International Journal of Quantum Technologies
Quantum-Corrected Gravity from Non-Associative Gauge Theory: A Preliminary Study of Galaxy Rotation Curves Without Dark Matter or Mond
Abstract
Jau Tang and Qiang Tang
We develop a modified gravitational model based on a non-associative gauge theory derived from algebraic spinor dynamics, which introduces a Yukawa-type correction to the Newtonian potential. This correction arises from the antisymmetric sector of the field tensor constructed on a discrete causal lattice using complexified sedenion algebra. The resulting dual-field structure modifies gravity at intermediate and large scales while remaining consistent with classical behavior at short ranges. We apply this framework to a sample of four astrophysical systems—two spiral galaxies (NGC 2403 and NGC 5055) and two galaxy clusters (Abell 2029 and Abell 2199)—chosen to represent both rotationally and pressure-supported dynamics. Unlike our earlier formulation, baryonic mass profiles are now derived from observationally motivated stellar and gas decompositions (e.g., exponential disks, HI maps, X-ray gas profiles), rather than generalized functional assumptions. The modified potential shows improved agreement with observed velocity and mass profiles, without invoking non-baryonic dark matter. We also analyze model complexity using Akaike and Bayesian criteria. While these results are promising, we emphasize that this is an initial study limited to a small sample, and further validation across larger galaxy sets is required.
The present analysis focuses on a small sample of galaxies, primarily to test the viability of the operator-based corrections under controlled conditions. We selected systems with well-characterized inner baryonic profiles and flat rotation curves within the radial range probed by current observations (typically within 10–20 kpc). While this region is still partly dominated by baryonic matter, it serves as a baseline for identifying whether operator-based corrections produce measurable effects in the inner halo. We acknowledge that dark matter–like deviations typically become prominent beyond this range. Therefore, future work will expand the dataset to include extended HI rotation curves and Gaia stellar halo measurements, allowing a more robust test at large radii.
We adopt photometrically derived disk scale lengths and assume exponential stellar profiles. Where available, HI gas profiles are included using standard mass–distance relations. The stellar mass-to-light ratio (M/L) is held fixed based on stellar population synthesis models (e.g., Kroupa IMF), primarily to isolate the effect of the operator-based gravitational corrections. We acknowledge that degeneracies exist between baryonic parameters (such as disk mass and scale radius) and gravitational model parameters (e.g., the Yukawa coupling strength α and range λ). In future work, a joint fitting approach using Bayesian sampling methods will be implemented to explore these degeneracies more thoroughly. However, our current approach allows a direct test of whether the operator model can reproduce rotation curves given physically reasonable baryonic inputs.