From UD Theory to Cosmology: A Rigorous Derivation of Spacetime Evolution

We derive the foundations of cosmology rigorously from the UD axioms. The cosmological principle is a derived consequence of the nature of U, not an independent assumption. The Hubble parameter is proven as a theorem—H = k · E/C—with the constant k identified as the eternal global expansion rate, calibrated from the local H₀ measurement. On the global scale, $E = C = 1/2$ eternally, giving Hglobal = k; on local scales, Hlocal(z) = k · E(z)/C(z) is always positive, guaranteeing eternal local expansion, though the rate varies with the local U-D competition. The fluctuation δ = E - C acquires a non-zero expectation value locally, driving the universe to choose U-dominated local configurations via unrestricted local dynamics; globally, δ = 0 is maintained by the corollary of Axiom 1, consistent with the eternal global equilibrium. The asymmetric equilibrium backgrounds between the spatial form S = Uᵤ + Ud and the material form M = Dd + Dᵤ directly imply that U expands unconditionally while D condenses conditionally. The apparent inflationary expansion is reinterpreted as a local and relative phenomenon: it occurs wherever E C locally, and persists in present-day cosmic voids, while regions of high matter density expand slowly or even contract locally. The universe originates from the breaking of a critical state devoid of space, time, and matter, not from a primordial singularity. Quantitative predictions that differ from standard ΛCDM are given. All derivations are self-contained.