Model-Agnostic Cosmological Inference with SDSS-IV eBOSS: Simultaneous Probing for Background and Perturbed Universe

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.