A relativistic description of MOND using the Palatini formalism in an extended metric theory of gravity

Abstract

We construct a relativistic metric description of MOND using the Palatini formalism following the f (χ) = χ b description of [1]. We show that in order to recover the non-relativistic MOND regime where, for circular orbits the Tully-Fisher law replaces Kepler's third law, the value of the parameter b = 3/2, which is coincident with the value found using a pure metric formalism [1]. Unlike this pure metric formalism, which yields fourth order field equations, the Palatini approach yields second order field equations, which is a desirable requirement from a theoretical perspective. Thus, the phenomenology associated to astrophysical phenomena with Tully-Fisher scalings can be accounted for using this proposal, without the need to introduce any non-baryonic dark matter particles.

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

“…It is our intention to explore this interpretation with applications to lensing and dynamics of individual, groups and clusters of galaxies as well as with cosmology. The advantage of this approach is that it is a full metric formalism and does not involve interpretations of gravity using Palatini formalism or torsion as we have previously explored [29,30]. Furthermore, it is a correct generalisation to the first attempts made by Bernal et al [12].…”

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

“…In previous studies, it has been shown that in order to build a relativistic version of MOND using f (R) theories in the pure metric approach or in the Palatini formalism or even with the inclusion of torsion, curvature-matter couplings need to be introduced into the gravitational action (Mendoza et al 2011;Bernal et al 2011b;Mendoza et al 2013;Barrientos & Mendoza 2016. Bertolami et al (2007) showed that for a particular generalisation of the f (R) theories in the metric approach, by coupling the f (R) function with the Lagrangian density of matter Lmatt, an extra-force arises which in the weak field limit can be connected with MOND's acceleration and possibly explain the Pioneer anomaly.…”

“…The search of a local relativistic theory of gravity in the full MONDian regime with a pure metric approach was carried on with success by Barrientos & Mendoza (2018), where the bending of light was successfully reproduced on such regime. Attempts on the construction of relativistic theories of MOND in the metric-affine formalism and with torsion were carried out by Barrientos & Mendoza (2016) and Barrientos & Mendoza (2017) respectively. The metric-affine one being non-local.…”

Galaxy rotation curves via conformal factors

“…Another approach is to consider Extended The-ories of Gravity (ETGs) -one modifies the geometric part of the field equations [32,33,35]. There are also attempts to obtain MOND result from ETGs, see for example [36][37][38][39][40][41]. Another interesting proposal for explaining rotation curves is by using the Weyl conformal gravity [42][43][44].…”