Galaxy Clusters in Hubble Volume Simulations: Cosmological Constraints from Sky Survey Populations

We use gigaparticle N-body simulations to study galaxy cluster populations in Hubble volumes of ΛCDM (Ω_m=0.3, Ω_Λ=0.7) and τCDM (Ω_m=1) world models. Mapping past light cones of locations in the computational space, we create mock sky surveys of dark matter structure to z~=1.4 over 10,000 deg² and to z~=0.5 over two full spheres. Calibrating the Jenkins mass function at z=0 with samples of ~1.5 million clusters, we show that the fit describes the sky survey counts to <~20% accuracy over all redshifts for systems more massive than poor galaxy groups (5×10¹³ h^-1 M_solar). Fitting the observed local temperature function determines the ratio β of specific thermal energies in dark matter and intracluster gas. We derive a scaling with power spectrum normalization β~σ^5/3₈ and find that the ΛCDM model requires σ₈=1.04 to match β=1.17 derived from gasdynamic cluster simulations. We estimate a 10% overall systematic uncertainty in σ₈, 4% arising from cosmic variance in the local sample and the bulk from uncertainty in the absolute mass scale of clusters. Considering distant clusters, the ΛCDM model matches Extended Medium-Sensitivity Survey and ROSAT Deep Cluster Survey X-ray-selected observations under economical assumptions for intracluster gas evolution. Using transformations of mass-limited cluster samples that mimic σ₈ variation, we explore Sunyaev-Zeldovich (SZ) search expectations for a 10 deg² survey complete above 10¹⁴ h^-1 M_solar. Cluster counts are shown to be extremely sensitive to σ₈ uncertainty, while redshift statistics, such as the sample median, are much more stable. Redshift information is crucial to extract the full cosmological diagnostic power of SZ cluster surveys. For ΛCDM, the characteristic temperature at a fixed sky surface density is a weak function of redshift, implying an abundance of hot clusters at z>1. Assuming constant β, one 8 keV cluster at z>2 and 10 5 keV clusters at z>3 are expected in the Sloan Digital Sky Survey area. Too many such clusters can falsify the model; detection of clusters more massive than Coma at z>1 violates ΛCDM at 95% confidence if their surface density exceeds 0.003 deg^-2, or 120 on the whole sky.