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

TL;DR

This work tests the cosmic distance duality relation (CDDR), which links luminosity and angular-diameter distances via $d_L(z)=d_A(z)(1+z)^2$, by combining HII-galaxy distances with 2D, 3D BAO measurements including DESI DR2. Distances are reconstructed in a model-independent way using an Artificial Neural Network to obtain $d_L(z)$ at BAO redshifts, while $d_A(z)$ enters through BAO observables; the analysis explores four parameterizations of $(z)$ and marginalizes over the sound horizon $r_d$. Across 2D-BAO, 3D-BAO, and 3D-DESI data, the inferred $1$ values are all consistent with zero within 68% confidence, indicating no significant deviation from the standard CDDR; tensions between BAO types do not materially affect the results, though uncertainties remain large due to the $L-\sigma$ scatter and limited HIIGx samples. The ANN-based reconstruction enables CDDR constraints at redshifts beyond those probed by Type Ia supernovae, reinforcing the CDDR and showcasing a robust, model-independent framework for combining heterogeneous distance probes in cosmology.

Abstract

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.

Figures (3)

• Figure 1: The 2D-BAO, 3D-BAO and 3D-DESI measurements of $\theta(z)=r_d/d_{M}(z)$. The grey line corresponds to the theoretical values of $\theta(z)$ from the $\Lambda$CDM model with $\Omega_{m} = 0.3$ and $H_0 = 70$ km/s/Mpc
• Figure 2: The observed values of $\log d_{L,\mathrm{HII}}(z)$ from HII galaxy measurements are shown as cyan data points, with error bars representing the 68% confidence level. The red line represents the reconstructed function, and the pink shaded region indicates the 68% confidence level obtained using the ANN method. The black line corresponds to the theoretical prediction of $\log d_{L,\mathrm{HII}}(z)$ from the $\Lambda$CDM model with $\Omega_{m} = 0.3$ and $H_0 = 70$ km/s/Mpc
• Figure 3: The normalized posterior distributions of $\eta$ obtained from HII galaxy data combined with 2D-BAO, 3D-BAO, and 3D-DESI BAO datasets. The vertical dashed line at $\eta = 0$ marks the value predicted by the standard CDDR.