Distance Duality Violation in DESI BAO Data: A Baryon-Fraction Parameterization with a Single Free Parameter

The Temporal Accumulation Hypothesis (TAH) proposes that elapsed cosmic time leaves a measurable imprint on the fabric of spacetime — a temporal substrate that accumulates differently for photons and matter. Photons, traveling at c since the Big Bang, have accumulated the maximum amount of this substrate, while matter, moving at v << c, has accumulated less. This difference means that distances measured using matter-based probes (such as Baryon Acoustic Oscillations) are not identical to distances measured using photon-based probes (such as Type Ia supernovae).

We quantify this with a redshift-dependent function η(z) = 1 − (Ω_b/Ω_m)² · exp(−z/z_s), where the amplitude ε = (f_b)² = 0.0244 is derived from the Planck baryon fraction — not fitted to BAO data — leaving a single free parameter z_s = 1.28. Using the CAMB Boltzmann solver and DESI DR1 BAO measurements, we find ΔBIC = −10 (strong preference over ΛCDM), χ² = 12.38 on 7 data points, and a predicted H₀ = 69.71 km/s/Mpc. The model resolves the Hubble tension as a density-dependent bias rather than new physics in the expansion history.

Crucially, applying the same modification to Pantheon+ Type Ia supernovae worsens the fit (ΔAIC = +2.1), confirming that the effect is specific to matter-based distance measures — exactly as TAH predicts. Eleven independent validation tests yield a combined significance of 6.4σ against the null hypothesis.