Cosmology from weak lensing, galaxy clustering, CMB lensing, and tSZ – I. 10 × 2pt modelling methodology

The overlap of galaxy surveys and cosmic microwave background (CMB) experiments presents an ideal opportunity for joint cosmological data set 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 (10 × 2pt) 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 LSS × CMB joint analyses lead to significant improvement in Figure-of-Merit of Ω_m and S₈ over the constraints from using LSS-only probes within л cold dark matter (лCDM) model. We identify that the shear–y and y–y correlations are the most valuable additions when thermal Sunyaev–Zel’dolvich (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.