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

We constrain the $\mathrm{\Lambda }$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 $N_{\text{obs}}=3644$ clusters with intrinsic richness ${\lambda }^{\ast }>20$ 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 $\mathit{\text{Euclid}}$ and LSST, which are expected to deliver thousands of distant and massive clusters.