Testing the cosmic distance duality relation with baryon acoustic oscillations and supernovae data

One of the most fundamental relationships in modern cosmology is the cosmic distance duality relation (CDDR), which describes the relationship between the angular diameter distance ( DA D A ) and the luminosity distance ( DL D L ), and is expressed as η (z)=DL(z)(1+z)⁻²/DA(z)=1 η ( z ) = D L ( z ) ( 1 + z ) - 2 / D A ( z ) = 1 . In this work, we conduct a comprehensive test of the CDDR by combining baryon acoustic oscillation (BAO) data from the SDSS and DESI surveys with type Ia supernova (SN) data from PantheonPlus and DESY5. We utilize an artificial neural network approach to match the SN and BAO data at the same redshift. To explore potential violations of the CDDR, we consider three different parameterizations: (i) η (z)=1+η ₀z η ( z ) = 1 + η 0 z ; (ii) η (z)=1+η ₀z/(1+z) η ( z ) = 1 + η 0 z / ( 1 + z ) ; (iii) η (z)=1+η ₀ln (1+z) η ( z ) = 1 + η 0 ln ( 1 + z ) . Our results indicate that the calibration of the SN absolute magnitude MB M B plays a crucial role in testing potential deviations from the CDDR, as there exists a significant negative correlation between η ₀ η 0 and MB M B