A Global Geometric Structure for Non-singular Periodic Cosmological Evolution

Abstract

We present a non-singular, periodic cosmological framework where the Universe manifold emerges as 3-dimensional intersection of two orthogonal 4-dimensional spheres. This framework reconciles kinematic contradictions inherent in traditional singularity-based models. Rooted in Special Relativity, cosmic evolution is modeled as a sequence of Lorentz contractions, establishing that the current universe radius stands at 93.2% of its maximal value. To ensure continuity, we introduce a transitional phase of geometric stasis where spatio-temporal coordinates remain invariant, while cosmic momentum is preserved via angular re-orientation in the embedding space. By shifting the evolutionary degrees of freedom from linear displacement to a rotation of the underlying manifold, the model bypasses traditional singularities, maintaining a continuous transition between cycles. This mechanism naturally accounts for the existence of mature, high-redshift galaxies observed by JWST, by allowing for information and matter distribution to survive the transition between phases and yielding a derived structural upper bound for direct redshifts at zmax ≈ 19.8, ignoring the redshifts from longer trajectories. The framework offers a novel resolution to the Hubble tension by characterizing early and late-Universe measurements as phase-dependent observations of the same holonomic constraints. Furthermore, we demonstrate that the fine-structure constant emerges as a phase-dependent identity linked to the kinematic expansion factor, suggesting a deep coupling between fundamental physical constants and the underlying manifold geometry. This model renders the thermal isotropy of the cosmic background radiation a topological necessity and resolves the flatness problem through the intrinsic scale of the geometric embedding, offering a framework consistent with current empirical observations.