Constraints from thermal Sunyaev-Zel'dovich cluster counts and power spectrum combined with CMB

The thermal Sunyaev-Zel'dovich (tSZ) effect is one of the recent probes of cosmology and large-scale structures. We update constraints on cosmological parameters from galaxy clusters observed by the Planck satellite in a first attempt to combine cluster number counts and the power spectrum of hot gas; we used a new value of the optical depth and, at the same time, sampling on cosmological and scaling-relation parameters. We find that in the Lambda CDM model, the addition of a tSZ power spectrum provides small improvements with respect to number counts alone, leading to the 68% c.l. constraints Omega(m) = 0.32 +/- 0.02, sigma(8) = 0.76 +/- 0.03; and sigma(8)(Omega(m) = 0.3)(1/3) = 0.78 +/- 0.03 and lowering the discrepancy with results for cosmic microwave background (CMB) primary anisotropies (updated with the new value of tau) to similar or equal to 1.8 sigma on sigma(8). We analysed extensions to the standard model, considering the effect of massive neutrinos and varying the equation of state parameter for dark energy. In the first case, we find that the addition of the tSZ power spectrum helps in improving cosmological constraints with respect to number count alone results, leading to the 95% upper limit Sigma m(nu) < 1.88 eV. For the varying dark energy equation of state scenario, we find no important improvements when adding tSZ power spectrum, but still the combination of tSZ probes is able to provide constraints, producing w = 1.0 +/- 0.2. In all cosmological scenarios, the mass bias to reconcile CMB and tSZ probes remains low at (1 b) less than or similar to 0 : 67 as compared to estimates from weak lensing and X-ray mass estimate comparisons or numerical simulations.