Here we explore certain subtle features imprinted in data from the completed Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) as a combined probe for the background and perturbed Universe. We reconstruct the baryon Acoustic Oscillation (BAO) and Redshift Space Distortion (RSD) observables as functions of redshift, using measurements from SDSS alone. We apply the Multi-Task Gaussian Process (MTGP) framework to model the interdependencies of cosmological observables $D_M(z)/r_d$, $D_H(z)/r_d$, and $f\sigma_8(z)$, and track their evolution across different redshifts. Subsequently, we obtain constrained three-dimensional phase space containing $D_M(z)/r_d$, $D_H(z)/r_d$, and $f\sigma_8(z)$ at different redshifts probed by the SDSS-IV eBOSS survey. Furthermore, assuming the $\Lambda$CDM model, we obtain constraints on model parameters $\Omega_{m}$, $H_{0}r_{d}$, $\sigma_{8}$ and $S_{8}$ at each redshift probed by SDSS-IV eBOSS. This indicates redshift-dependent trends in $H_0$, $\Omega_m$, $\sigma_8$ and $S_8$ in the $\Lambda$CDM model, suggesting a possible inconsistency in the $\Lambda$CDM model. Ours is a template for model-independent extraction of information for both background and perturbed Universe using a single galaxy survey taking into account all the existing correlations between background and perturbed observables and this can be easily extended to future DESI-3YR as well as Euclid results.

翻译：本文利用已完成的斯隆数字巡天第四期（SDSS-IV）扩展重子振荡光谱巡天（eBOSS）数据中蕴含的某些精细特征，将其作为背景宇宙与扰动宇宙的联合探针进行研究。我们仅基于SDSS的测量数据，重构了作为红移函数的重子声学振荡（BAO）与红移空间畸变（RSD）可观测量。应用多任务高斯过程（MTGP）框架对宇宙学可观测量 $D_M(z)/r_d$、$D_H(z)/r_d$ 和 $f\sigma_8(z)$ 之间的相互依赖性进行建模，并追踪它们在不同红移处的演化。随后，我们获得了包含SDSS-IV eBOSS巡天所探测的不同红移处 $D_M(z)/r_d$、$D_H(z)/r_d$ 和 $f\sigma_8(z)$ 的受限三维相空间。此外，在假设 $\Lambda$CDM 模型的前提下，我们得到了SDSS-IV eBOSS在每个探测红移处对模型参数 $\Omega_{m}$、$H_{0}r_{d}$、$\sigma_{8}$ 和 $S_{8}$ 的约束。这表明在 $\Lambda$CDM 模型中 $H_0$、$\Omega_m$、$\sigma_8$ 和 $S_8$ 存在红移依赖的趋势，暗示了 $\Lambda$CDM 模型可能存在不一致性。我们的工作为利用单一星系巡天、同时考虑背景与扰动可观测量之间所有现有关联性、以模型无关的方式提取背景宇宙与扰动宇宙信息提供了一个模板，此方法可轻松扩展应用于未来的DESI-3YR以及欧几里得（Euclid）巡天结果。