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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-Lo{e}ve) 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 $1sigma$ 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 $sigma_{sigma_8}=^{+0.120}_{-0.162}$.
We show that the counts of galaxy clusters in future deep cluster surveys can place strong constraints on the matter density, Omega_m, the vacuum energy density, Omega_L, and the normalization of the matter power spectrum, sigma_8. Degeneracies betwe
We use the presently observed number density of large X-ray clusters and linear mass power spectra to constrain the shape parameter ($Gamma$), the spectral index ($n$), the amplitude of matter density perturbations on the scale of $8 h^{-1}$Mpc ($sig
We present the final data from the spectroscopic survey of the ROSAT-ESO Flux-Limited X-ray (REFLEX) catalog of galaxy clusters. The REFLEX survey covers 4.24 steradians (34% of the entire sky) below a declination of 2.5 deg and at high Galactic lati
I review the status of large-scale structure studies based on redshift surveys of galaxies and clusters of galaxies. In particular, I compare recent results on the power spectrum and two-point correlation correlation function from the 2dF and REFLEX
The origin of the micro-Gauss magnetic fields in galaxy clusters is one of the outstanding problem of modern cosmology. We have performed three-dimensional particle-in-cell simulations of the nonrelativistic Weibel instability in an electron-proton p