Theoretical Predictions and Observational Comparisons at the Cosmological Scale — Dark Energy, Gravitational Waves, and Inflation in the Order Parameter Spacetime Theory

The Order Parameter Spacetime Theory yields four testable predictions at the cosmological scale: (1) dark energy as the infrared behavior of the ground-state quantum mutual information background, with w(z) evolving with redshift and recently crossing −1; (2) the Hubble tension as the cumulative effect of the cosmological evolution of the information dissipation tensor; (3) Mach-force-driven inflation, with the tensor-to-scalar ratio r satisfying a scaling relation with the critical exponent; (4) polarization-dependent attenuation of gravitational waves. This paper systematically compares these four predictions with publicly available DESI DR2 BAO, Planck 2018 CMB, Pantheon+ supernova, and SH0ES data. The joint analysis of DESI DR2, Planck, and Pantheon+ shows w(z) may have crossed −1 with >4σ significance, qualitatively consistent with the theory's dynamic dark energy prediction. The 5σ Hubble tension between Planck and SH0ES is interpreted as the cumulative effect of information dissipation. Under a power-law assumption, quantitative connections exist among the four predictions. If confirmed by future data (Euclid, CMB-S4, Einstein Telescope), the theory will receive experimental corroboration at the cosmological scale.