Interpreting large-scale redshift-space distortion measurements

TL;DR

This study interrogates the reliability of large-scale redshift-space distortion (RSD) analyses by identifying and modeling key systematics—sample geometry, nonlinear growth, and radial selection—using LasDamas mocks and SDSS DR7 LRG data. It develops a comprehensive framework combining plane-parallel linear theory with wide-angle, nonlinear, and AP effects, validating it against mocks and applying it to measure growth-related parameters (bσ8, fσ8) under GR and alternative growth prescriptions. The results show consistency with ΛCDM + GR within current uncertainties, while highlighting the importance of BAO damping and μ-distribution corrections and the relative insensitivity of AP degeneracies when strong geometry priors are included. The work provides a robust pathway for exploiting future, larger surveys (e.g., BOSS, Euclid) to constrain gravity and structure growth through large-scale RSD with careful treatment of observational and theoretical systematics.

Abstract

The simplest theory describing large-scale redshift-space distortions (RSD), based on linear theory and distant galaxies, depends on the growth of cosmological structure, suggesting that strong tests of General Relativity can be constructed from galaxy surveys. As data sets become larger and the expected constraints more precise, the extent to which the RSD follow the simple theory needs to be assessed in order that we do not introduce systematic errors into the tests by introducing inaccurate simplifying assumptions. We study the impact of the sample geometry, non-linear processes, and biases induced by our lack of understanding of the radial galaxy distribution on RSD measurements. Using LasDamas simulations of the Sloan Digital Sky Survey II (SDSS-II) Luminous Red Galaxy (LRG) data, these effects are shown to be important at the level of 20 per cent. Including them, we can accurately model the recovered clustering in these mock catalogues on scales 30 -- 200 Mpc/h. Applying this analysis to robustly measure parameters describing the growth history of the Universe from the SDSS-II data, gives $f(z=0.25)σ_8(z=0.25)=0.3512\pm0.0583$ and $f(z=0.37)σ_8(z=0.37)=0.4602\pm0.0378$ when no prior is imposed on the growth-rate, and the background geometry is assumed to follow a $Λ$CDM model with the WMAP + SNIa priors. The standard WMAP constrained $Λ$CDM model with General Relativity predicts $f(z=0.25)σ_8(z=0.25)=0.4260\pm0.0141$ and $f(z=0.37)σ_8(z=0.37)=0.4367\pm0.0136$, which is fully consistent with these measurements.

Figures (17)

• Figure 1: Histogram showing the redshift distribution of galaxies in the SDSS DR7 LRG catalog used in our analysis.
• Figure 2: Measurements of $\hat{\xi_\ell}(r)$ from SDSS DR7 LRGs in a redshift range $0.16<z<0.44$. The statistical error-bars were calculated as described in Section \ref{['sec:mocks']} and represent only the diagonal elements of the whole covariance matrix. The absence of lower error-bar on some measurements indicates that they are consistent with zero. Solid line shows a theoretical prediction with the shape corresponding to the best fit cosmology to current WMAP and SNIa measurements and the amplitude given by the best-fit values to the data.
• Figure 3: Measurements of $\hat{Q}(r)$ from SDSS DR7 LRGs in a redshift range $0.16<z<0.44$. Error-bars were calculated as described in Section \ref{['sec:mocks']} and show only the diagonal elements of statistical covariance matrix. Solid line shows a theoretical prediction with the shape corresponding to the best fit cosmology to current WMAP and SNIa measurements and the amplitude given by the best-fit values to the data.
• Figure 4: Radial distribution of galaxies in different random catalogs. Dashed line corresponds to the "shuffled" random catalog, which has radial distribution identical to that of data. Dashed line corresponds to "spline" random catalog and solid line corresponds to "proper" random catalog.
• Figure 5: Relative errors introduced in the measurement of the first two even Legendre momenta of the correlation function using different random catalog. The solid line shows statistical errors.