The impact of 2D and 3D BAO measurements on the Cosmic Distance Duality Relation with HII galaxies

The cosmic distance duality relation (CDDR) is a fundamental and practical condition in observational cosmology that connects the luminosity distance and angular diameter distance. Testing its validity offers a powerful tool to probe new physics beyond the standard cosmological model. In this work, for the first time, we present a novel consistency test of CDDR by combining HII galaxy data with a comprehensive set of Baryon Acoustic Oscillations (BAO) measurements. The BAO measurements include two-dimensional (2D) BAO and three-dimensional (3D) BAO from the Sloan Digital Sky Survey (SDSS), as well as the latest 3D BAO data from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2). We adopt four different parameterizations of the distance duality relation parameter, η(z), to investigate possible deviations and their evolution with cosmic time. To ensure accurate redshift matching across datasets, we reconstruct the distance measures through a model-independent Artificial Neural Network (ANN) approach. We find no significant deviation from the CDDR (less than 68% confidence level) among four parameterizations. Furthermore, our results show that the constraints on η(z) obtained separately from 2D and 3D BAO measurements are consistent at the 68% confidence level. This indicates that there is no significant tension between the two datasets under the four parameterizations considered. Our ANN reconstruction of HII galaxies could provide constraints on the CDDR at redshifts beyond the reach of Type Ia supernovae. Finally, the consistency of our results supports the standard CDDR and demonstrates the robustness of our analytical approach.