Dark matter as a dynamic effect due to a non-minimal gravitational coupling with matter

TL;DR

This paper explores how non-minimal coupling between matter and geometry in modified gravity models can explain galactic rotation curve flattening without dark matter, through dynamical effects and energy-momentum tensor deviations.

Contribution

It introduces a novel mechanism where non-minimal coupling effects mimic dark matter by altering gravitational dynamics and energy-momentum conservation.

Findings

Non-minimal coupling can produce effects similar to dark matter in galaxy rotation curves.

Numerical estimates suggest parameter ranges compatible with observed galactic dynamics.

Potential cosmological implications of these modified gravity effects are discussed.

Abstract

In this work the phenomenology of models possessing a non-minimal coupling between matter and geometry is discussed, with a particular focus on the possibility of describing the flattening of the galactic rotation curves as a dynamically generated effect derived from this modification to General Relativity. Two possibilities are discussed: firstly, that the observed discrepancy between the measured rotation velocity and the classical prediction is due to a deviation from geodesic motion, due to a non-(covariant) conservation of the energy-momentum tensor; secondly, that even if the principle of energy conservation holds, the dynamical effects arising due to the non-trivial terms in the Einstein equations of motion can give rise to an extra density contribution that may be interpreted as dark matter. The mechanism of the latter alternative is detailed, and a numerical session ascertaining the order of magnitude of the relevant parameters is undertaken, with possible cosmological implications discussed.