The Dark Energy Camera All Data Everywhere cosmic shear project V: Constraints on cosmology and astrophysics from 270 million galaxies across 13,000 deg$^2$ of the sky
We present constraints on models of cosmology and astrophysics using cosmic shear data vectors from three datasets: the northern and southern Galactic cap of the Dark Energy Camera All Data Everywhere (DECADE) project, and the Dark Energy Survey (DES) Year 3. These data vectors combined consist of 270 million galaxies spread across 13,000 ${\rm deg}^2$ of the sky. We first extract constraints for $\Lambda$CDM cosmology and find $S_8= 0.805^{+0.019}_{-0.019}$ and $\Omega_{\rm m} = 0.262^{+0.023}_{-0.036}$, which is consistent within $1.9 \sigma$ of constraints from the Planck satellite. Extending our analysis to dynamical dark energy models shows that lensing provides some (but still minor) improvements to existing constraints from supernovae and baryon acoustic oscillations. Finally, we study six different models for the impact of baryons on the matter power spectrum. We show the different models provide consistent constraints on baryon suppression, and associated cosmology, once the astrophysical priors are sufficiently wide. Current scale-cut approaches for mitigating baryon contamination result in a residual bias of $\approx 0.3\sigma$ in the $S_8, \Omega_{\rm m}$ posterior. Using all scales with dedicated baryon modeling leads to negligible improvement as the new information is used solely to self-calibrate the baryon model on small scales. Additional non-lensing datasets, and/or calibrations of the baryon model, will be required to access the full statistical power of the lensing measurements. The combined dataset in this work represents the largest lensing dataset to date (most galaxies, largest area) and provides an apt testing ground for analyses of upcoming datasets from Stage IV surveys. The DECADE shear catalogs, data vectors, and likelihoods are made publicly available.