Sound-Horizon-Independent Test of Cosmic Distance Duality Relation Using Artificial Neural Networks and Gaussian Processes
Abstract
The cosmic distance duality relation (CDDR), DL(z)(1+z)−2/DA(z) ≡ 1, is a fundamental relation in modern cosmology linking luminosity distance DL and angular diameter distance DA. We define η(z) ≡ DL(z)(1+z)−2/DA(z) and reconstruct the relevant quantities over 0 < z < 2.5 using two independent non-parametric methods: Gaussian processes (GP) and artificial neural networks (ANN). Specifically, we reconstruct DL from three different Type Ia supernovae (SNeIa) compilations (PantheonPlus, Union3, and DES-Dovekie), the baryon acoustic oscillation distance ratio DM/DH from SDSS and DESI, and the Hubble function H(z) from cosmic chronometer (CC) data. Our CDDR test is independent of both the cosmological model and the sound horizon rd calibration, as DM/DH naturally eliminates rd. We render our GP reconstructions insensitive to mean-function and kernel choices via full Bayesian marginalization over hyperparameters, with ANN as a cross-check−revealing the impact of data sparsity on the latter. Our results show no significant deviation from the CDDR exceeding 2σ, and for the CC+BAO+DES-Dovekie combination it remains within 1σ over most of the redshift range. With rd eliminated, varying the only remaining external parameter MB systematically shifts η(z) through the MB-H0 degeneracy, indicating that the observed η≠1 signal is closely tied to H0 tension among datasets and is likely driven by MB systematics rather than a true CDDR violation. Future high-quality CC, BAO, and SNeIa data−with either improved MB calibration or MB-free distance measurements−will be essential for extending this calibration-free approach.
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BibTeX
@misc{jiang2026soundhorizonindependent,
title = {{Sound-Horizon-Independent Test of Cosmic Distance Duality Relation Using Artificial Neural Networks and Gaussian Processes}},
author = {Bo-Hao Jiang and Guo-Jian Wang and Tao Yang},
howpublished = {arXiv},
year = {2026},
month = sep,
doi = {10.48550/arxiv.2609.24203},
eprint = {2609.24203},
archivePrefix = {arXiv},
url = {https://arxiv.org/abs/2609.24203},
}
RIS
TY - UNPB
TI - Sound-Horizon-Independent Test of Cosmic Distance Duality Relation Using Artificial Neural Networks and Gaussian Processes
AU - Bo-Hao Jiang
AU - Guo-Jian Wang
AU - Tao Yang
PY - 2026
DA - 2026/09/21
PB - arXiv
DO - 10.48550/arxiv.2609.24203
UR - https://arxiv.org/abs/2609.24203
AB - The cosmic distance duality relation (CDDR), D_L(z)(1+z)^−2/D_A(z) ≡ 1, is a fundamental relation in modern cosmology linking luminosity distance D_L and angular diameter distance D_A. We define η(z) ≡ D_L(z)(1+z)^−2/D_A(z) and reconstruct the relevant quantities over 0 < z < 2.5 using two independent non-parametric methods: Gaussian processes (GP) and artificial neural networks (ANN). Specifically, we reconstruct D_L from three different Type Ia supernovae (SNeIa) compilations (PantheonPlus, Union3, and DES-Dovekie), the baryon acoustic oscillation distance ratio D_M/D_H from SDSS and DESI, and the Hubble function H(z) from cosmic chronometer (CC) data. Our CDDR test is independent of both the cosmological model and the sound horizon r_d calibration, as D_M/D_H naturally eliminates r_d. We render our GP reconstructions insensitive to mean-function and kernel choices via full Bayesian marginalization over hyperparameters, with ANN as a cross-check−revealing the impact of data sparsity on the latter. Our results show no significant deviation from the CDDR exceeding 2σ, and for the CC+BAO+DES-Dovekie combination it remains within 1σ over most of the redshift range. With r_d eliminated, varying the only remaining external parameter M_B systematically shifts η(z) through the M_B-H_0 degeneracy, indicating that the observed η≠1 signal is closely tied to H_0 tension among datasets and is likely driven by M_B systematics rather than a true CDDR violation. Future high-quality CC, BAO, and SNeIa data−with either improved M_B calibration or M_B-free distance measurements−will be essential for extending this calibration-free approach.
ER -