Dark Energy Survey Year 6 Results: Cosmological Constraints from Galaxy Clustering and Weak Lensing

We present cosmology results combining galaxy clustering and weak gravitational lensing measured in the full six years (Y6) of observations by the Dark Energy Survey (DES) covering $\sim$5000 deg${}^2$. We perform a large-scale structure analysis using three two-point correlation functions (3$\times$2pt): (i) cosmic shear from 140 million source galaxy shapes, (ii) galaxy clustering of 9 million lens galaxy positions, and (iii) galaxy-galaxy lensing from their cross-correlation. We model the data in flat $\mathrm{\Lambda }$CDM and $w$CDM cosmologies. The combined analysis yields $S_8\equiv {\sigma }_8({\mathrm{\Omega }}_{\mathrm{m}}\mathrm{/}0.3{)}^{0.5}=0.789_{-0.012}^{+0.012}$ and matter density ${\mathrm{\Omega }}_{\mathrm{m}}=0.333_{-0.028}^{+0.023}$ in $\mathrm{\Lambda }$CDM (68% CL), where ${\sigma }_8$ is the clustering amplitude. These constraints show a (full-space) parameter difference of 1.8$\sigma$ from a combination of cosmic microwave background (CMB) primary anisotropy datasets from Planck 2018, ACT-DR6, and SPT-3G DR1. Projected only into $S_8$ the difference is $2.6\sigma$. In $w$CDM the Y6 3$\times$2pt results yield $S_8=0.782_{-0.020}^{+0.021}$, ${\mathrm{\Omega }}_{\mathrm{m}}=0.325_{-0.035}^{+0.032}$, and dark energy equation-of-state parameter $w=-1.12_{-0.20}^{+0.26}$. For the first time, we combine all DES dark-energy probes: 3$\times$2pt, SNe Ia, BAO and Clusters. In $\mathrm{\Lambda }$CDM this combination yields a $2.8\sigma$ parameter difference from the CMB. When combining DES 3$\times$2pt with other low-redshift datasets (DESI DR2 BAO, DES SNe Ia, SPT clusters), we find a 2.3$\sigma$ parameter difference with CMB. A joint fit of Y6 3$\times$2pt, CMB, and those low-redshift datasets produces the tightest $\mathrm{\Lambda }$CDM constraints to date: $S_8=0.806_{-0.007}^{+0.006}$, ${\mathrm{\Omega }}_{\mathrm{m}}=0.302_{-0.003}^{+0.003}$, $h=0.683_{-0.002}^{+0.003}$, and $\sum m_{\nu }<0.14$ eV (95% CL). In $w$CDM, this combination yields $w=-0.981_{-0.022}^{+0.021}$.