Testing the Distance Duality Relation with Cosmological Observations at high Redshift using Artificial Neural Network
Yukang Xie, Yang Liu, Puxun Wu, Xiangyun Fu, Nan Liang
TL;DR
This paper tests the cosmic Distance Duality Relation (DDR), η(z)=1, in a model-independent way at high redshift by reconstructing $D_L(z)$ from Pantheon+ SN Ia and $D_A(z)$ from DESI DR2 BAO and strong lensing data using an artificial neural network (ANN) framework. It employs two DDR parameterizations, η(z)=1+η_0 z and η(z)=1+η_0 z/(1+z), and calibrates the SN absolute magnitude with two priors, $M_B^{\rm SH0ES}$ and $M_B^{\rm M24}$, to explore potential departures from the standard DDR. The ANN reconstructs $m(z)$ for $0.01<z\le1.4$ and $\mu(z)$ for $z>1.4$, combining a χ^2 term with a KL-divergence loss and using full-batch training with the SiLU activation; the analysis shows DDR consistent with the null within $\sim1$–$2\sigma$ for most data combinations, with mild tensions depending on the SGL sample (C19* vs A20*) and the SN calibration. The work demonstrates a robust, model-independent DDR test leveraging high-redshift probes and outlines a path toward sub-percent precision DDR tests with upcoming surveys such as LSST, Euclid, SKA, and the Einstein Telescope.
Abstract
The cosmic Distance Duality Relation (DDR) is a fundamental prediction of metric gravity under photon number conservation. In this work, we perform a model-independent test of the DDR using Pantheon+ type Ia supernovae (SN Ia), \emph{Fermi} gamma-ray bursts (GRBs) with the FULL and GOLD samples, the Dark Energy Spectroscopic Instrument (DESI) Data Release 2 (DR2) baryon acoustic oscillation (BAO) measurements, and the galaxy-scale strong gravitational lensing (SGL) system samples at high redshift $0.01 < z \lesssim 8$ using an artificial neural network (ANN) approach. Our results show that the standard DDR is consistent with cosmological observations at high redshift within the $\sim 2 σ$ confidence level.