发表机构
School of Physics and Technology, Wuhan University（武汉大学物理科学与技术学院）
机构由 AI 辅助整理，请以论文原文为准。AI 中文总结
本文用高斯过程和人工神经网络非参数重建宇宙距离对偶关系，检验其是否成立；结果无显著偏离，观测到的信号与$H_0$张力和$M_B$系统效应相关，而非真实违反。
AI 中文摘要
宇宙距离对偶关系（CDDR），即$D_L(z)(1+z)^{-2}/D_A(z) \equiv 1$，是现代宇宙学中将光度距离$D_L$与角直径距离$D_A$联系起来的基本关系。我们定义$\eta(z) \equiv D_L(z)(1+z)^{-2}/D_A(z)$，并使用两种独立的非参数方法——高斯过程（GP）和人工神经网络（ANN）——在$0 < z < 2.5$范围内重建相关量。具体而言，我们从三个不同的Ia型超新星（SNe Ia）汇编（PantheonPlus、Union3和DES-Dovekie）重建$D_L$，从SDSS和DESI重建重子声学振荡距离比$D_M/D_H$，以及从宇宙计时器（CC）数据重建哈勃函数$H(z)$。我们的CDDR检验既独立于宇宙学模型，也独立于声视界$r_d$校准，因为$D_M/D_H$自然地消去了$r_d$。我们通过对超参数进行完全贝叶斯边际化，使GP重建对均值函数和核函数的选择不敏感，并以ANN作为交叉检验，揭示数据稀疏性对后者的影响。我们的结果显示，没有超过$2\sigma$的显著CDDR偏离，对于CC+BAO+DES-Dovekie组合，在大部分红移范围内偏离保持在$1\sigma$以内。由于$r_d$已被消去，改变唯一剩余的外部参数$M_B$会通过$M_B$-$H_0$简并系统地移动$\eta(z)$，这表明观测到的$\eta\neq1$信号与数据集之间的$H_0$张力密切相关，且很可能由$M_B$系统效应驱动，而非真正的CDDR违反。未来高质量的CC、BAO和SNe Ia数据——无论是改进$M_B$校准还是采用无$M_B$的距离测量——对于扩展这种免校准方法至关重要。
英文摘要
The cosmic distance duality relation (CDDR), $D_L(z)(1+z)^{-2}/D_A(z) \equiv 1$, is a fundamental relation in modern cosmology linking luminosity distance $D_L$ and angular diameter distance $D_A$. We define $η(z) \equiv D_L(z)(1+z)^{-2}/D_A(z)$ 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 (SNe$~$Ia) 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 $η\neq1$ 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 SNe$~$Ia data$-$with either improved $M_B$ calibration or $M_B$-free distance measurements$-$will be essential for extending this calibration-free approach.
Comments11 pages,6 figures, 3 tables
