Cosmology from weak lensing, galaxy clustering, CMB lensing and tSZ: I. 10x2pt Modelling Methodology

The overlap of galaxy surveys and CMB experiments presents an ideal opportunity for joint cosmological dataset analyses. In this paper we develop a halo-model-based method for the first joint analysis combining these two experiments using 10 correlated two-point functions (10x2pt) derived from galaxy position, galaxy shear, CMB lensing convergence, and Compton-y fields. We explore this method using the Vera Rubin Observatory Legacy Survey of Space and Time (LSST) and the Simons Observatory (SO) as examples. We find such LSSxCMB joint analyses lead to significant improvement in Figure-of-Merit of $\Omega_m$ and $S_8$ over the constraints from using LSS-only probes within $\Lambda$CDM. We identify that the shear-$y$ and $y$-$y$ correlations are the most valuable additions when tSZ is included. We further identify the dominant sources of halo model uncertainties in the small-scale modelling, and investigate the impact of halo self-calibration due to the inclusion of small-scale tSZ information.

Comment: 12 pages, 9 figures, to be submitted. Comments are welcome