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Thermal Sunyaev-Zel'dovich effect is one of the recent probes of cosmologyand large scale structures. We update constraints on cosmological parametersfrom galaxy clusters observed by the Planck satellite in a first attempt tocombine cluster number counts and power spectrum of hot gas, using the newvalue of the optical depth, and sampling at the same time on cosmological andscaling-relation parameters. We find that in the $\Lambda$CDM model, theaddition of tSZ power spectrum provides only small improvements with respect tonumber counts only, leading to the $68\%$ c.l. constraints $\Omega_m = 0.32 \pm0.02$, $\sigma_8 = 0.77\pm0.03 $ and $\sigma_8 (\Omega_m/0.3)^{1/3}=0.78\pm0.03$ and lowering the discrepancy with CMB primary anisotropies results(updated with the new value of $\tau$) to $\simeq 1.6\, \sigma$ on $\sigma_8$.We analyse extensions to standard model, considering the effect of massiveneutrinos and varying the equation of state parameter for dark energy. In thefirst case, we find that the addition of tSZ power spectrum helps in stronglyimproving cosmological constraints with respect to number counts only results,leading to the $95\%$ upper limit $\sum m_{\nu}< 1.53 \, \text{eV}$. For thevarying dark energy EoS scenario, we find again no important improvements whenadding tSZ power spectrum, but still the combination of tSZ probes is able inproviding constraints, producing $w = -1.0\pm 0.2$. In all cosmological scenarithe mass bias to reconcile CMB and tSZ probes remains low: $(1-b)\lesssim 0.66$as compared to estimates from weak lensing and Xray mass estimate comparisonsor numerical simulations.

Constraints from thermal Sunyaev-Zeldovich cluster counts and power spectrum combined with CMB