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 < \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 % .