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 $\mathrm{\Lambda }$CDM model. This work presents the first set of cosmological constraints derived with ~16,000 optically selected redMaPPer clusters across nearly 5,000 ${\mathrm{d}\mathrm{e}\mathrm{g}}^2$ 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 $S_8=0.864\pm 0.035$ and ${\mathrm{\Omega }}_{\mathrm{m}}=0.265_{-0.031}^{+0.019}$ from the cluster-based data vector. We find that cluster constraints and 3x2pt constraints are consistent under the $\mathrm{\Lambda }$CDM model with a Posterior Predictive Distribution (PPD) value of $0.53$. The consistency between clusters and 3x2pt provides a stringent test of $\mathrm{\Lambda }$CDM across different mass and spatial scales. Jointly analyzing clusters with 3x2pt further improves cosmological constraints, yielding $S_8=0.811_{-0.020}^{+0.022}$ and ${\mathrm{\Omega }}_{\mathrm{m}}=0.294_{-0.033}^{+0.022}$, a $24\mathrm{\%}$ improvement in the ${\mathrm{\Omega }}_{\mathrm{m}}-S_8$ 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 $S_8$ tension claims. Finally, combining DES 3x2pt, DES clusters, and Planck CMB places an upper limit on the sum of neutrino masses of $\sum m_{\nu }<0.26$ eV at 95% confidence under the $\mathrm{\Lambda }$CDM 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.