On the Unified Geometric Origin of Gravity and Cosmological Expansion

This preprint proposes a conceptual framework in which gravity and cosmological expansion are jointly derived from the global topological closure of the universe — two consequences typically treated as independent problems. Assuming a compact, boundaryless spacetime manifold (∂ℳ = Ø) with a conserved global curvature budget (ℬ₀ = const.), the framework addresses why gravity must exist and what cosmological expansion means in a universe with no exterior. The Einstein field equations and FLRW formalism are preserved without modification; only their interpretation is revised. A minimal phenomenological extension parameterized by β yields logarithmic corrections to the Hubble relation, reducing to standard ΛCDM for β = 0, with small testable deviations detectable by Euclid and the Rubin Observatory. The proposal is presented as a foundational research program, not a completed derivation.