of redshift z and the apparent magnitude µ is given by [34,67]:…”

“…In Barrientos and Mendoza [30], Bernal et al [31], Mendoza et al [32], Barrientos and Mendoza [33], Barrientos et al [34], the authors proposed general gravitational actions with curvature-matter couplings in order to obtain a feasible explanation for the MOdified Newtonian Dynamics (MONDian) behavior of gravitational phenomena. The general conclusions reached by the works of Bernal et al [31], Mendoza et al [32], Barrientos et al [34] is that it is possible to recover the MONDian expression for the acceleration in the regime a < a 0 for a pure metric f (R) theory provided a non-local action construction. Non-locality in these attempts is introduced as an extra scalar field with dimensions of mass that can be conveniently thought of as the causally-connected mass to each point in space-time.…”

Magnetized discs and photon rings around Yukawa-like black holes

“…64-66, and references therein] and in the universe as a whole at the present epoch [cf. [67][68][69], an extension to the Einstein equations can be postulated. At the other extreme, when gravitation is very strong, i.e.…”