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-Loeve (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 that affect 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 is consistent with a Gaussian random field on the 93.4 per cent 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 a 95.4 per cent confidence interval for the matter density of 0.03 < Omega(m)h(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 per cent.