From Static Vacuum to Cosmic Expansion: Dynamics of the Compact S³ Universe

This work belongs to the Spectral Bifurcation Cosmology (SBC) series. Building on the static vacuum framework established in Series I, we investigate the dynamical evolution of a closed spatial manifold with compact $S^3$ geometry. We demonstrate how perturbation of the static vacuum triggers cosmic expansion without manually introducing an inflaton field. The model naturally incorporates topological effects and yields testable cosmological predictions, including features in the cosmic microwave background and constraints on late-time cosmic dynamics. The fully geometric construction contains no free tuning parameters. Further extensions covering particle physics and fundamental constants are discussed in subsequent companion papers of the SBC series.