Constraints from thermal Sunyaev-Zeldovich cluster counts and power
  spectrum combined with CMB
  Thermal Sunyaev-Zel'dovich 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 power spectrum of hot gas, using the new
value of the optical depth, and sampling at the same time on cosmological and
scaling-relation parameters. We find that in the $\Lambda$CDM model, the
addition of tSZ power spectrum provides only small improvements with respect to
number counts only, leading to the $68\%$ c.l. constraints $\Omega_m = 0.32 \pm
0.02$, $\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 massive
neutrinos and varying the equation of state parameter for dark energy. In the
first case, we find that the addition of tSZ power spectrum helps in strongly
improving cosmological constraints with respect to number counts only results,
leading to the $95\%$ upper limit $\sum m_{\nu}< 1.53 \, \text{eV}$. For the
varying dark energy EoS scenario, we find again no important improvements when
adding tSZ power spectrum, but still the combination of tSZ probes is able in
providing constraints, producing $w = -1.0\pm 0.2$. In all cosmological scenari
the 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 comparisons
or numerical simulations.
