Dark energy survey year 3 results: Cosmological constraints from cluster abundances, weak lensing, and galaxy clustering

Galaxy clusters provide a unique probe of the late-time cosmic structure and serve as a powerful independent test of the ΛCDM model. This work presents the first set of cosmological constraints derived with ~16,000 optically selected redMaPPer clusters across nearly 5,000 deg² using DES Year 3 data sets. Our analysis leverages a consistent modeling framework for galaxy cluster cosmology and DES-Y3 joint analyses of galaxy clustering and weak lensing (3x2pt), ensuring direct comparability with the DES-Y3 3x2pt analysis. We obtain constraints of S₈ = 0.864 ± 0.035 and Ωₘ = 0.265+0.019-0.031 from the cluster-based data vector. We find that cluster constraints and 3x2pt constraints are consistent under the ΛCDM model with a Posterior Predictive Distribution (PPD) value of $0.53$. The consistency between clusters and 3x2pt provides a stringent test of ΛCDM across different mass and spatial scales. Jointly analyzing clusters with 3x2pt further improves cosmological constraints, yielding S₈ = 0.811+0.022-0.020 and Ωₘ = 0.294+0.022-0.033, a $24%$ improvement in the Ωₘ-S₈ figure-of-merit over 3x2pt alone. Moreover, we find no significant deviation from the Planck CMB constraints with a probability to exceed (PTE) value of $0.6$, significantly reducing previous S₈ tension claims. Finally, combining DES 3x2pt, DES clusters, and Planck CMB places an upper limit on the sum of neutrino masses of ∑ m_ν<0.26 eV at 95% confidence under the ΛCDM model. These results establish optically selected clusters as a key cosmological probe and pave the way for cluster-based analyses in upcoming Stage-IV surveys such as LSST, Euclid, and Roman.