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 analyze mock cluster catalogs .
Each cluster is sampled from the mass function in a fiducial cosmology and given an eROSITA count rate and redshift , where count rates are modeled 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 DES and HSC or from the future Euclid and LSST surveys .
Using a count rate selection , we generate a baseline cluster cosmology catalog that contains 13k clusters over 14,892 deg ^ { 2 } of extragalactic sky .
Low mass groups are excluded using raised count rate thresholds at low redshift .
Forecast parameter uncertainties for \Omega _ { \mathrm { M } } , \sigma _ { 8 } 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 BAO measurements from DESI an improved determination of w to 0.043 becomes possible .
With Planck CMB priors , \Omega _ { \text { M } } ( \sigma _ { 8 } ) can be determined to 0.005 ( 0.007 ) , and the summed neutrino mass limited to \sum m _ { \nu } < 0.241 eV ( at 95 % ) .
If systematics on the group mass scale can be controlled , the eROSITA group and cluster sample with 43k objects and LSST WL could constrain \Omega _ { \mathrm { M } } and \sigma _ { 8 } to 0.007 and w to 0.050 .