Cosmological constraints from the abundance, weak lensing, and clustering of galaxy clusters: Application to the SDSS

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Aims. The clustering of galaxy clusters is a powerful cosmological tool. When it is combined with other cosmological observables, it can help to resolve parameter degeneracies and improve constraints, especially on Ωm and σ8. We aim to demonstrate its potential in constraining cosmological parameters and scaling relations when combined with cluster counts and weak-lensing mass information. As a case study, we use the redMaPPer cluster catalog derived from the Sloan Digital Sky Survey (SDSS). Methods. We extended a previous analysis of the number counts and weak-lensing signal by the two-point correlation function. We derived cosmological and scaling relation posteriors for all possible combinations of the three observables to assess their constraining power, parameter degeneracies, and possible internal tensions. Results. We find no evidence for tensions between the three data sets we analyzed. We demonstrate that the constraining power of the sample can be greatly improved by including the clustering statistics because this can break the Ωm − σ8 degeneracy that is characteristic of cluster abundance studies. In particular, for a flat ΛCDM model with massive neutrinos, we obtain Ωm = 0.28 ± 0.03 and σ8 = 0.82 ± 0.05, which is an improvement of 33% and 50% compared to the posteriors derived by combining cluster abundance and weak-lensing analyses. Our results are consistent with cosmological posteriors from other cluster surveys, and also with Planck results for the cosmic microwave background (CMB) and DES-Y3 galaxy clustering and weak-lensing analysis.