Abstract: We present a complete and robust framework for non-singular bouncing cosmology in a closed universe (k=+1), where the scalar field space is endowed with a regularized hyperbolic geometry. The field space metric is rigorously derived from fundamental physical principles: exponential suppression during contraction enabling the bounce mechanism, asymptotic saturation to unity during inflation preserving perturbative unitarity, and positive-definiteness ensuring ghost-freedom.

Abstract: We investigate a two-field cosmological model in a closed (k=+1) universe where the field space is endowed with a hyperbolic geometry. We demonstrate that the curvature of the field space introduces a kinetic coupling that exponentially suppresses the scalar field kinetic energy, allowing the spatial curvature to dominate and trigger a non-singular bounce. The model achieves a successful bounce at sub-Planckian energy densities and transitions naturally to an inflationary phase with observable predictions consistent with Planck data.