Improvements in the X-ray luminosity function and constraints on the cosmological parameters from X-ray luminous clusters

Aims. We improve the current constraints on Ωm, the dark-energy equation-of-state parameter, w, and σ8, obtained from measurements of the X-ray luminosity function of galaxy clusters, namely MACS, the local BCS, and the REFLEX galaxy cluster samples with luminosities L > 3 × 1044 erg/s in the 0.1-2.4 keV band. Methods. To this aim, we use Tinker and collaborators mass function instead of Jenkins and collaborators and the mass-luminosity relationship obtained by Del Popolo and collaborators. Results. Using the same methods and priors as Mantz and collaborators, we find Ωm = 0.28+0.05 -0.04 and σ8 = 0.78+0.04-0.05, for a ΛCDM universe, while the result of Mantz and collaborators gives less tight constraints Ωm = 0.28+0.11 -0.07 and σ8 = 0.78+0.11-0.13. In the case of a wCDM model, we find Ωm = 0.27 +0.07-0.06, σ8 = 0.81 +0.05-0.06 and w =-1.3+0.3-0.4, while in Mantz and collaborators they are again less tight Ωm = 0.24+0.15-0.07, σ8 = 0.85 +0.13-0.20 and w =-1.4+0.4-0.7. Combining the XLF analysis with the fgas+CMB+SNIa data set results in the constraint Ωm = 0.269 ± 0.012, σ8 = 0.81 ± 0.021 and w =-1.02 ± 0.04, to be compared with Mantz and collaborators, Ωm = 0.269 ± 0.016, σ8 = 0.82 ± 0.03 and w =-1.02 ± 0.06. The tightness of the last constraints obtained by Mantz and collaborators, are fundamentally due to the tightness of the fgas+CMB+SNIa constraints and not to their XLF analysis. Our findings, consistent with w =-1, lend additional support to the cosmological-constant model. © ESO, 2010.