Growth rate measurements from a joint analysis of the large-scale galaxy clustering in Fourier and configuration space

TL;DR

This work develops and validates a joint configuration- and Fourier-space RSD analysis within a Lagrangian EFTofLSS framework to extract growth information from large-scale structure. It compares Gaussian-consensus and joint-space consensus methods, validating them on AbacusSummit N-body mocks and EZmocks, and applies them to the BOSS+eBOSS LRG data. The joint-space approach, especially JS$_{\mathrm{sep}}$, yields tight, consistent constraints on $q_\parallel$, $q_\perp$, and $f\sigma_8$, e.g., $f\sigma_8 = 0.463 \pm 0.052$, in agreement with official DR16 results while highlighting the importance of covariance treatment. Overall, the study demonstrates that combining configuration- and Fourier-space clustering with robust priors and covariance handling improves robustness against systematics and provides precise growth-rate measurements for current and future surveys.

Abstract

In this work, we test a framework to perform the analysis of redshift-space distortions simultaneously in configuration and Fourier space. We test our methods with the AbacusSummit suite of N-body simulations as well as a more numerous set of approximate EZmocks, reproducing the sample of luminous red galaxies of from the Baryon Oscillation Spectroscopic Survey (BOSS) and its extension (eBOSS). Our clustering models are based on the effective field theory of large-scale structures in a Lagrangian frame, used in the latest results from the Dark Energy Spectroscopic Instrument. We perform a template type of analysis, including dilation parameters and the slope parameter from the ShapeFit framework. We find that the joint space inference yields unbiased and robust constraints on simulated datasets, consistent with results from individual spaces or previous methods to obtain consensus results. Our joint space analysis on the the BOSS+eBOSS LRG sample obtains $ fσ_8 = 0.463 \pm 0.052 $, in good agreement with the official 2020 results.

Figures (12)

• Figure 1: Configuration space RSD results from fits to the average clustering of 25 LRG cubic-box n-body simulations as a function of the minimum separation scale, $r_\mathrm{{min}}$. Best-fit values of $q_\parallel$, $q_\perp$, $df$ and $dm$ are compared to their expected values in the top panels. The mid panel shows the reduced chi-squared ${}_r\chi^2$, and the bottom three panels display estimated uncertainties $\sigma_{q_\parallel}$, $\sigma_{q_\perp}$, $\sigma_{d f}$ and $\sigma_{d m}$. Filled markers represent the baseline fit, while empty markers indicate fits that include the additional ShapeFit parameter $m$.
• Figure 2: Same as Figure \ref{['fig:scale_rmin']} but for Fourier space (FS, red circles) and the joint space analyses (JS and JS$_\mathrm{sep}$, grey circles and green squares respectively). For reference, CS results for $r_\mathrm{{min}} = 30h^{-1}\,\text{Mpc}$ are shown in blue.
• Figure 3: Fourier space (FS) power spectrum multipoles (left panel) and correlation function (CS) multipoles (right panel) with their best-fit models. We consider the monopole (blue), quadrupole (orange) and hexadecapole (green) in both spaces. The three bottom panels show the normalized residuals and the shaded areas correspond to $2\sigma$. The best-fit model of FS and CS are shown in solid lines while joint-space $\mathrm{JS}_\mathrm{sep}$ model is represented with a dashed-line.
• Figure 4: Likelihood posterior ($1\sigma$-$2\sigma$) for FS (red), CS (blue), and JS (grey) obtained from fits to the average of the 25 LRG CubicBox mocks. JS contours without the cross covariance (labelled "w/o crosscov") are displayed in dashed-grey. The dotted black lines represent the expected values. Results are shown for $k_{\text{max}} = 0.20 \, h\,\text{Mpc}^{-1}$ and $r_{\text{min}} = 30 \, h^{-1}\,\text{Mpc}$.
• Figure 5: Contours of 68 an 95 per cent of the posterior distributions for FS (red), CS (blue), $\mathrm{JS}_\mathrm{sep}$ (green), and GA (orange), derived from fits to the average clustering of 25 LRG cubic-box mocks from N-body simulations.