Recovering a MOND-like acceleration law in mimetic gravity

TL;DR

This paper shows that mimetic gravity with a non-minimal matter coupling can produce a MOND-like acceleration law, explaining flat galaxy rotation curves without dark matter, and potentially addressing larger scale mass discrepancies.

Contribution

It introduces a non-minimal matter coupling in mimetic gravity that yields MOND-like dynamics in the weak field limit, linking modified gravity to galaxy rotation observations.

Findings

Reproduces flat galactic rotation curves

Derives a MOND-like acceleration law from mimetic gravity

Suggests potential to address mass discrepancies on larger scales

Abstract

We reconsider the recently proposed mimetic gravity, focusing in particular on whether the theory is able to reproduce the inferred flat rotation curves of galaxies. We extend the theory by adding a non-minimal coupling between matter and mimetic field. Such coupling leads to the appearance of an extra force which renders the motion of test particles non-geodesic. By studying the weak field limit of the resulting equations of motion, we demonstrate that in the Newtonian limit the acceleration law induced by the non-minimal coupling reduces to a Modified Newtonian Dynamics (MOND)-like one. In this way, it is possible to reproduce the successes of MOND, namely the explanation for the flat galactic rotation curves and the Tully-Fisher relation, within the framework of mimetic gravity, without the need for particle dark matter. The scale-dependence of the recovered acceleration scale opens up the possibility of addressing the missing mass problem not only on galactic but also on cluster scales: we defer a full study of this issue, together with a complete analysis of fits to spiral galaxy rotation curves, to an upcoming companion paper.