Kaleidoscopic Cosmology: Scale Self-Duality Invariance and the Closed 3-Sphere Universe

Kaleidoscopic Cosmology: Scale Self-Duality Invariance and the Closed 3-Sphere Universe AbstractThis work presents a fully geometric, axiomatically founded framework for fundamental physics, designated Kaleidoscopic Cosmology. Rooted in two core principles—Scale Self-Duality Invariance and the Closed 3-Sphere Cosmic Ontology—this theory achieves a consistent unification of general relativity, quantum mechanics, and the four fundamental interactions, while offering a self-contained explanation for dark matter, dark energy, and the origin of quantum phenomena. The first axiom, Scale Self-Duality Invariance, posits that the fundamental laws of physics are form-invariant under reciprocal scale transformations, bounded by the Planck length and the cosmic curvature radius as dual poles. The second axiom defines the cosmic spacetime as a Lorentzian manifold, where the spatial component is a closed 3-sphere. From these axioms, we derive the Einstein field equations and the full gauge group structure of the Standard Model (SU(3)×SU(2)×U(1)) without introducing extra dimensions, free parameters, or ad-hoc particles. We explain the geometric origin of fermion spin, the Pauli exclusion principle, and charge quantization. Dark matter and dark energy are reinterpreted as manifestations of the 3-sphere's inherent curvature and topological defects, resolving the cosmological constant problem. The non-local topology of the 3-sphere provides a natural framework for quantum entanglement, reconciling quantum non-locality with relativistic causality.