Recovering MOND from extended metric theories of gravity

TL;DR

This paper demonstrates that MOND can be derived as the weak-field limit of a specific extended metric theory of gravity, linking it to fundamental constants and symmetry principles.

Contribution

It introduces a particular extended metric gravity theory where MOND naturally emerges as the weak-field limit, incorporating Milgrom's acceleration constant.

Findings

MOND recovered as weak-field limit of extended gravity

Scale invariance of gravity is broken in this framework

A conserved quantity is derived via Noether's symmetry approach

Abstract

We show that the Modified Newtonian Dynamics (MOND) regime can be fully recovered as the weak-field limit of a particular theory of gravity formulated in the metric approach. This is possible when Milgrom's acceleration constant is taken as a fundamental quantity which couples to the theory in a very consistent manner. As a consequence, the scale invariance of the gravitational interaction is naturally broken. In this sense, Newtonian gravity is the weak-field limit of general relativity and MOND is the weak-field limit of that particular extended theory of gravity. We also prove that a Noether's symmetry approach to the problem yields a conserved quantity coherent with this relativistic MONDian extension.