Quantum Geometrodynamics (QGD): On the Geometric Origin of the Universe

This paper develops Quantum Geometrodynamics (QGD), a unified framework proposing that all fundamental physics—quantum mechanics, gravity, and gauge interactions—emerges from the geometry and topology of a four-dimensional spatial manifold. The key insight is remarkably minimal: if the primordial vacuum has quaternionic structure (ℍ), the Skolem-Noether theorem constrains it to self-dual geometry, from which four operational axioms follow as mathematical necessities rather than independent postulates:- A1: Self-dual gravitational instanton with BPS condition (M = ℓ = a)- A2: Kinematic time emergence (dw = c dt)- A3: Quantum mechanics from Hopf fibration topology of S³- A4: Standard Model Higgs as the scalar sector This yields derivations of action quantization, the Born rule, spin-statistics, the Schrödinger equation, and Einstein's equations. The cosmological implications are significant. The "dark sector" receives a geometric reinterpretation: Dark Energy as vacuum strain energy (w = −1/3), Dark Matter as cosmic background acceleration (a₀ = cH₀). The framework predicts—with zero adjustable parameters—Ω_DM = 1/π ≈ 0.318 and a density evolution ρ(z) ∝ (1+z)² that naturally resolves tensions in current cosmological data, including the JWST early galaxy problem and the Hubble constant discrepancy. At the particle scale, QGD derives the proton's internal pressure from first principles, obtaining ~10³⁵ Pa—consistent with recent Jefferson Lab measurements and confirming the framework's validity from the smallest to the largest scales. QGD offers a perspective where the universe's apparent complexity emerges from the simplest possible foundation: the mathematical structure of emptiness itself. In this framework, matter is not something that exists within geometry—it is geometry, specifically stable topological excitations of the cosmic vacuum.