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All existing treatments of bimetric MOND (BIMOND) -- a class of relativistic versions of MOND -- have dealt with a rather restricted sub-class: The Lagrangian of the interaction between the gravitational degrees of freedom -- the two…

A general account of MOND theory is given. I start with the basic tenets of MOND, which posit departure from standard dynamics in the limit of low acceleration -- below an acceleration constant a0 -- where dynamics become scale invariant. I…

Disc galaxies represent a promising laboratory for the study of gravitational physics, including alternatives to dark matter, owing to the possibility of coupling rotation curves' dynamical data with strong gravitational lensing…

General relativity (GR) is the most successful theory of gravity, with great observational support on local scales. However, to keep GR valid over cosmic scales, some phenomena (such as flat galaxy rotation curves and the cosmic expansion…

Quantum and noncommutative corrections to the Newtonian law of inertia are considered in the general setting of Verlinde's entropic force postulate. We demonstrate that the form for the modified Newtonian dynamics (MOND) emerges in a…

Verlinde's heuristic argument for the interpretation of the standard Newtonian gravitational force as an entropic force is generalized by the introduction of a minimum temperature (or maximum wave length) for the microscopic degrees of…

In superfluid dark matter the exchange of phonons can create an additional force that has an effect similar to Modified Newtonian Dynamics (MOND). To test whether this hypothesis is compatible with observation, we study a set of strong…

I discuss open theoretical questions pertaining to the modified dynamics (MOND)--a proposed alternative to dark matter, which posits a breakdown of Newtonian dynamics in the limit of small accelerations. In particular, I point the reasons…

We analyse the rotation curves and gravitational stability of a sample of six bulgeless galaxies for which detailed images reveal no evidence for strong bars. We explore two scenarios: Newtonian dark matter models and MOdified Newtonian…

Modified Newtonian Dynamics (MOND) is a gravitational framework designed to explain the astronomical observations in the Universe without the inclusion of particle dark matter. Modified Newtonian Dynamics, in its current form, cannot…

We investigate a model of modified gravity recovering the modified Newtonian dynamics (MOND) in the non-relativistic limit, based on the introduction of a preferred time foliation violating Lorentz invariance in the weak-field regime.…

In this article we construct an extended relativistic f(R) theory of gravity with matter-curvature couplings F(R,L_matt) for which its weak field limit of approximation recovers the simplest version of MOND. We do this by (a) performing an…

The modified Newtonian dynamics (MOND), suggested by Milgrom as an alternative to dark matter, implies that isothermal spheres with a fixed anisotropy parameter should exhibit a near perfect relation between the mass and the fourth power of…

Explaining the effects of dark matter using modified gravitational dynamics (MOND) has for decades been both an intriguing and controversial possibility. By insisting that the gravitational interaction that accounts for the Newtonian force…

We study the amplitude of the weak gravitational lensing signal as a function of stellar mass around a sample of relatively isolated galaxies. This selection of lenses simplifies the interpretation of the observations, which consist of data…

Strong gravitational lensing by galaxies in MOdified Newtonian Dynamics (MOND) has until now been restricted to spherically symmetric models. These models were able to account for the size of the Einstein ring of observed lenses, but were…

To further test MOdified Newtonian Dynamics (MOND) on galactic scales -- originally proposed to explain the rotation curves of disk galaxies without dark matter -- we study a sample of six strong gravitational lensing early-type galaxies…

An important and useful relation is known to hold in two specific MOND theories. It pertains to low-acceleration, isolated systems of pointlike masses, m_p, at positions r_p, subject to gravitational forces F_p. It reads sum_p…

A relativistic MOND theory, promising in reproducing cosmology as well as the MOND phenomenology in the low acceleration regime, was recently proposed. We present the post-Newtonian (PN) approximation and relativistic perturbation equations…

The stability of galaxies is either explained by the existence of dark matter or caused by a modification of Newtonian acceleration (MOND). Here we show that the modification of the Newtonian dynamics can equally well be obtained by a…