Testing the cosmic distance duality relation with Type Ia supernova and transverse BAO measurements

In this work, we test the cosmic distance duality relation (CDDR) by comparing the angular diameter distance (ADD) derived from the transverse Baryon Acoustic Oscillations (BAO) data with the luminosity distance (LD) from the Pantheon type Ia supernova (SNIa) sample. The binning method and Gaussian process are employed to match ADD data with LD data at the same redshift. First, we use nonparametric and parametric methods to investigate the impact of the specific prior values of the absolute magnitude $M_{\rm B}$ from SNIa observations and the sound horizon scale $r_{\rm s}$ from transverse BAO measurements on the CDDR tests. The results obtained from the parametric and non-parametric methods indicate that specific prior values of $M_{\rm B}$ and $r_{\rm s}$ lead to significant biases on the CDDR test. Then, to avoid these biases, we propose a method independent of $M_{\rm B}$ and $r_{\rm s}$ to test CDDR by considering the fiducial value of $\kappa\equiv10^{M_{\rm B} \over 5}r_{\rm s}$ as a nuisance parameter and then marginalizing its influence with a flat prior in the analysis. No violation of the CDDR is found, and the transverse BAO measurement can be used as a powerful tool to verify the validity of CDDR in the cosmological-model-independent method.