The SRG/eROSITA All-Sky Survey: Cosmology Constraints from Cluster Abundances in the Western Galactic Hemisphere

The evolution of the cluster mass function traces the growth of linear density perturbations, providing valuable insights into the growth of structures, the nature of dark matter, and the cosmological parameters governing the Universe. The primary science goal of eROSITA, on board the Spectrum Roentgen Gamma (SRG) mission, is to constrain cosmology through the evolution of the cluster mass function. In this paper, we present a set of cosmological constraints obtained from 5259 clusters of galaxies detected over an area of 12791 deg(2) in the western Galactic hemisphere of eROSITA's first All-Sky Survey (eRASS1). The common footprint region (4968 deg(2)) between the eROSITA Survey and Dark Energy Survey (DES), the Kilo-Degree Survey (KiDS), and the Hyper Supreme Camera (HSC) survey is used for calibration of the scaling between X-ray count rate of the clusters and their total mass through measurements of their weak gravitational lensing signal. The eRASS1 cluster abundances constrain the Lambda CDM parameters, namely, the energy density of the total matter to Omega(m) = 0.29(-0.02)(+0.01) and the normalization of the density fluctuations to sigma(8) = 0.88 +/- 0.02, and their combination yields S-8 = sigma(8)(Omega(m)/0.3)(0.5) = 0.86 +/- 0.01. These results are consistent and achieve at a similar precision with state-of-the-art cosmic microwave background (CMB) measurements. Furthermore, the eRASS1 cosmological experiment places a most stringent upper limit on the summed masses of left-handed light neutrinos to & sum; m(v) < 0.43 eV (95% confidence interval) from cluster number counts alone. By combining eRASS1 cluster abundance measurements with CMB- and ground-based neutrino oscillation experiments, we measured the summed neutrino masses to be & sum; m(v) = 0.09(-0.02)(+0.04) eV or & sum; m(v) = 0.12(-0.02)(+0.03) eV, assuming a normal or inverted mass hierarchy scenario for neutrino eigenstates. The eRASS1 cluster abundances significantly improve the constraints on the dark energy equation of state parameter to w = -1.12 +/- 0.12. When & sum; m(v) and w are left free, we find consistent results with the concordance Lambda CDM cosmology. Our results from the first All-Sky Survey improve the cosmological constraints by over a factor of 5 to 9 over the previous cluster surveys, establishing cluster abundance measurements for precision cosmology and setting the stage for deeper eROSITA All-Sky Surveys, as well as for future cluster abundance experiments.