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 \citet{mendozatula}. 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 Capozziello et al. (2011). Unlike the pure metric formalism, which yields 4th 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.

7 pages

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Cited by in corpus (7)

• Metric-affine f(R,T) theories of gravity and their applications
• Extending Friedmann equations using fractional derivatives using a Last Step Modification technique: the case of a matter dominated accelerated expanding Universe
• Strong gravitational lensing in $f\left(\chi \right)={\chi }^{3/2}$ gravity
• MOND as the weak field limit of an extended metric theory of gravity with a matter-curvature coupling
• Galaxy Rotation Curves via Conformal Factors
• A simple model for explaining Galaxy Rotation Curves
• 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