Validating the methodology for constraining the linear growth rate from clustering anisotropies

Abstract

Redshift-space clustering distortions provide one of the most powerful probes to test the gravity theory on the largest cosmological scales. In this paper we perform a systematic validation study of the state-of-the-art statistical methods currently used to constrain the linear growth rate from redshift-space distortions in the galaxy two-point correlation function. The numerical pipelines are tested on mock halo catalogues extracted from large N-body simulations of the standard cosmological framework, in the redshift range 0.5 z 2. We consider both the monopole and quadrupole multipole moments of the redshift-space two-point correlation function, as well as the radial and transverse clustering wedges, in the comoving scale range 10 < r[h −1 Mpc] < 55. Moreover, we investigate the impact of redshift measurement errors, up to δz ∼ 0.5%, which introduce spurious clustering anisotropies. We quantify the systematic uncertainties on the growth rate and linear bias measurements due to the assumptions in the redshiftspace distortion model. Considering both the dispersion model and two widely-used models based on perturbation theory, that is the Scoccimarro (2004) model and the Taruya et al. (2010) model, we find that the linear growth rate is underestimated by about 5 − 10% at z < 1, while limiting the analysis at larger scales, r > 30 h −1 Mpc, the discrepancy is reduced below 5%. At higher redshifts, we find instead an overall good agreement between measurements and model predictions. The Taruya et al. (2010) model is the one which performs better, with growth rate uncertainties below about 3%. The effect of redshift errors is degenerate with the one of small-scale random motions, and can be marginalised over in the statistical analysis, not introducing any statistically significant bias in the linear growth constraints, especially at z ≥ 1.

C$^3$-Cluster Clustering Cosmology I. New constraints on the cosmic growth rate at z~0.3 from redshift-space clustering anisotropies

“…We note that according to García-Farieta et al (2020) the systematic uncertainty due to the assumed TNS model assumptions is of the order of 5% at the scales and redshifts considered, which is reasonably low for the current work. Improved RSD models will be required, however, for cluster clustering analyses of next-generation cluster samples to keep systematics below the expected statistical uncertainties.…”

“…(2020), where an extensive validation study has been performed to quantify the systematic uncertainties on the growth rate and linear bias measurements as a function of sample selection and redshift uncertainties. The results found by García-Farieta et al (2020) show that the model systematics are below the statistical uncertainties at the scales and redshifts considered in this work.…”

“…Large redshift errors, as in photometric redshift surveys, lead to severe distortion effects that reflect in the 2PCF measurement, complicating its analysis and cosmological interpretation (see e.g. Marulli et al 2012;Sereno et al 2015;García-Farieta et al 2020). In order to construct a spectroscopic cluster sample, we take advantage of the spectroscopic data from the SDSS, focusing on the final spectroscopic DR12 from BOSS (Dawson et al 2013;Alam et al 2015Alam et al , 2017, which is part of the SDSS-III program.…”

“…This has been demonstrated to be a convenient choice. In fact, within this model we do not need to include any measurement redshift uncertainties explicitly, as their effects are degenerate with those of small-scale random motions, parameterised by σ 12 , and do not introduce any statistically significant biases in the linear growth rate constraints (Marulli et al 2012;Sridhar et al 2017;García-Farieta et al 2020).…”

C$^3$-Cluster Clustering Cosmology II. First detection of the BAO peak in the three-point correlation function of galaxy clusters

“…Among them, e.g., significant work on void detection and modelization has been done, including new functions to detect, count, and model cosmic void statistics (Ronconi & Marulli 2017;Contarini et al 2019;Ronconi et al 2019). Moreover, new modules have been added for improved 2PCF modeling (García-Farieta et al 2020).…”