We analyze the potential of the future X-ray cluster telescope eROSITA to simultaneously constrain cosmological and X-ray scaling-relation parameters via measurement of the abundances and angular clustering of a photon-count limited sample of clusters up to z~1.5. Special attention is dedicated to the primordial non-Gaussianity alternative. eROSITA will be launched in the 2012 and will observe ~1.5x10^5 clusters of galaxies within the currently planned all-sky survey, above the detection limit of 50 photons with a typical exposure time of 3 ks and above masses of 5 x 10^13 solar masses.
We perform a Fisher Matrix analysis keeping in full consideration a flat Lambda-CDM model of 5 standard cosmological parameters to which we add the non-linearity parameter fNL; 4 parameters which describe the Luminosity--Mass relations are also included. We find that, even with the large statistics of a future survey like eROSITA, a cluster count experiment alone without redshifts does not allow us to place any good constraint on the parameters of interest. Once the redshifts are included, the errors on the parameters of the Luminosity-Mass sector are strongly improved with respect to current knowledge. For the cosmological parameters, yet marginalizing also over Luminosity-Mass sector, it will be possible to get results competitive with Planck when combining cluster abundances and angular clustering measurements with redshift information at the photometric-redshift accuracy. In particular, for the parameter of the primordial non-Gaussianity of the local type, fNL, the large-scale scale-dependent bias feature breaks the degeneracies with the other parameters: when combining angular cluster measurements in different z-slices, it will be possible to shrink the 1-$sigma$ error on fNL down to Delta fNL <= 10, showing how clusters of galaxies can provide strong constraints to primordial non-Gaussianity complementary to the CMB measurements.
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