Assessing the Importance of Noise from Thermal Sunyaev-Zel{'}dovich Signals for CMB Cluster Surveys and Cluster Cosmology

We explore the significance of noise from thermal Sunyaev-Zel{'}dovich (tSZ) signals for cluster detection using cosmic microwave background (CMB) surveys. The noise arises both from neighboring objects and also from haloes below the detection limit. A wide range of surveys are considered: SPT-SZ, SPTpol, and SPT-3G from the South Pole Telescope; SO-Baseline and SO-Goal configurations for Simons Observatory; CMB-S4's wide area (S4-Wide) and deep (S4-Ultra deep) surveys; and the futuristic CMB-HD experiment. We find that the noise from tSZ signals has a significant impact on CMB-HD and to some extent on S4-Ultra deep. For other experiments, the effect is negligible as the noise in the tSZ map is dominated by residual foregrounds or experimental noise. In the limit when the noise from tSZ signals is important, we find that removing the detected clusters and rerunning the cluster finder allows us to find a new set of less massive and distant clusters. Since the detected clusters are the dominant source of the tSZ power, removing them reduces the power at $\ell=3000$ by: $\times5$ for CMB-HD; $\times3.1$ of S4-Ultra deep; $\times2.4$ for S4-Wide and SPT-3G; $\times1.5$ for SO-Goal and SPTpol; $\times1.35$ for SO-Baseline; and $\times1.08$ for SPT-SZ. We forecast the expected number of clusters and also derive parameter constraints by combining cluster counts with primary CMB and tSZ power spectra finding that the future surveys can reduce the error on the dark energy equation of state parameter to sub-percent levels and can also enable $\ge3\sigma$ detection of the sum of neutrino masses. The simulation products and results can be downloaded from https://github.com/sriniraghunathan/tSZ_cluster_forecasts.