  In this work we propose a novel method for testing the validity of the
fiducial LCDM cosmology by measuring the cumulative distribution function of
the most massive haloes in a sample of subvolumes of identical size tiled on
the sky at a fixed redshift. The fact that the most massive clusters probe the
high-mass tail of the mass function, where the difference between LCDM and
alternative cosmological models is strongest, makes our method particularly
interesting as a cosmological probe. We utilise general extreme value
statistics (GEV) to obtain a cumulative distribution function of the most
massive objects in a given volume. We sample this distribution function
according to the number of patches covered by the survey area for a range of
different "test cosmologies" and for differently accurate mass estimations of
the haloes. By fitting this sample with the GEV distribution function, we can
study which parameters are the most sensitive with respect to the test
cosmologies. We find that the peak of the probability distribution function of
the most massive halo is well suited to test the validity of the fiducial LCDM
model, once we are able to establish a sufficiently complete large-area survey
with M_lim=10^14.5 M_sun/h (M_lim=10^14 M_sun/h) at redshifts above z=1
(z=1.5). Being of cumulative nature the proposed measure is robust and an
accuracy of 20-30% in the cluster masses would be sufficient to test for
alternative models. Since one only needs the most massive system in each
angular patch, this method would be ideally suited as a first fast consistency
check before going into a more complex statistical analysis of the observed
halo sample.
