Emergent Yukawa-Like Gravitational Potential from Non-Associative Sedenionic Gravity: Reproducing Galaxy Rotation Curves and Cluster Mass Profiles Without Dark Matter or MOND

We investigate the astrophysical implications of Sedenionic Quantum Gravity (SQG), a theoretical framework derived from the non-associative structure of sedenion algebra. In this approach, the antisymmetric sector of the sedenionic field generates an effective Yukawa-type correction to the gravitational interaction, introducing a finite interaction range that modifies gravitational dynamics on galactic and cluster scales. In the weak-field limit, the antisymmetric sector produces a massive field equation whose solution yields a Yukawa-type modification to the gravitational potential. We test the phenomenological consequences of this framework using rotation curves of three well-studied spiral galaxies—NGC 2403, NGC 3198, and NGC 5055—and hydrostatic mass profiles of two relaxed galaxy clusters, Abell 2029 and Abell 478, derived from X-ray observations of the intracluster medium. Using a stretched-exponential baryonic density distribution and least-squares fitting, the SQG model successfully reproduces the rapid inner rise and extended quasi-flat behavior observed in galaxy rotation curves as well as the circular-velocity profiles of galaxy clusters, without invoking dark matter halos or MOND-like prescriptions. The model is also consistent with the baryonic Tully–Fisher relation as an emergent scaling behavior of the Yukawa-modified gravitational interaction and may provide a plausible explanation for cluster-merger phenomena such as the Bullet Cluster through the antisymmetric, nonlocal gravitational sector. These results suggest that the non-associative algebraic structure underlying SQG may provide a unified explanation for gravitational phenomena traditionally attributed to dark matter across multiple astrophysical scales.