Quantum Gravity Based on Hypercomplex Spinor Geometry: Modified Gravity and Emergent Hubble Tension and Cosmological Constant
Abstract
Jau Tang
We present a unified theoretical framework in which particle physics, gravity, and cosmology emerge from a common hypercomplex steering–spinor algebra. The theory is based on a sixteen-dimensional algebra generated by basis elements e0 ,...,e15, organized into five spinor sectors Γ, Θ, U, V, and W. Within this structure, the gauge interactions of the Standard Model arise naturally from spinor products: the electromagnetic interaction from the Γsector, the weak interaction from the Θsector, and the strong interaction from cross-sector couplings between Γand U. The three fermion generations correspond to the spinor sectors U, V, and W, providing a geometric interpretation of the generation structure. The electroweak mixing angle and the approximate mass ratio of the W and Z bosons follow from the normalization of the spinor sectors. A key feature of the framework is the non-associative structure of the algebra, whose associator generates corrections to the gravitational connection and curvature. In the weak-field limit this produces a Yukawa-type modification of the Newtonian potential that can reproduce flat galaxy rotation curves without invoking dark matter particles. The vacuum curvature of the spinor manifold yields an effective cosmological constant, providing a geometric origin for cosmic acceleration. The resulting cosmological dynamics reproduce the phenomenology of the ΛCDM model while introducing scale-dependent corrections that may help explain the observed Hubble tension. These results suggest that gauge interactions, gravity, and cosmological dynamics may arise from a common hypercomplex algebraic structure.
