This work extends the Unified Dimensional Cohesion Theory (UDCT) v2.2 to photon propagation. We construct an effective geometric correction to luminosity distance using the same first-principles relaxation timescale τ = 1/H₀ derived from Hubble cosmology and S¹ compactification topology. For effective projection scales in the range of 800–1200 Mpc, the model increases luminosity distances by approximately 3.8–4.5% near z ≈ 1, corresponding to a 35–55% reduction in the Hubble tension while remaining broadly consistent with current Type Ia Supernova observations. Note: The cosmological extension presented in this work is constructed as an effective model. A rigorous derivation of the null geodesic correction from the underlying higher-dimensional geometry has not yet been completed. This paper builds upon UDCT v2.1 and v2.2, which focused on galactic dynamics.