For the first time the large-scale clustering and the mean abundance of galaxy clusters are analysed simultaneously to get precise constraints on the normalized cosmic matter density \Omega _ { m } and the linear theory RMS fluctuations in mass \sigma _ { 8 } .
A self-consistent likelihood analysis is described which combines , in a natural and optimal manner , a battery of sensitive cosmological tests where observational data are represented by the ( Karhunen-Loéve ) eigenvectors of the sample correlation matrix .
This method breaks the degeneracy between \Omega _ { m } and \sigma _ { 8 } .
The cosmological tests are performed with the ROSAT ESO Flux-Limited X-ray ( REFLEX ) cluster sample .
The computations assume cosmologically flat geometries and a non-evolving cluster population mainly over the redshift range 0 < z < 0.3 .
The REFLEX sample gives the cosmological constraints and their 1 \sigma random errors of \Omega _ { m } = 0.341 ^ { +0.031 } _ { -0.029 } and \sigma _ { 8 } = 0.711 ^ { +0.039 } _ { -0.031 } .
Possible systematic errors are evaluated by estimating the effects of uncertainties in the value of the Hubble constant , the baryon density , the spectral slope of the initial scalar fluctuations , the mass/X-ray luminosity relation and its intrinsic scatter , the biasing scheme , and the cluster mass density profile .
All these contributions sum up to total systematic errors of \sigma _ { \Omega _ { m } } = ^ { +0.087 } _ { -0.071 } and \sigma _ { \sigma _ { 8 } } = ^ { +0.120 } _ { -0.162 } .