Weyl-Invariant Gravity and the Nature of Dark Matter

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.