Improving Cosmological Constraints from Galaxy Cluster Number Counts with CMB-cluster-lensing Data: Results from the SPT-SZ Survey and Forecasts for the Future

We show the improvement to cosmological constraints from galaxy cluster surveys with the addition of cosmic microwave background (CMB)-cluster lensing data. We explore the cosmological implications of adding mass information from the 3.1 sigma detection of gravitational lensing of the CMB by galaxy clusters to the Sunyaev-Zel'dovich (SZ) selected galaxy cluster sample from the 2500 deg(2) SPT-SZ survey and targeted optical and X-ray follow-up data. In the ACDM model, the combination of the cluster sample with the Planck power spectrum measurements prefers sigma(8) (Omega(m)/0.3)(0.5) = 0.831 +/- 0.020. Adding the cluster data reduces the uncertainty on this quantity by a factor of 1.4, which is unchanged whether the 3.1 sigma CMB-cluster lensing measurement is included or not. We then forecast the impact of CMB-cluster lensing measurements with future cluster catalogs. Adding CMB-cluster lensing measurements to the SZ cluster catalog of the ongoing SPT-3G survey is expected to improve the expected constraint on the dark energy equation of state w by a factor of 1.3 to sigma(w) = 0.19. We find the largest improvements from CMB-cluster lensing measurements to be for sigma(8), where adding CMB-cluster lensing data to the cluster number counts reduces the expected uncertainty on sigma(8) by respective factors of 2.4 and 3.6 for SPT-3G and CMB-S4.