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.

星系和星系团中明显缺失的质量，通常被视为暗物质的证据，可能源自引力耦合参数G和活动引力质量M _{act 的}梯度，而不是假设的超标准模型粒子. 我们认为，在广义相对论的外尔不变扩展（的弱场极限）中，可以简单地影响变化 Φ _b ( x ) → Φ _b ( x ) + Φ _DM ( x )，其中 Φ _b是重子-sourced 潜力和 Φ _DM是“超额”潜力。这是由GM的梯度补偿的 _作用和重子密度中O (-4Φ _DM ( x ))的分数增加，远低于所有相关尺度上的当前检测阈值。