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AMICO galaxy clusters in KiDS-DR3: Constraints on cosmological parameters and on the normalisation of the mass-richness relation from clustering

We analysed the clustering of a photometric sample of galaxy clusters selected from the Third Data Release of the Kilo-Degree Survey, focusing on the redshift-space two-point correlation function (2PCF). We compared our measurements to theoretical predictions of the standard $Λ$ cold dark matter ($Λ$CDM) cosmological model. We measured the 2PCF of the sample in the cluster centric radial range $r\in[5,80]$ $h^{-1}$Mpc, considering 4934 galaxy clusters with richness $λ^*\geq15$ in the redshift range $z\in[0.1,0.6]$. A Markov chain Monte Carlo analysis has been performed to constrain the cosmological parameters $Ω_{\rm m}$, $σ_8$, and $S_8 \equiv σ_8(Ω_{\rm m}/0.3)^{0.5}$, assuming Gaussian priors on the mass-richness relation given by the posteriors obtained from a joint analysis of cluster counts and weak lensing. In addition, we constrained the normalisation of the mass-richness relation, $α$, with fixed cosmological parameters. We obtained $Ω_{\rm m}=0.28^{+0.05}_{-0.04}$, $σ_8=0.82^{+0.14}_{-0.12}$, and $S_8=0.80^{+0.08}_{-0.08}$. The constraint on $S_8$ is consistent within 1$σ$ with the results from WMAP and Planck. Furthermore, by fixing the cosmological parameters to those provided by Planck, we obtained $α=0.12^{+0.06}_{-0.06}$, which is fully consistent with the result obtained from the joint analysis of cluster counts and weak lensing performed for this sample.