Emergent Quantum Gravity from Sedenion Spinor Geometry: Framework of Associator-Induced Gravity and Connections to Cosmology

We develop a theoretical framework in which spacetime geometry and gravitational dynamics emerge from a non-associative spinor algebra defined on the sixteen-dimensional sedenion structure. In this approach, the spacetime metric is constructed from bilinear combinations of fundamental spinor fields, leading naturally to an effective four-dimensional geometry despite the higher-dimensional algebraic foundation. A central role is played by the associator, which measures the failure of associativity and introduces additional geometric degrees of freedom. Incorporation of the associator into the gravitational action yields modified Einstein equations with an effective geometric stress–energy contribution. In the weak-field limit, this leads to a Yukawa-type correction to the Newtonian potential, providing a geometric origin for phenomena commonly attributed to dark matter. The framework also suggests a natural interpretation of dark energy through associator vacuum contributions and establishes a connection between galactic dynamics and cosmological expansion scales. Furthermore, the model offers a pathway toward understanding early-universe coherence and the emergence of large-scale structure. These results indicate that non-associative spinor geometry may provide a unified algebraic foundation for quantum gravity and cosmology.