Constraining baryonic feedback and cosmology from DES Y3 and Planck PR4 6$\times$2pt data. I. $\Lambda$CDM models

We combine weak lensing, galaxy clustering, cosmic microwave background (CMB) lensing, and their cross-correlations (so-called 6$\times$2pt) to constrain cosmology and baryonic feedback scenarios using data from the Dark Energy Survey (DES) Y3 Maglim catalog and the Planck satellite PR4 data release. We include all data points in the DES Y3 cosmic shear two-point correlation function (2PCF) down to 2.$^\prime$5 and model baryonic feedback processes via principal components (PCs) that are constructed from the ANTILLES simulations. We find a tight correlation between the amplitude of the first PC $Q_1$ and mean normalized baryon mass fraction $\bar{Y_\mathrm{b}}=\bar{f}_\mathrm{b}/(\Omega_\mathrm{b}/\Omega_\mathrm{m})$ from the ANTILLES simulations and employ an independent $\bar{Y_\mathrm{b}}$ measurement from Akino et al. (2022) as a prior of $Q_1$. We train a neural network $6\times2$pt emulator to boost the analysis speed by $\mathcal{O}(10^3)$, which enables us to run an impressive number of simulated analyses to validate our analysis against various systematics. For our 6$\times$2pt analysis, we find $S_8=0.8073\pm0.0094$ when including a $Q_1$ prior from $\bar{Y_\mathrm{b}}$ observations. This level of cosmological constraining power allows us to put tight constraints on the strength of baryonic feedback. We find $Q_1=0.025^{+0.024}_{-0.029}$ for our 6$\times$2pt analysis and $Q_1=0.043\pm{0.016}$ when combining with external information from Planck, ACT, DESI. All these results indicate weak feedback, e.g., the tensions to Illustris ($Q_1=0.095$) and OWLS AGN T8.7 ($Q_1=0.137$) are 2.9$\sigma$-3.3$\sigma$ and 4.7$\sigma$-5.9$\sigma$, respectively.