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.