C$^3$-Cluster Clustering Cosmology I. New constraints on the cosmic
  growth rate at z~0.3 from redshift-space clustering anisotropies
  Redshift-space distortions in the clustering of galaxy clusters provide a
novel probe to test the gravity theory 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 catalogue 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.
Modelling 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 normalisation parameter
$f\sigma_{8}=0.44\pm0.05$, at an effective redshift $z=0.275$.
