Unified age of the universe Theory vs Hubble tension Friedman equations and "cosmic wardrobe"

Author's note: Sensitivity analysis update: Stability verified for Omega_m=0.29 and R=59.2 Gly. Improved graphical labels for technical readability. Based on the Friedmann equations derived from Einstein's field theory, this paper presents the Unified Age Theory (UAT), proposing a spatially closed universe (k =+1). We demonstrate that the cosmic age t0 acts as a fundamental physical invariant, while the cosmic radius R and the expansion rate 𝐻0 function as adaptive geometric parameters. By liberating the FLRW metric from the zero-curvature constraint, we identify a stable geometric continuum. For the standard Planck density ( ), the model yields an equilibrium point at 𝐻0 ≈ 70.1 km/s/Mpc and a cosmic radius of 𝑅 =40.1 Gly , ( ≈ 13.8 Gyr). Furthermore, sensitivity analysis shows that for a matter density of (aligned with DES observations), the model identifies a solution at 𝐻0 ≈ 68.5 km/s/Mpc and 𝑅 = 59.2 Gly, providing the necessary temporal room ( ≈ 14.5 Gyr) for the oldest stellar objects. Our solution effectively resolves the Hubble tension by transforming it from a measurement discrepancy into a predictable property of a closed, non-Euclidean geometry. The UAT operates without any ad-hoc parameters.