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 Ω_M, 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, Ω_M (σ₈) can be determined to 0.005 (0.007), and the summed neutrino mass limited to ∑m_ν < 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 Ω_M and σ₈ to 0.007 and w to 0.050.