AMICO galaxy clusters in KiDS-DR3: cosmological constraints from
  large-scale stacked weak lensing profiles
  Context. The large-scale mass distribution around dark matter haloes hosting
galaxy clusters provides sensitive cosmological information. Aims. In this
work, we make use of a large photometric galaxy cluster sample, constructed
from the public Third Data Release of the Kilo-Degree Survey, and the
corresponding shear signal, to assess cluster masses and test the concordance
${\Lambda}$-cold dark matter (${\Lambda}$CDM) model. In particular, we study
the weak gravitational lensing effects on scales beyond the cluster virial
radius, where the signal is dominated by correlated and uncorrelated matter
density distributions along the line-of-sight. The analysed catalogue consists
of 6962 galaxy clusters, in the redshift range $0.1 \leq z \leq 0.6$ and with
signal-to-noise ratio larger than 3.5. Methods. We perform a full Bayesian
analysis to model the stacked shear profiles of these clusters. The adopted
likelihood function considers both the small-scale 1-halo term, used primarily
to constrain the cluster structural properties, and the 2-halo term, that can
be used to constrain cosmological parameters. Results. We find that the adopted
modelling is successful to assess both the cluster masses and the total matter
density parameter, ${\Omega}_M$, when fitting shear profiles up to the largest
available scales of 35 Mpc/h. Moreover, our results provide a strong
observational evidence of the 2-halo signal in the stacked gravitational
lensing of galaxy clusters, further demonstrating the reliability of this probe
for cosmological studies. The main result of this work is a robust constraint
on ${\Omega}_M$, assuming a flat ${\Lambda}$CDM cosmology. We get ${\Omega}_M =
0.29 \pm 0.02$, estimated from the full posterior probability distribution,
consistent with the estimates from cosmic microwave background experiments.
