Forecasts for cosmological measurements based on the angular power spectra of AGN and clusters of galaxies in the SRG/eROSITA all-sky survey

Abstract abridged. The eROSITA X-ray telescope aboard the SRG orbital observatory, in the course of its all-sky survey, is expected to detect about three million active galactic nuclei (AGN) and hundred thousand clusters and groups of galaxies. Such a sample complemented with redshift information, will open a new window into the studies of the Large-Scale structure (LSS) of the Universe and the determination of its cosmological parameters. The purpose of this work is to assess the prospects of cosmological measurements with the eROSITA sample of AGN and clusters of galaxies. We assume the availability of photometric redshift measurements for eROSITA sources and explore the impact of their quality on our forecasts. We use the redshift-resolved angular power spectrum of objects. We use a Fisher-matrix formalism and assume flat LambdaCDM cosmology to forecast the constraining power. We compute the LSS-relevant characteristics of AGN and clusters in the framework of the halo model and their X-ray luminosity functions. We find that the accuracy of photometric redshift estimates has a more profound effect on cosmological measurements than the fraction of catastrophic errors. Under realistic assumptions about the photometric redshift quality, the marginalized errors on the cosmological parameters achieve 1 - 10% accuracy depending on the cosmological priors used from other experiments. The statistical significance of BAO detection in angular power spectra of AGN and clusters of galaxies considered individually achieves 5 - 6 sigma. Our results demonstrate that the eROSITA sample of AGN and clusters of galaxies used in combination with currently available photometric redshift estimates will provide cosmological constraints on a par with dedicated optical LSS surveys.