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 power spectrum between redshifts 0.6 and 1.0

TL;DR

This work presents a combined BAO and full-shape analysis of the DR16 CMASS+eBOSS LRG sample to measure $D_M/r_{\rm drag}$, $D_H/r_{\rm drag}$, and $f\sigma_8$ at $z_{\rm eff}=0.698$ using the anisotropic power spectrum. Reconstruction enhances BAO detection, and a comprehensive RSD/bias modelling framework (McDonald–Roy bias, TNS RSD, and 2-loop perturbation theory) is applied, with covariance validated by large ensembles of mocks. The resulting consensus constraints, $D_M/r_{\rm drag}=17.65\pm0.30$, $D_H/r_{\rm drag}=19.77\pm0.47$, and $f\sigma_8=0.473\pm0.044$, are in excellent agreement with flat $\Lambda$CDM and GR, representing the most precise late-time measurements in $0.6\le z\le1.0$. The study also provides a thorough systematic error budget and framework for combining Fourier and configuration-space results, strengthening the reliability of the cosmological interpretation and setting a benchmark for upcoming surveys.

Abstract

We analyse the clustering of the Sloan Digital Sky Survey IV extended Baryon Oscillation Spectroscopic Survey Data Release 16 luminous red galaxy sample (DR16 eBOSS LRG) in combination with the high redshift tail of the Sloan Digital Sky Survey III Baryon Oscillation Spectroscopic Survey Data Release 12 (DR12 BOSS CMASS). We measure the redshift space distortions (RSD) and also extract the longitudinal and transverse baryonic acoustic oscillation (BAO) scale from the anisotropic power spectrum signal inferred from 377,458 galaxies between redshifts 0.6 and 1.0, with effective redshift of $z_{\rm eff}=0.698$ and effective comoving volume of $2.72\,{\rm Gpc}^3$. After applying reconstruction we measure the BAO scale and infer $D_H(z_{\rm eff})/r_{\rm drag} = 19.30\pm 0.56$ and $D_M(z_{\rm eff})/r_{\rm drag} =17.86 \pm 0.37$. When we perform a redshift space distortions analysis on the pre-reconstructed catalogue on the monopole, quadrupole and hexadecapole we find, $D_H(z_{\rm eff})/r_{\rm drag} = 20.18\pm 0.78$, $D_M(z_{\rm eff})/r_{\rm drag} =17.49 \pm 0.52$ and $fσ_8(z_{\rm eff})=0.454\pm0.046$. We combine both sets of results along with the measurements in configuration space of \cite{LRG_corr} and report the following consensus values: $D_H(z_{\rm eff})/r_{\rm drag} = 19.77\pm 0.47$, $D_M(z_{\rm eff})/r_{\rm drag} = 17.65\pm 0.30$ and $fσ_8(z_{\rm eff})=0.473\pm 0.044$, which are in full agreement with the standard $Λ$CDM and GR predictions. These results represent the most precise measurements within the redshift range $0.6\leq z \leq 1.0$ and are the culmination of more than 8 years of SDSS observations.

Figures (26)

• Figure 1: Number density of objects with spectroscopic observations for DR12 BOSS CMASS LRGs (in blue) and DR16 eBOSS LRGs (in orange), for the NGC (solid lines) and SGC (dashed lines). In black is shown the addition of CMASS and eBOSS densities. Note that such additions only correspond to those regions with overlapping area between eBOSS and BOSS CMASS galaxies, which approximately correspond to the whole eBOSS LRG area. The effective redshift of the combined sample corresponds to $z_{\rm eff}=0.698$ according to the definition of Eq. \ref{['eq:zeff']}.
• Figure 2: Power spectrum multipoles measured from the DR16 CMASS+eBOSS LRG sample, monopole (orange symbols), quadrupole (green symbols) and hexadecapole (purple symbols). The filled and empty symbols correspond to measurements from the NGC and SGC, respectively. The empty symbols are displaced horizontally for visibility. The black dashed and dotted lines correspond to the clustering of the mean of the 1000 realisations of the EZmocks with all the systematics applied, for NGC and SGC, respectively. The amplitude mismatch, more evident for the monopole, is due to the effect of completeness on the normalisation factor of the power for data and mocks.
• Figure 3: DR16 CMASS+eBOSS LRG power spectrum measurements for the pre- (left panel) and post-reconstructed catalogue (right panel). The orange points display the power spectrum monopole and the green points the $\mu^2$-moment (see Eq. \ref{['eq:mu2moment']} for definition). The associated errors are drawn from the covariance of 1000 mocks and the black solid line represent the best-fitting solution (quoted in Table \ref{['table:BAOresults']} using the anisotropic templated at the fixed values of $\Sigma_\parallel=7.0\,\,h^{-1}\,{\rm Mpc}$ and $\Sigma_\perp=2.0\,\,h^{-1}\,{\rm Mpc}$ for post-recon and $\Sigma_\parallel=9.4\,\,h^{-1}\,{\rm Mpc}$ and $\Sigma_\perp=4.8\,\,h^{-1}\,{\rm Mpc}$ for pre-recon). The bottom sub-panels show the difference between model and measurement divided by the 1-$\sigma$ errors.
• Figure 4: Likelihood posterior for $1-$ and $2-\sigma$ contours (only statistical contribution), from the BAO type of analysis on the DR16 CMASS+eBOSS LRG data for the pre-reconstructed catalogues (in orange) and the post-reconstructed catalogues (in blue) in terms of $D_M(z_{\rm eff})/r_{\rm drag}$ and $D_H(z_{\rm eff})/r_{\rm drag}$ variables, at $z_{\rm eff}=0.698$. Results corresponding to the first two rows of Table \ref{['table:BAOresults']}.
• Figure 5: Power spectrum multipoles measured from the DR16 CMASS+eBOSS LRG sample (weight-averaged between NGC and SGC), monopole (circular orange symbols), quadrupole (square green symbols) and hexadecapole (triangle purple symbols), along with the error-bars predicted by the rms of the 1000 EZmocks. The solid and dashed black lines represent the FS best-fit model (weight-averaged between NGC and SGC) when the monopole and quadrupole only are fitting (black dashed lines) and when the hexadecapole is also used (black solid line). In the bottom sub-panel the differences between the measurement and the model, relative to the value of $1\sigma$ error-bar, are also displayed using the same colour notation. The results for the best-fitting parameters are reported in Table \ref{['tab:resultsPk']} for the narrow prior on the amplitude of shot noise, $0.5\leq A_{\rm noise} \leq 1.5$.