MOND as the weak-field limit of an extended metric theory of gravity

TL;DR

This paper demonstrates that Modified Newtonian Dynamics (MOND) can be derived as the weak-field limit of a specific extended metric theory of gravity, linking it to a fundamental acceleration constant and breaking scale invariance.

Contribution

It introduces a new extended metric gravity theory where MOND emerges naturally as the weak-field limit, connecting it to fundamental constants.

Findings

MOND is recoverable as a weak-field limit of the proposed theory

The theory incorporates Milgrom's acceleration constant as fundamental

Scale invariance of gravity is naturally broken in this framework

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.