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.
