AMICO galaxy clusters in KiDS-DR3: constraints on $\Lambda$CDM from extreme value statistics

We constrain the $\Lambda$CDM cosmological parameter $\sigma_{8}$ 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 $\lambda^{*} > 20$ in the redshift range $z\in[0.10, 0.60]$. We obtain $\sigma_{8}=0.90_{-0.18}^{+0.20}$, consistent within $1\sigma$ 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.