AMICO galaxy clusters in KiDS-DR3: constraints on $Λ$CDM from extreme value statistics
We constrain the $Λ$CDM cosmological parameter $σ_{8}$ by applying the extreme value statistics for galaxy cluster mass on the AMICO KiDS-DR3 catalog. We sample the posterior distribution of the parameters by considering the likelihood of observing the largest cluster mass value in a sample of $N_{\textrm{obs}} = 3644$ clusters with intrinsic richness $λ^{*} > 20$ in the redshift range $z\in[0.10, 0.60]$. We obtain $σ_{8}=0.90_{-0.18}^{+0.20}$, consistent within $1σ$ with the measurements obtained by the Planck collaboration and with previous results from cluster cosmology exploiting AMICO KiDS-DR3. The constraints could improve by applying this method to forthcoming missions, such as $\textit{Euclid}$ and LSST, which are expected to deliver thousands of distant and massive clusters.