Quantum–Geometric Origin of Dark Energy and Λ-CDM: Predictive Sedenionic Gauge Field Cosmology

This work presents a unified algebraic framework for cosmology—Sedenionic Quantum Gravity (SQG)—in which spacetime curvature, dark energy, and entropy arise from a common underlying principle: the quantized commutator structure of a 16-dimensional sedenionic gauge field. In this theory, the cosmological constant is not an arbitrary parameter but an algebraic curvature invariant derived from the relation where is the sedenionic covariant derivative. This non-associative operator framework replaces geometric curvature with algebraic curvature, linking microscopic internal spinor dynamics to the macroscopic expansion of the Universe. Unlike the constant Λ of the standard Λ-CDM model, the SQG framework predicts a slowly varying cosmological term where the single algebraic parameter determines the rate of vacuum relaxation. The model naturally reproduces late-time acceleration, baryon acoustic oscillations (BAO), and large-scale structure formation while avoiding ultraviolet divergences through intrinsic non-associativity. Key predictions include: (i) a logarithmic phase drift in the BAO power spectrum; (ii) a small deviation of the dark-energy equation-of-state parameter from −1, and (iii) finite black-hole entropy derived from internal spinor microstates. These results unify dark energy, quantum information, and gravitational curvature within a single predictive algebraic formalism, offering a physically testable alternative to both Λ-CDM and Finsler-kinetic cosmologies.