Cosmological constraints from the Planck cluster catalogue with DES shear profiles and Chandra observations

We present cosmological constraints from the Planck PSZ2 cosmological cluster sample, using weak-lensing shear profiles from Dark Energy Survey (DES) data and X-ray observations from the Chandra telescope for the mass calibration. We compute hydrostatic mass estimates for all clusters in the PSZ2 sample with a scaling relation between their Sunyaev-Zeldovich signal and X-ray derived hydrostatic mass, calibrated with the Chandra data. We introduce a method to correct these masses with a hydrostatic mass bias using shear profiles from wide-field galaxy surveys. We simultaneously fit the number counts of the PSZ2 sample and the mass calibration with the DES data, finding $\Omega_\text{m}=0.312^{+0.018}_{-0.024}$, $\sigma_8=0.777\pm 0.024$, $S_8\equiv \sigma_8 \sqrt{\Omega_\text{m} / 0.3}=0.791^{+0.023}_{-0.021}$, and $(1-b)=0.844^{+0.055}_{-0.062}$ for our baseline analysis when combined with BAO data. When considering a hydrostatic mass bias evolving with mass, we find $\Omega_\text{m}=0.353^{+0.025}_{-0.031}$, $\sigma_8=0.751\pm 0.023$, and $S_8=0.814^{+0.019}_{-0.020}$. We verify the robustness of our results by exploring a variety of analysis settings, with a particular focus on the definition of the halo centre used for the extraction of shear profiles. We compare our results with a number of other analyses, in particular two recent analyses of cluster samples obtained from SPT and eROSITA data that share the same mass calibration data set. We find that our results are in overall agreement with most late-time probes, in very mild tension with CMB results (1.6$\sigma$), and in significant tension with results from eROSITA clusters (2.9$\sigma$). We confirm that our mass calibration is consistent with the eROSITA analysis by comparing masses for clusters present in both Planck and eROSITA samples, eliminating it as a potential cause of tension.