Improving Constraints on Fundamental Physics Parameters with the
  Clustering of Sunyaev-Zeldovich Selected Galaxy Clusters
  Upcoming millimeter experiments that probe the cosmic microwave background
(CMB) will observe tens of thousands of galaxy clusters through the thermal
Sunyaev-Zeldovich (tSZ) effect. tSZ selected clusters are powerful probes of
cosmological models, as they trace the late-time growth of structure. Late-time
structure growth is highly sensitive to extensions to the standard cosmological
model ($\Lambda$CDM), such as the sum of the neutrino masses, the dark energy
equation of state, and modifications to general relativity. The nominal
statistic used for cluster observations is their abundances as a function of
redshift. We investigate what additional cosmological information is gained
after including the clustering signal of clusters, the cluster power spectrum.
We forecast the cluster power spectra for the upcoming Simons Observatory and a
CMB Stage-4-like experiment and find that the cluster power spectrum reduces
marginalized constraints on the dark energy equation of state by $3$--$12\%$
and the growth index by $5$--$8\%$, for example. We present the constraints
using a generalized figure of merit and find improvements ranging from
$12$--$18\%$ for extensions, $12$--$19\%$ for the astrophysical nuisance
parameters, and $14$--$25\%$ for $\Lambda$CDM parameters. We also find that if
the bias of clusters as a tracer of the matter density can be measured to
within $3\%$ or better, these improvements can be increased by up to a factor
of $6$. We discuss the possibility of utilizing the clustering signal to
address specific systematic uncertainties present in cluster abundance
measurements.
