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Thermal Sunyaev-Zeldovich (tSZ) power spectrum is one of the most sensitivemethods to constrain cosmological parameters, scaling as the amplitude$\sigma_8^8$. It is determined by the integral over the halo mass functionmultiplied by the total pressure content of clusters, and further convolved bythe cluster gas pressure profile. It has been shown that various feedbackeffects can change significantly the pressure profile, possibly even pushingthe gas out to the virial radius and beyond, strongly affecting the tSZ powerspectrum at high $l$. Energetics arguments and SZ-halo mass scaling relationssuggest feedback is unlikely to significantly change the total pressurecontent, making low $l$ tSZ power spectrum more robust against feedbackeffects. Furthermore, the separation between the cosmic infrared background(CIB) and tSZ is more reliable at low $l$. Low $l$ modes are however probingvery small volumes, giving rise to very large non-gaussian sampling varianceerrors. By computing the trispectrum contribution we identify $90<l<350$ as theminimum variance scale where the combined error is minimized. Using themeasurement at this $l$ provides constraints that are almost as strong as usingthe entire power spectrum. We extend the work by the Planck collaboration byincluding a full trispectrum and feedback effects in the analysis. We perform aMarkov-Chain Monte Carlo analysis over the two dimensional parameter space andfind constraints on $\sigma_8$ by marginalizing over the feedback nuisanceparameter.We obtain $\sigma_8=0.820^{+0.021}_{-0.009}\left(\Omega_m/0.31\right)^{0.4}$, when fixing otherparameters to Planck cosmology values. Our results suggest it is possible toobtain competitive cosmological constraints from tSZ without cluster redshiftinformation, and that the current tSZ power spectrum shows no evidence for alow amplitude of $\sigma_8$.

Cosmological constraints from thermal Sunyaev Zeldovich power spectrum revisited