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Abstract We provide the first combined cosmological analysis of the South Pole Telescope (SPT) and Planck cluster catalogs. The aim is to provide an independent calibration for Planck scaling relations, exploiting the cosmological constraining power of the SPT-SZ cluster catalog and its dedicated weak lensing (WL) and X-ray follow-up observations. We build a new version of the Planck cluster likelihood. In the ν Λ CDM scenario, focusing on the mass slope and mass bias of Planck scaling relations, we find α SZ = 1.49 − 0.10 + 0.07 and 1 − b SZ = 0.69 − 0.14 + 0.07 , respectively. The results for the mass slope show a ∼4 σ departure from the self-similar evolution, α SZ ∼ 1.8. This shift is mainly driven by the matter density value preferred by SPT data, Ω m = 0.30 ± 0.03, lower than the one obtained by Planck data alone, Ω m = 0.37 − 0.06 + 0.02 . The mass bias constraints are consistent both with outcomes of hydrodynamical simulations and external WL calibrations, (1 − b ) ∼ 0.8, and with results required by the Planck cosmic microwave background cosmology, (1 − b ) ∼ 0.6. From this analysis, we obtain a new catalog of Planck cluster masses M 500 . We estimate the ratio between the published Planck M SZ masses and our derived masses M 500 , as a “measured mass bias,” 1 − b M . We analyze the mass, redshift, and detection noise dependence of 1 − b M , finding an increasing trend toward high redshift and low mass. These results mimic the effect of departure from self-similarity in cluster evolution, showing different dependencies for the low-mass, high-mass, low- z , and high- z regimes. 

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 3.1σdetection of gravitational lensing of the CMB by galaxy clusters to the Sunyaev–Zel’dovich (SZ) selected galaxy cluster sample from the 2500 deg²SPT-SZ survey and targeted optical and X-ray follow-up data. In the ΛCDM model, the combination of the cluster sample with the Planck power spectrum measurements prefers${\sigma }_8{\left({\mathrm{\Omega }}_m/0.3\right)}^{0.5}=0.831\pm 0.020$. Adding the cluster data reduces the uncertainty on this quantity by a factor of 1.4, which is unchanged whether the 3.1σCMB-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 statewby a factor of 1.3 toσ(w) = 0.19. We find the largest improvements from CMB-cluster lensing measurements to be forσ₈, where adding CMB-cluster lensing data to the cluster number counts reduces the expected uncertainty onσ₈by respective factors of 2.4 and 3.6 for SPT-3G and CMB-S4.