The REFLEX Galaxy Cluster Survey VII: Omega_m and sigma_8 from cluster abundance and large-scale clustering

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 $Ω_m$ and the linear theory RMS fluctuations in mass $σ_8$. 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 $Ω_m$ and $σ_8$. 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

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