From Nonparametric Distance Reconstruction to Testing the Etherington Relation and Cosmic Curvature Using 2D and 3D BAO Measurements

TL;DR

This work tests the cosmic distance duality relation (CDDR) and spatial curvature jointly by combining angular BAO distances with a non-parametric, Gaussian Process–reconstructed luminosity distance from Cosmic Chronometers. It systematically compares 2D, 3D, and DESI BAO measurements to assess potential tensions and their impact on η(z) and $Ω_{k0}$, while probing four parameterizations of η(z) to capture redshift evolution. The analysis demonstrates no statistically significant violation of the CDDR and finds $Ω_{k0}$ consistent with zero within 95–99% confidence, though mild dataset- and parameterization-dependent shifts occur due to degeneracies between η1 and $Ω_{k0}$. The DESI BAO results provide the strongest, most consistent support for a flat universe and the validity of the CDDR, with the BAO-type tensions contributing only subdominant effects given current data precision. Overall, the study delivers robust, model-independent constraints on cosmic curvature and the CDDR, highlighting the importance of dataset choice and priors while pointing toward future improvements from upcoming BAO and CC measurements.

Abstract

We present a joint test of cosmic curvature, $Ω_{k0}$, and the cosmic distance-duality relation (CDDR) using the Etherington relation, which connects the luminosity and angular diameter distances at the same redshift. In this work, we combine the angular diameter distance measurements from recent Baryon Acoustic Oscillation (BAO) observations with luminosity distances reconstructed from Cosmic Chronometers data of Hubble parameter $H(z)$ using a non-parametric technique, Gaussian Process. A key part of our analysis is the systematic comparison of different BAO measurements (2D BAO, 3D BAO, and 3D DESI BAO) to determine whether any potential tension between angular and anisotropic BAO data affects constraints on the distance duality parameter $η(z)$ and $Ω_{k0}$. We adopt four representative parameterizations of $η(z)$ to examine the correlation between $η(z)$ and $Ω_{k0}$. Our results show no evidence for violation of the CDDR, with $η(z)$ consistent with unity at the 99\% confidence level for all BAO datasets and parameterizations. In all scenarios, the best-fit values of $Ω_{k0}$ mildly favor a non-flat universe, although a spatially flat universe remains compatible at the 95\% confidence level. The constraints on $η_1$ and $Ω_{k0}$ indicate slight variations across different BAO datasets, but the discrepancies between the 2D and 3D BAO measurements do not introduce any significant bias, and no statistically meaningful tension is observed. Our work provides robust constraints on cosmic curvature and the validity of the CDDR based on non-parametric distance reconstruction.

Figures (5)

• Figure 1: Posterior distributions and 68% and 95% confidence levels for $\eta_1$ and $\Omega_{k0}$ corresponding to the parameterizations P1–P4. The results use 2D BAO measurements with different $H_0$ priors (GP, Planck, SH0ES), in direct correspondence with Table \ref{['tab_cddr_bao_2d_results']}. The dashed vertical lines indicate $\eta_1 = 0$ and $\Omega_{k0} = 0$, representing the standard cosmic distance duality relation and a spatially flat universe, respectively, to highlight potential deviations from these standard values.
• Figure 2: Posterior distributions and 68% and 95% confidence levels for $\eta_1$ and $\Omega_{k0}$ corresponding to the parameterizations P1–P4. The results use 3D BAO measurements with different $H_0$ priors (GP, Planck, SH0ES), in direct correspondence with Table \ref{['tab_cddr_bao_3d_results']}. The dashed vertical lines indicate $\eta_1 = 0$ and $\Omega_{k0} = 0$, representing the standard cosmic distance duality relation and a spatially flat universe, respectively, to highlight potential deviations from these standard values.
• Figure 3: Posterior distributions and 68% and 95% confidence levels for $\eta_1$ and $\Omega_{k0}$ corresponding to the parameterizations P1–P4. The results use DESI BAO measurements with different $H_0$ priors (GP, Planck, SH0ES), in direct correspondence with Table \ref{['tab_cddr_bao_desi_results']}. The dashed vertical lines indicate $\eta_1 = 0$ and $\Omega_{k0} = 0$, representing the standard cosmic distance duality relation and a spatially flat universe, respectively, to highlight potential deviations from these standard values.
• Figure 4: The whisker plots show the best-fit values and 68% confidence intervals for $\eta_1$ under three $H_0$ priors: GP, Planck, and SH0ES. Each horizontal row on the y-axis corresponds to a BAO dataset, labeled as 2D BAO, 3D BAO, and 3D DESI DR2. Different colors indicate the four parameterizations P1–P4, and the red dashed vertical line at $\eta_1 = 0$ represents the standard cosmic distance duality relation.
• Figure 5: The whisker plots show the best-fit values and 68% confidence intervals for $\Omega_{k0}$ under three $H_0$ priors: GP, Planck, and SH0ES. Each horizontal row on the y-axis corresponds to a BAO dataset, labeled as 2D BAO, 3D BAO, and 3D DESI DR2. Different colors indicate the four parameterizations P1–P4, and the red dashed vertical line at $\Omega_{k0}=0$ represents a spatially flat universe.