Reconciling the Hubble Tension via the CURA Framework: A Dual-Constraint Analysis of Cosmic Age and Curvature

This version features results re-calibrated against the latest knowledges. Assuming the universe is governed by the Friedmann equations derived from Einstein’s field equations, our analysis shows it is closed with a cosmic radius 𝑅 ≈ 43 Gly. The proposed procedure, designated by the acronym CURA (Cosmic Unified Radius and Age), reveals fundamental geometric correlations that remain obscured within standard flat models.We show that while a density of 𝛀𝒎≈𝟎.𝟐𝟗𝟔 aligns with high local expansion rates reported by Riess et al. 𝑯𝟎= 𝟕𝟑.𝟔𝟒 km/s/Mpc at the cost of a younger universe (~13.27 Gyr), a lower density of 𝛀𝒎≈𝟎.𝟐𝟖𝟏 recovers an older universe (~13.88 Gyr) consistent with Planck’s resultsThis procedure identifies a fundamental reference baseline of 𝑯𝟎𝒓𝒆𝒇=𝟔𝟑.𝟔𝟎 km/s/Mpc, and an invariant curvature 𝛀𝐤=−𝟎.𝟎𝟗𝟓, and a These values, invariant for all considered Ω𝑚 within the model, are consistent with the Planck 2018 non-flat constraints (𝐻0=63.6−2.3+2.1 km/s/Mpc and Ω𝑘=−0.056−0.050+0.044 ). The invariant deceleration parameter is 𝒒=−𝟎.𝟓𝟒𝟖.