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 Φ_b(x) → Φ_b(x) + Φ_DM(x), where Φ_b is the baryon-sourced potential and Φ_DM is the 'excess' potential. This is compensated by gradients of GM _act and a fractional increase of O(−4Φ_DM(x)) in the baryon density, well below current detection thresholds on all relevant scales. (paper)