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Upcoming millimeter experiments that probe the cosmic microwave background(CMB) will observe tens of thousands of galaxy clusters through the thermalSunyaev-Zeldovich (tSZ) effect. tSZ selected clusters are powerful probes ofcosmological models, as they trace the late-time growth of structure. Late-timestructure growth is highly sensitive to extensions to the standard cosmologicalmodel ($\Lambda$CDM), such as the sum of the neutrino masses, the dark energyequation of state, and modifications to general relativity. The nominalstatistic used for cluster observations is their abundances as a function ofredshift. We investigate what additional cosmological information is gainedafter including the clustering signal of clusters, the cluster power spectrum.We forecast the cluster power spectra for the upcoming Simons Observatory and aCMB Stage-4-like experiment and find that the cluster power spectrum reducesmarginalized constraints on the dark energy equation of state by $3$--$12\%$and the growth index by $5$--$8\%$, for example. We present the constraintsusing a generalized figure of merit and find improvements ranging from$12$--$18\%$ for extensions, $12$--$19\%$ for the astrophysical nuisanceparameters, and $14$--$25\%$ for $\Lambda$CDM parameters. We also find that ifthe bias of clusters as a tracer of the matter density can be measured towithin $3\%$ or better, these improvements can be increased by up to a factorof $6$. We discuss the possibility of utilizing the clustering signal toaddress specific systematic uncertainties present in cluster abundancemeasurements.

Improving Constraints on Fundamental Physics Parameters with the Clustering of Sunyaev-Zeldovich Selected Galaxy Clusters