From Quantum Structure to Galactic Rotation: Eliminating Dark Matter with Planck-Covariant Gravity

This work presents a novel approach to explaining galactic rotation curves and related phenomena without invoking dark matter. By applying a Lorentz-covariant, Planck-scale averaging to the stress-energy source in Einstein’s field equations, a MOND-like acceleration law naturally emerges from unmodified General Relativity. The smeared source induces a logarithmic gravitational potential component in thin disk galaxies, reproducing flat rotation curves, the Baryonic Tully–Fisher relation, and the Radial Acceleration Relation. Crucially, the approach respects the classical Newtonian and Keplerian limits on smaller scales and maintains consistency with early-universe cosmological observations (CMB, BBN, BAO). This framework offers a minimal-covariant bridge from quantum spacetime structure to large-scale cosmic dynamics, providing a falsifiable alternative to dark matter and modified gravity theories. Related Works: 10.5281/zenodo.16933270 Zander, A. (2025). From Quantum to Cosmos: The Natural Law of Quantum Fields General Relativity 10.5281/zenodo.15578802 Zander, A. (2025). From Quantum to Cosmos: About Space and Time, Mass and Inertia (Also includes every Paper in an extra Zip in English): 10.5281/zenodo.16925937 Zander, A. (2025). From Quantum Structure to Galactic Rotation: Eliminating Dark Matter with Planck-Covariant Gravity.10.5281/zenodo.16925299 Zander, A. (2025). From Quantum to Cosmos: ZE-Qubit10.5281/zenodo.16925145 Zander, A. (2025). From Quantum to Cosmos - Schrödinger-Zander and Einstein-Zander Equation10.5281/zenodo.16924975 Zander, A. (2025). From Quantum to Cosmos – No Singularities: Planck-Covariant Averaging as Natural Cutoff10.5281/zenodo.16922391 Zander, A. (2025). From Quantum to Cosmos - Planck Two-Measure: Vacuum Catastrophe Fixed, Muon g-2 Consistent10.5281/zenodo.16921499 Zander, A. (2025). From Quantum to Cosmos: Solving the Λ Problem via (ℓₚ·tₚ)/(Rₒᵦₛ·t₀) ⇒ α_σ ≈ 4.60×10⁻¹²³ ⇒ Λ = α_σ/ℓₚ² ≈ 10⁻¹²³10.5281/zenodo.16929728 Zander, A. (2025). From Quantum to Cosmos: The Hawking Information Paradox -- Full Quantum10.5281/zenodo.16929833 Zander, A. (2025). From Quantum to Cosmos: Defusing the Hubble Tension with Planck-Covariant Spacetime Fine-Structure 10.5281/zenodo.16929899 Zander, A. (2025). From Quantum to Cosmos: Planck-Covariant Flavor: Fermion Mass Hierarchies Without New Sectors10.5281/zenodo.16929940 Zander, A. (2025). From Quantum to Cosmos: A Planck-Covariant, Unitary Solution to the Measurement Problem10.5281/zenodo.16910481 Zander, A. (2025). From Quantum to Cosmos: The Hawking Information Paradox Solved (3+1D, No Islands)10.5281/zenodo.16930310 Zander, A. (2025). From Quantum to Cosmos: A Requiem for LCDM - full Scientific + Extra Paper for readers without specialized background Contact & SupportAdrian Zander (Independent Researcher)[email protected]: 0009-0005-2388-5440 Support Scientific Continuation:IBAN: DE73 6149 0150 0132 6850 00BIC: GENODES1AAVReference: Zander Research