In this paper, we test the cosmic distance duality relation (CDDR), as required by the Etherington reciprocity theorem, which connects the angular diameter distance and the luminosity distance via the relation \ (D ₋ (z) = D ₀ (z) (1+z) ² \). Our analysis is based on the latest baryon acoustic oscillation (BAO) measurements provided by the Dark Energy Survey (DES), the Baryon Oscillation Spectroscopic Survey (BOSS) /Extended BOSS (eBOSS), and the Dark Energy Spectroscopic Instrument (DESI) surveys. Specifically, an unbiased test of the CDDR is performed through a novel, model-independent method inspired by the two-point diagnostic approach, with DES-SN5YR and Pantheon type Ia supernova (SN Ia) sample reconstructed using the Artificial Neural Network (ANN) technique. This methodology effectively eliminates all nuisance parameters, including the sound horizon scale \ (r ₃ \) from BAO and the absolute magnitude \ (M ₁ \) from SN Ia. A set of \ (N-1 \) independent CDDR ratios \ (η₈₉ \) are constructed for statistical analysis. At the current observational level, no significant deviation from the CDDR is observed at low redshifts, whereas we find positive evidence (>2σ C. L. ) of deviation from the CDDR at two high redshifts (z=2. 33 and z=2. 334). Therefore, our results confirm that the BAO measurement provides a powerful tool to test such fundamental relation in modern cosmology.
Wang et al. (Sun,) studied this question.
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