The Completed SDSS-IV extended Baryon Oscillation Spectroscopic Survey: measurement of the BAO and growth rate of structure of the luminous red galaxy sample from the anisotropic correlation function between redshifts 0.6 and 1

TL;DR

This work leverages the configuration-space anisotropic clustering of the completed SDSS-IV eBOSS LRG sample (0.6<z<1, $z_{\rm eff}=0.698$) to jointly constrain geometric distances $D_M(z)/r_d$ and $D_H(z)/r_d$ and the growth rate $f\sigma_8(z)$ via BAO and RSD, using a reconstruction-enhanced BAO analysis and two independent RSD models (CLPT-GS and TNS). The analysis is validated with realistic mocks, and a consensus combination across configuration and Fourier spaces yields $D_M/r_d=17.65\pm0.30$, $D_H/r_d=19.77\pm0.47$, and $f\sigma_8=0.473\pm0.044$ at $z_{\rm eff}=0.698$, with systematic errors explicitly quantified. The results are consistent with a flat $\Lambda$CDM model under General Relativity and improve constraints relative to previous DR14/DR12 measurements, while highlighting the importance of accurately modeling systematics for future surveys. The methodology, including the consensus pipeline and robustness checks, provides a state-of-the-art framework for extracting cosmology from large-scale structure in upcoming surveys such as DESI and Euclid.

Abstract

We present the cosmological analysis of the configuration-space anisotropic clustering in the completed Sloan Digital Sky Survey IV (SDSS-IV) extended Baryon Oscillation Spectroscopic Survey (eBOSS) DR16 galaxy sample. This sample consists of luminous red galaxies (LRGs) spanning the redshift range $0.6 < z < 1$, at an effective redshift of $z_{\rm eff}=0.698$. It combines 174 816 eBOSS LRGs and 202 642 BOSS CMASS galaxies. We extract and model the baryon acoustic oscillations (BAO) and redshift-space distortions (RSD) features from the galaxy two-point correlation function to infer geometrical and dynamical cosmological constraints. The adopted methodology is extensively tested on a set of realistic simulations. The correlations between the inferred parameters from the BAO and full-shape correlation function analyses are estimated. This allows us to derive joint constraints on the three cosmological parameter combinations: $D_M(z)/r_d$, $D_H(z)/r_d$ and $fσ_8(z)$, where $D_M$ is the comoving angular diameter distance, $D_H$ is Hubble distance, $r_d$ is the comoving BAO scale, $f$ is the linear growth rate of structure, and $σ_8$ is the amplitude of linear matter perturbations. After combining the results with those from the parallel power spectrum analysis of Gil-Marin et al. 2020, we obtain the constraints: $D_M/r_d = 17.65 \pm 0.30$, $D_H/r_d = 19.77 \pm 0.47$, $fσ_8 = 0.473 \pm 0.044$. These measurements are consistent with a flat $Λ$CDM model with standard gravity.

Figures (21)

• Figure 1: The observed number density of eBOSS LRGs (dashed curve), BOSS CMASS galaxies (dotted curve), and combined CMASS+LRG sample galaxies (solid curve) at $0.6<z<1$. This combines NGC and SGC fields.
• Figure 2: Anisotropic two-point correlation function of eBOSS LRG+CMASS galaxies at $0.6<z<1$. The left (right) panel shows the pre-reconstruction (post-reconstruction) two-point correlation function in bins of $r_\perp$ and $r_\parallel$. Bins of size $1.25~h^{-1}~$Mpc and a bi-cubic spline interpolation have been used to produce the contours.
• Figure 3: Multipoles of the correlation function of data compared to the mock catalogs. The data is the combined eBOSS LRG + CMASS (NGC+SGC) samples and the mocks are the average multipoles of 1000 EZmocks realisations (solid line), 84 Nseries realisations (dashed line) and 27 MockChallenge mocks populated with L11 HOD model (dotted lines). Top panels show the monopole, quadrupole and hexadecapole of the pre-reconstruction samples while bottom panels show the same for the post-reconstruction case.
• Figure 4: Impact of choice of fiducial cosmology in the recovered values of $\alpha_\parallel$ and $\alpha_\perp$ from the stacks of 1000 multipoles from the EZmocks (blue) and 84 Nseries mocks (orange), for pre- (top panels) and post- (bottom panels) reconstruction. Associated error bars correspond to the error on the mean of the mocks. The gray shaded areas correspond to one per cent errors. For comparison, the error on real data is near 1.9 per cent for $\alpha_\perp$ and 2.6 per cent for $\alpha_\parallel$ in the post-reconstruction case.
• Figure 5: Distribution of dilation parameters $\alpha_\perp$ and $\alpha_\parallel$ and its estimated errors for pre and post reconstruction EZmock catalogs with systematic effects. The color scale indicates the difference in $\chi^2$ values between a model with and without BAO peak. The red stars shows results with real data. There is a known mismatch in the BAO peak amplitude between data and EZmocks causing the accuracy of the data point to be slightly smaller than the error distribution in the EZmocks (see Section \ref{['sec:mocks_description']}).