On a novel approach using massive clusters at high redshift as cosmological probe

In this work we propose a novel method for testing the validity of the fiducial Λ cold dark matter (ΛCDM) 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 ΛCDM and alternative cosmological models is strongest, makes our method particularly interesting as a cosmological probe. We utilize general extreme value (GEV) statistics 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 ΛCDM model, once we are able to establish a sufficiently complete large-area survey with Mlim≃ 1014.5 M⊙ h-1 (Mlim≃ 1014 M⊙ h-1) at redshifts above z= 1 (z= 1.5). Being of cumulative nature the proposed measure is robust and an accuracy of 20-30 per cent 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.