A Density-Dependent Gravitational Coupling from Galactic Dynamics: Theory, Cosmological Consequences, and Observational Tests

We present a theory of gravity where the effective gravitational coupling Geff de-pends on the local energy density ρ through the relation Geff (ρ) = G0/[1 − βρ/ρP ],with ρP = c5/(ℏG20) the Planck density. The dimensionless constant β = 1/(8π) ≈0.0398 is empirically determined from the SPARC catalog of galaxy rotation curves,where it appears in the scaling relation (Vobs/Vbar)2 = 1 + β(ρbar/ρ∗). Fromthis single postulate we derive: (1) galaxy rotation curves without dark matter,achieving χ2red = 1.1 for SPARC galaxies with no free per-galaxy parameters;(2) modified Friedmann equations producing effective dark energy with weff (z) ≈−0.95+0.30z/(1+z); (3) natural resolution of the H0 and S8 tensions through time-varying Geff ; (4) unique predictions for gravitational lensing, BAO anisotropies, andstructure growth. The theory makes falsifiable predictions testable with DESI, Eu-clid, and SKA data within 1-5 years. 10.5281/zenodo.18139898 Svetlana KryukovaIndependent ResearcherORCID: 0009-0006-5152-069XJanuary 3, 2026 Keywords: dark matter, modified gravity, cosmological tensions, galaxy dynamics,fundamental constants