Constraining the Matter Power Spectrum Normalization Using the Sloan Digital Sky Survey/ROSAT All-Sky Survey and REFLEX Cluster Surveys

We describe a new approach to constraining the amplitude of the power spectrum of matter perturbations in the universe, parameterized by σ8 as a function of the matter density Ω0. We compare the galaxy cluster X-ray luminosity function of the ROSAT-ESO Flux-Limited X-Ray (REFLEX) survey with the theoretical mass function of Jenkins et al., using the mass-luminosity relationship obtained from weak lensing data for 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 find σ8 = 0.38Ω, which is significantly different from most previous results derived from comparable calculations that used 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.