Cosmological constraints from galaxy clusters and groups in the eROSITA final equatorial depth survey

We present the first cosmological study of a sample of eROSITA clusters, which were identified in the eROSITA Final Equatorial Depth Survey (eFEDS). In a joint selection on X-ray and optical observables, the sample contains 455 clusters within a redshift range of 0.1 < z < 1.2, of which 177 systems are covered by the public data from the Hyper Suprime-Cam (HSC) survey that enables uniform weak-lensing cluster mass constraints. With minimal assumptions, at each cluster redshift we empirically model (1) the scaling relations between the cluster halo mass and the observables, which include the X-ray count rate, the optical richness, and the weak-lensing mass, and (2) the X-ray selection in terms of the completeness function C. Using the richness distribution of the clusters, we directly measure the X-ray completeness and adopt those measurements as informative priors for the parameters of C. In a blinded analysis, we obtain the cosmological constraints Ω m= 0.245 +0.048-0.058, σ 8= 0.833 +0.075 -0.063, and S 8σ 8 (Ω m/0.3\right)0.3= 0.791 +0.028 -0.031 in a flat ΛCDM cosmology. Extending to a flat wCDM cosmology leads to the constraint on the equation of state parameter of the dark energy of w = -1.25 ± 0.47. The eFEDS constraints are in good agreement with the results from the Planck mission, the galaxy-galaxy lensing and clustering analysis of the Dark Energy Survey, and the cluster abundance analysis of the SPT-SZ survey at a level of 1σ. With the empirical modelling, this work presents the first fully self-consistent cosmological constraints based on a synergy between wide-field X-ray and weak lensing surveys.