Directional Tests of the Cosmic Distance Duality Relation using Pantheon+ and BAO

Abstract

We present a model-independent test of anisotropy in the cosmic distance duality relation (CDDR), $D_L=(1+z)^2 D_A$, using the Pantheon+ type Ia supernova sample and baryon acoustic oscillation (BAO) data. The angular diameter distance is reconstructed via Gaussian Processes, enabling an estimate of $\eta(z)=D_L/[D_A(1+z)^2]$ without assuming a background cosmology. We also allow for a possible isotropic evolution, parameterized as $\eta(z)=1+\eta_1 z$, and find a redshift-dependent deviation whose significance depends on the assumed supernova calibration. Anisotropy is modeled through a dipole modulation and constrained using a full covariance-based likelihood. To assess statistical significance, we construct null realizations that preserve both the redshift distribution and the survey selection function. We find that the observed dipole amplitude is consistent with isotropic expectations and lies below the levels induced by statistical fluctuations and survey geometry. We obtain a robust 95\% upper bound $A_{95}=0.025$, stable across different supernova calibration choices. We find no evidence for intrinsic anisotropy in the CDDR. Our results highlight the importance of accounting for survey selection effects in anisotropy searches and provide a viable framework for testing directional deviations in cosmological relations.