Impact of weak lensing mass calibration on eROSITA galaxy cluster cosmological studies - a forecast

We forecast the impact of weak lensing (WL) cluster mass calibration on the cosmological constraints from the X-ray-selected galaxy cluster counts in the upcoming eROSITA survey. We employ a prototype cosmology pipeline to analyse mock cluster catalogues. Each cluster is sampled from the mass function in a fiducial cosmology and given an eROSITA count rate and redshift, where count rates are modelled using the eROSITA effective area, a typical exposure time, Poisson noise, and the scatter and form of the observed X-ray luminosity - and temperature-mass-redshift relations. A subset of clusters have mock shear profiles to mimic either those from Dark Energy Survey (DES) and Hyper-Suprime-Cam (HSC) or from the future Euclid and Large Synoptic Survey Telescope (LSST) surveys. Using a count rate selection, we generate a baseline cluster cosmology catalogue that contains 13k clusters over 14 892 deg2 of extragalactic sky. Low-mass groups are excluded using raised count rate thresholds at low redshift. Forecast parameter uncertainties for ΩM, σ8, and w are 0.023 (0.016; 0.014), 0.017 (0.012; 0.010), and 0.085 (0.074; 0.071), respectively, when adopting DES+HSC WL (Euclid; LSST), while marginalizing over the sum of the neutrino masses. A degeneracy between the distance-redshift relation and the parameters of the observable-mass scaling relation limits the impact of the WL calibration on the w constraints, but with baryonic acoustic oscillation measurements from Dark Energy Spectroscopy Instrument an improved determination of w to 0.043 becomes possible. With Planck cosmic microwave background priors, ΩM (σ8) can be determined to 0.005 (0.007), and the summed neutrino mass limited to ∑mν < 0.241 eV (at 95 per cent). If systematics on the group mass scale can be controlled, the eROSITA group and cluster sample with 43k objects and LSST WL could constrain ΩM and σ8 to 0.007 and w to 0.050.