A Non-Associative Sedenionic Operator-Based Quantum Gravity: Cosmic Dynamics, Dark Matter and Dark Energy
Abstract
Jau Tang
We present a quantum gravitational framework based on a non-associative operator algebra constructed over the sedenion extension of the standard field theory. In this approach, associators — trilinear algebraic structures — generate curvature-like and mass-generating terms without introducing new fields or particles. We show that the operator associator naturally produces Yukawa-type corrections to the Newtonian potential, which lead to flattened galactic rotation curves and enhanced lensing effects without the need for dark matter. Simultaneously, the same algebraic mechanism gives rise to an effective repulsive component at cosmological scales, accounting for late-time acceleration without invoking a cosmological constant. This unified algebraic origin of dark energy and galaxy-scale gravitational anomalies suggests a new non-perturbative path toward quantum gravity, grounded in operator dynamics rather than geometric curvature alone.
