Constraining the Matter Power Spectrum Normalization Using the Sdss/rass and Reflex Cluster Surveys

We describe a new approach to constrain the amplitude of matter perturbations in the Universe using galaxy clusters. We combine the galaxy cluster X-ray luminosity function of the REFLEX survey with the mass– luminosity relationship obtained via gravitational lensing from a sample of galaxy clusters identified in Sloan Digital Sky Survey commissioning data and confirmed through cross-correlation with the ROSAT all-sky survey. We compare the resulting cluster mass function with the theoretical mass function of Jenkins et al. (2001) to determine the matter power spectrum normalization σ8 as a function of the matter density Ω0. We find σ8 = 0.38Ω −0.48+0.27Ω0 0 as the best fitting formula between σ8 and Ω0, which is significantly different from most previous relations between these two cosmological parameters derived from comparable calculations using the X-ray temperature function. We discuss possible sources of systematic error that may cause such a discrepancy, and in the process uncover a possible inconsistency between the REFLEX luminosity function and the relation between cluster X-ray luminosity and mass obtained by Reiprich & Böhringer (2001). Subject headings: cosmological parameters — galaxies: clusters — methods: analytical — surveys