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We consistently include the effect of massive neutrinos in the thermalSunyaev Zeldovich (SZ) power spectrum and cluster counts analyses, highlightingsubtle dependencies on the total neutrino mass and data combination. Inparticular, we find that using the transfer functions for Cold Dark Matter(CDM) + baryons in the computation of the halo mass function, instead of thetransfer functions including neutrino perturbations, as prescribed in recentwork, yields a $\approx$ 0.25\% downward shift of the $\sigma_8$ constraintfrom tSZ power spectrum data, with a fiducial neutrino mass $\Sigma m_\nu=0.06$eV. In $\Lambda$CDM, with an X-ray mass bias corresponding to the expectedhydrostatic mass bias, i.e., $(1-b)\simeq0.8$, our constraints from Planck SZdata are consistent with the latest results from SPT, DES-Y1 andKiDS+VIKING-450. In $\nu\Lambda$CDM, our joint analyses of Planck SZ withPlanck 2015 primary CMB yield a small improvement on the total neutrino massbound compared to the Planck 2015 primary CMB constraint, as well as$(1-b)=0.64\pm0.04$~(68\%~CL). For forecasts, we find that competitive neutrinomass measurements using cosmic variance limited SZ power spectrum requiremasking the heaviest clusters and probing the small-scale SZ power spectrum upto $\ell_\mathrm{max}\approx10^4$. Although this is challenging, we find thatSZ power spectrum can realistically be used to tightly constrain intra-clustermedium properties: we forecast a 2\% determination of the X-ray mass bias bycombining CMB-S4 and our mock SZ power spectrum with $\ell_\mathrm{max}=10^3$.

Including massive neutrinos in thermal Sunyaev Zeldovich power spectrum and cluster counts analyses