Abundances, masses, and weak-lensing mass profiles of galaxy clusters as
  a function of richness and luminosity in LambdaCDM cosmologies
  We test the concordance LCDM cosmology by comparing predictions for the mean
properties of galaxy clusters to observations. We use high-resolution N-body
simulations of cosmic structure formation and semi-analytic models of galaxy
formation to compute the abundance, mean density profile, and mass of galaxy
clusters as a function of richness and luminosity, and we compare these
predictions to observations of clusters in the Sloan Digital Sky Survey (SDSS)
maxBCG catalogue. We discuss the scatter in the mass-richness relation, the
reconstruction of the cluster mass function from the mass-richness relation,
and fits to the weak-lensing cluster mass profiles. The impact of cosmological
parameters on the predictions is investigated by comparing results from galaxy
models based on the Millennium Simulation (MS) and another WMAP1 simulation to
those from a WMAP3 simulation. We find that the simulated weak-lensing mass
profiles and the observed profiles of the SDSS maxBCG clusters agree well in
shape and amplitude. The mass-richness relations in the simulations are close
to the observed relation, with differences lesssim 30%. The MS and WMAP1
simulations yield cluster abundances similar to those observed, whereas
abundances in the WMAP3 simulation are 2-3 times lower. The differences in
cluster abundance, mass, and density amplitude between the simulations and the
observations can be attributed to differences in the underlying cosmological
parameters, in particular the power spectrum normalisation sigma_8. Better
agreement between predictions and observations should be reached with a
normalisation $0.722<sigma_8<0.9$ (probably closer to the upper value), i.e.
between the values underlying the two simulation sets.
