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The ROSAT-ESO Flux-Limited X-Ray (REFLEX) Galaxy Cluster Survey VI: Constraints on the cosmic matter density from the KL power spectrum

The Karhunen-Loéve (KL) eigenvectors and eigenvalues of the sample correlation matrix are used to analyse the spatial fluctuations of the REFLEX clusters of galaxies. The method avoids the disturbing effects of correlated power spectral densities which affects all previous cluster measurements on Gpc scales. Comprehensive tests use a large set of independent REFLEX-like mock cluster samples extracted from the Hubble Volume Simulation. It is found that unbiased measurements on Gpc scales are possible with the REFLEX data. The distribution of the KL eigenvalues are consistent with a Gaussian random field on the 93.4% confidence level. Assuming spatially flat cold dark matter models, the marginalization of the likelihood contours over different sample volumes, fiducial cosmologies, mass/X-ray luminosity relations and baryon densities, yields the 95.4% confidence interval for the matter density of $0.03<Ω_mh^2<0.19$. The N-body simulations show that cosmic variance, although difficult to estimate, is expected to increase the confidence intervals by about 50%.