The Relaxation of Cosmic Expansion: Resolving the Hubble Tension via Non-autonomous Chaotic Dynamics

The discrepancy between early-universe and late-universe measurements of the Hubble constant (H₀), known as the Hubble Tension, poses a significant challenge to the standard CDM model. In this paper, we propose a resolution based on the Cosmic Relaxation Hypothesis, which treats the universe not as a static Hamiltonian system but as a non-autonomous dynamical system undergoing "computational aging. " Governed by a logarithmic decay law uₙ 1/ n (derived from number-theoretic constraints), fundamental physical parameters undergo an intrinsic drift. By mapping observational data to a relaxation parameter = 1/ (t/t₏₋₀₍₂₊), we demonstrate that the apparently contradictory measurements from Planck (z 1100), TRGB (z 0, ancient stars), and SH0ES (z 0, young stars) align precisely on a single dynamical trajectory H (t) 1/ t. This unification resolves the tension without introducing exotic physics and predicts a "phantom-like" acceleration driven solely by system relaxation, ultimately leading to a "Computational Freeze" rather than a Big Rip.