Title: Combined analysis of galaxy cluster number count, thermal Sunyaev-Zel'dovich power spectrum, and bispectrum,
Abstract: The Sunyaev-Zel'dovich (SZ) effect is a powerful probe of the evolution of
structures in the universe, and is thus highly sensitive to cosmological
parameters $\sigma_8$ and $\Omega_m$, though its power is hampered by the
current uncertainties on the cluster mass calibration. In this analysis we
revisit constraints on these cosmological parameters as well as the hydrostatic
mass bias, by performing (i) a robust estimation of the tSZ power-spectrum,
(ii) a complete modeling and analysis of the tSZ bispectrum, and (iii) a
combined analysis of galaxy clusters number count, tSZ power spectrum, and tSZ
bispectrum. From this analysis, we derive as final constraints $\sigma_8 = 0.79
\pm 0.02$, $\Omega_{\rm m} = 0.29 \pm 0.02$, and $(1-b) = 0.71 \pm 0.07$. These
results favour a high value for the hydrostatic mass bias compared to numerical
simulations and weak-lensing based estimations. They are furthermore consistent
with both previous tSZ analyses, CMB derived cosmological parameters, and
ancillary estimations of the hydrostatic mass bias.