Redshift-space distortions in the clustering of galaxy clusters provide a novel probe to test the theory of gravity on cosmological scales. The aim of this work is to derive new constraints on the linear growth rate of cosmic structures from the redshift-space two-point correlation function of galaxy clusters. We construct a large spectroscopic catalog of optically selected clusters from the Sloan Digital Sky Survey. The selected sample consists of 43,743 clusters in the redshift range 0.1 < z < 0.42, with masses estimated from weak-lensing calibrated scaling relations. We measure the transverse and radial wedges of the two-point correlation function of the selected clusters. Modeling the redshift-space clustering anisotropies, we provide the first constraints on the linear growth rate from cluster clustering. The cluster masses are used to set a prior on the linear bias of the sample. This represents the main advantage in using galaxy clusters as cosmic probes, instead of galaxies. Assuming a standard cosmological model consistent with the latest cosmic microwave background constraints, we do not find any evidence of deviations from general relativity. Specifically, we get the value of the growth rate times the matter power spectrum normalization parameter fσ ₈ = 0.44 ± 0.05, at an effective redshift of z = 0.275.

Modified gravity and massive neutrino cosmologies are two of the most interesting scenarios that have been recently explored to account for possible observational deviations from the concordance Λ cold dark matter (ΛCDM) model. In this context, we investigated the large-scale structure of the Universe by exploiting the dustgrain-pathfinder simulations that implement, simultaneously, the effects of f(R) gravity and massive neutrinos. To study the possibility of breaking the degeneracy between these two effects, we analysed the redshift-space distortions in the clustering of dark matter haloes at different redshifts. Specifically, we focused on the monopole and quadrupole of the two-point correlation function, both in real and redshift space. The deviations with respect to ΛCDM model have been quantified in terms of the linear growth rate parameter. We found that redshift-space distortions provide a powerful probe to discriminate between ΛCDM and modified gravity models, especially at high redshifts (z ≳ 1), even in the presence of massive neutrinos.

We study the halo mass function (HMF) in modified gravity (MG) models using a set of large $N$-body simulations—the elephant suite. We consider two popular beyond-general-relativity scenarios: the Hu-Sawicki chameleon $f(R)$ model and the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld. We show that in MG, analytic formulation based on the Press-Schechter framework offers a grossly inaccurate description of the HMF. We find, however, that once the HMF is expressed in terms of the dimensionless multiplicity function it approximately assumes a redshift-independent universal character for all the models. Exploiting this property, we propose universal fits for the MG HMF in terms of their fractional departures from the $\mathrm{\Lambda }\mathrm{CDM}$ case. We find two enclosed formulas, one for $f(R)$ and another for nDGP, that provide a reliable description of the HMF over the mass range covered by the simulations. These are accurate to a few percent with respect to the $N$-body data. We test the extrapolation potential of our fits against separate simulations with a different cosmological background and mass resolution and find very good accuracy, within $\sim 10\%$. A particularly interesting finding from our analysis is a Gaussian-like shape of the HMF deviation that seems to appear universally across the whole $f(R)$ family, peaking at a mass variance scale characteristic for each $f(R)$ variant. We attribute this behavior to the specific physics of the environmentally dependent chameleon screening models.

We investigate clustering properties of dark matter halos and galaxies to search for optimal statistics and scales where possible departures from general relativity (GR) could be found. We use large $N$-body cosmological simulations to perform measurements based on the two-point correlation function (2PCF) in GR and in selected modified gravity (MG) structure formation scenarios. As a test bed, we employ two popular beyond-GR models: $f(R)$ gravity and the normal branch of the Dvali-Gabadadze-Porrati (nDGP) braneworld. We study a range of simulated halo and galaxy populations and reveal a noticeable MG signal in the monopole and quadrupole moments of the redshift-space 2PCF and in the so-called clustering wedges. However, once expressed in terms of the linear distortion parameter $\beta$, the statistical significance of these signals largely diminishes due to a strong degeneracy between MG-enhanced clustering and modified tracer bias. To circumvent this, we consider statistics less dependent on the bias: relative clustering ratios. We generalize the monopole ratio proposed in earlier work to multipole moments and clustering wedges and introduce a new estimator of the $\beta$ parameter. The clustering ratios we extract foster noticeable differences between MG and GR models, reaching a maximum deviation of 10% at $2\sigma$ significance for specific variants of $f(R)$ and the nDGP. We show that such departures could be measured for $\beta$ if nonlinear effects at intermediate scales are correctly modeled. Our study indicates that the clustering ratios give great promise to search for signatures of MG in the large-scale structure. We also find that the selection of an optimal tracer sample depends on a particular statistics and gravity model to be considered.

Redshift-space clustering distortions provide one of the most powerful probes to test the gravity theory on the largest cosmological scales. 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. 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[$h^{-1}\, \mbox{Mpc}$] < 55. Moreover, we investigate the impact of redshift measurement errors on the growth rate and linear bias measurements due to the assumptions in the redshift-space distortion model. Considering both the dispersion model and two widely used models based on perturbation theory, we find that the linear growth rate is underestimated by about $5\!-\! 10\, {\rm {per\ cent}}$ at $z$ < 1, while limiting the analysis at larger scales, r > 30 $h^{-1}\, \mbox{Mpc}$, the discrepancy is reduced below $5\, {\rm {per\ cent}}$. At higher redshifts, we find instead an overall good agreement between measurements and model predictions. Though this accuracy is good enough for clustering analyses in current redshift surveys, the models have to be further improved not to introduce significant systematics in RSD constraints from next-generation galaxy surveys. The effect of redshift errors is degenerate with the one of small-scale random motions, and can be marginalized over in the statistical analysis, not introducing any statistically significant bias in the linear growth constraints, especially at $z$ ≥ 1.