Cosmological Evolution as a Non-autonomous Chaotic System: From Riemann Zeta Zeros to the Time Drift of the Fine-Structure Constant

The distribution of the non-trivial zeros of the Riemann ζ function has long been known to follow the statistics of the Gaussian Unitary Ensemble (GUE), suggesting a deep connection between number theory and quantum chaotic systems. However, the underlying generative dynamical mechanism remains elusive. In this paper, we propose a novel perspective by modeling the generation of Riemann zeros as a Non-autonomous Logistic Map. We find that when the control parameter evolves according to a logarithmic decay law uₙ = uc - k/ln n (where k ≈ 12.73), the system reproduces statistical features that highly approximate GUE while retaining a deterministic dynamical structure.Based on this model, we interpret the iteration step n as quantized cosmic evolution time (Planck time steps). The model predicts that the fundamental physical constants of the universe are not absolute constants but undergo extremely minute drifts scaling with 1/ln n. We compared the theoretical drift predicted by our model with observational data from high-redshift quasar absorption spectra (Webb et al.) and found remarkable consistency. This result not only provides a theoretical explanation for the "time variation of the fine-structure constant" but also supports Einstein's conjecture regarding the determinism of the underlying physical world, suggesting that macroscopic quantum randomness may originate from finite-precision chaotic computations at the Planck scale.