Galaxy cluster number count data constraints on cosmological parameters

We use data on massive galaxy clusters (M-cluster > 8 x 10(14)h(-1)M(circle dot) within a comoving radius of R-cluster = 1.5h(-1) Mpc) in the redshift range 0.05 less than or similar to z less than or similar to 0.83 to place constraints, simultaneously, on the nonrelativistic matter density parameter Omega(m), on the amplitude of mass fluctuations sigma(8), on the index n of the power-law spectrum of the density perturbations, and on the Hubble constant H-0, as well as on the equation-of-state parameters (w(0), w(a)) of a smooth dark energy component. For the first time, we properly take into account the dependence on redshift and cosmology of the quantities related to cluster physics: the critical density contrast, the growth factor, the mass conversion factor, the virial overdensity, the virial radius and, most importantly, the cluster number count derived from the observational temperature data. We show that, contrary to previous analyses, cluster data alone prefer low values of the amplitude of mass fluctuations, sigma(8) <= 0.69 (1 sigma C.L.), and large amounts of nonrelativistic matter, Omega(m) >= 0.38 (1s C.L.), in slight tension with the Lambda CDM concordance cosmological model, though the results are compatible with Lambda CDM at 2 sigma. In addition, we derive a s8 normalization relation, sigma(8)Omega(1/3)(m) = 0.49 +/- 0.06 (2s C.L.). Combining cluster data with sigma(8)-independent baryon acoustic oscillation observations, cosmic microwave background data, Hubble constant measurements, Hubble parameter determination from passively evolving red galaxies, and magnitude-redshift data of type Ia supernovae, we find Omega(m) = 0.28(-0.02)(+0.03) and sigma(8) = 0.73(-0.03)(+0.03), the former in agreement and the latter being slightly lower than the corresponding values in the concordance cosmological model. We also find H-0 = 69.1(-1.5)(+1.3) km/s/Mpc, the fit to the data being almost independent on n in the adopted range [0.90, 1.05]. Concerning the dark energy equation-of-state parameters, we show that the present data on massive clusters weakly constrain (w(0), w(a)) around the values corresponding to a cosmological constant, i.e. (w(0), w(a)) = (-1, 0). The global analysis gives w(0) =-1.14(-0.16)(+0.14) and w(a) = 0.85(-0.60)(+0.42) (1 sigma C.L. errors). Very similar results are found in the case of time-evolving dark energy with a constant equation-of-state parameter w = const (the XCDM parametrization). Finally, we show that the impact of bounds on (w(0), w(a)) is to favor top-down phantom models of evolving dark energy.