Entanglement-Weighted Operator Geometry (EWOG): Cosmology

We present a complete, mathematically rigorous formulation of Entanglement-Weighted Operator Geometry (EWOG), a framework in which spacetime geometry and gravitational dynamics emerge from quantum information-theoretic axioms. The theory posits that the fundamental description of geometry is operator-valued, with classical tensors appearing only after an entanglement-weighted ensemble average. From five core axioms, we rigorously derive: (1) an effective gravitational action where the Einstein-Hilbert term is modulated by an entanglement weight functional \ (W\) ; (2) field equations that reduce to General Relativity (GR) in the limit of uniform entanglement but generate effective dark matter and dark energy from entanglement gradients and vacuum energy in the general case; (3) a unitary cosmological bounce replacing the Big Bang singularity; (4) modified structure formation capable of explaining high-redshift JWST observations; and (5) a geometric origin for flat galaxy rotation curves without particulate dark matter. We develop a comprehensive statistical framework for comparing EWOG against \ (\) CDM, string theory, Loop Quantum Gravity (LQG), and Conformal Cyclic Cosmology (CCC) using Bayesian evidence, AIC, BIC, and the Figure of Merit (FoM). The theory makes 14 falsifiable predictions testable with next-generation cosmological surveys.