A Non-Minimal Quantum-Relativistic Coupling Framework for Galactic Dynamics and Cosmological Anomalies: A Dark Matter Alternative

This paper proposes an alternative quantum-relativistic framework to address fundamental discrepancies in classical Gravitation and General Relativity, bypassing the necessity for unobserved Cold Dark Matter (CDM). By formulating a non-minimal coupling between the Kerr metric's off-diagonal frame-dragging component (gtφ) and a resonant quantum vacuum environment (Φ, Ψ), we derive a conserved Stress-Energy Tensor (Tμνᵉⁿᵛ). We demonstrate that the framework is strictly Ostrogradsky ghost-free due to its canonical first-derivative kinetic structure and incorporates an intrinsic density-dependent screening mechanism that recovers exact General Relativity in high-density Solar System regimes. In the weak-field limit, the temporal component (T₀₀ᵉⁿᵛ) yields a localized positive effective mass density (ρeff). We show that this framework accounts for four major empirical anomalies: Flat galactic rotation curves from the SPARC database (e.g., NGC 3198). Interplanetary spacecraft acceleration residuals (Pioneer 10/11 anomaly). Early massive galaxy formation observed by JWST at high redshifts (z ~ 7.4-9.1). Cosmic shear distribution maps from Hubble COSMOS.