Forecasts on dark energy from the X-ray cluster survey with eROSITA: constraints from counts and clustering

We forecast the potential of the forthcoming X-ray galaxy-cluster survey with eROSITA to constrain dark-energy models. We focus on spatially flat cosmological scenarios with either constant or time-dependent dark-energy equation-of-state parameters. Fisher information is extracted from the number density and spatial clustering of a photon-count-limited sample of clusters of galaxies up to z similar to 2. We consider different scenarios for the availability of (i) X-ray follow-up observations, (ii) photometric and spectroscopic redshifts, and (iii) accurate knowledge of the observable - mass relation down to the scale of galaxy groups, but no additional observation-related systematics are taken into account. With about 125 000 clusters (detected with more than 50 photons and with mass M-500c greater than or similar to 10(13) h(-1) M-circle dot) from an average all-sky exposure of 1.6 ks, eROSITA will give marginalized, one-dimensional, 1 sigma errors of Delta sigma(8) = +/- 0.008 (similar to 1 per cent), Delta Omega(m) = +/- 0.006 (2.2 per cent), Delta w(0) = +/- 0.07 (7 per cent), and Delta w(a) = +/- 0.25 (optimistic scenario) in combination with (and largely improving upon) current constraints from various cosmological probes (cosmic microwave background, baryonic acoustic oscillations, Type Ia SNe). Our findings correspond to a dark-energy figure of merit in the range of 116-162 (after the 4 yr of all-sky survey), making eROSITA one of the first Stage IV experiments to come on line according to the classification of the Dark Energy Task Force. To secure improved mass calibrations and to include high-redshift clusters (z greater than or similar to 0.5) as well as objects at the group-mass scale (M-500c less than or similar to 5 x 10(13) h(-1) M-circle dot) will be vital to reach such accuracies.