Weyl-Invariant Gravity and the Nature of Dark Matter

TL;DR

This paper proposes that the observed dark matter effects in galaxies could be explained by a Weyl-invariant gravity theory where variations in gravitational coupling and active mass mimic dark matter, without needing new particles.

Contribution

It introduces a Weyl-invariant extension of General Relativity that accounts for dark matter phenomena through modifications in gravitational coupling and active mass, avoiding new particle hypotheses.

Findings

Dark matter effects can be modeled by gradients in gravitational coupling and active mass.

The proposed model predicts fractional increases in baryon density below detection thresholds.

The theory explains galaxy rotation curves without invoking dark matter particles.

Abstract

The apparent missing mass in galaxies and galaxy clusters, commonly viewed as evidence for dark matter, could possibly originate from gradients in the gravitational coupling parameter, $G$, and active gravitational mass, $M_{act}$, rather than hypothetical beyond-the-standard-model particles. We argue that in (the weak field limit of) a Weyl-invariant extension of General Relativity, one can simply affect the change $\Phi_{b}(x)\rightarrow\Phi_{b}(x) + \Phi_{DM}(x)$, where $\Phi_{b}$ is the baryon-sourced potential and $\Phi_{DM}$ is the `excess' potential. This is compensated by gradients of $GM_{act}$ and a fractional increase of $O(-4\Phi_{DM}(x))$ in the baryon density, well below current detection thresholds on all relevant scales.