Testing the Cosmic Distance Duality Relation with Neural Kernel Gaussian Process Regression

Abstract: In this work, we test the cosmic distance duality relation (CDDR) by combining Pantheon+ Type Ia supernova (SNe Ia) data and DESI DR2 baryon acoustic oscillation (BAO) measurements. To resolve the redshift mismatch between the two datasets, we develop a new method called Neural Kernel Gaussian Process Regression (NKGPR), which uses two neural networks to simultaneously learn the mean and kernel functions of a Gaussian process. This approach improves upon traditional Gaussian process regression by mitigating trend mismatches and removing the need for manual kernel selection. We investigate possible deviations from the CDDR by adopting three parameterizations of the deviation function and constrain the model-independent parameter $\eta_0$ through a marginalized likelihood analysis. Our results show no significant departure from the expected relation, confirming the consistency of the CDDR within current observational uncertainties.