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In the near future, the overlap of the Rubin Observatory Legacy Survey ofSpace and Time (LSST) and the Simons Observatory (SO) will present an idealopportunity for joint cosmological dataset analyses. In this paper we simulatethe joint likelihood analysis of these two experiments using six two-pointfunctions derived from galaxy position, galaxy shear, and CMB lensingconvergence fields. Our analysis focuses on realistic noise and systematicsmodels and we find that the dark energy Figure-of-Merit (FoM) increases by 53%(92%) from LSST-only to LSST+SO in Year 1 (Year 6). We also investigate thebenefits of using the same galaxy sample for both clustering and lensinganalyses, and find the choice improves the overall signal-to-noise by ~30-40%,which significantly improves the photo-z calibration and mildly improves thecosmological constraints. Finally, we explore the effects of catastrophicphoto-z outliers finding that they cause significant parameter biases whenignored. We develop a new mitigation approach termed "island model", whichcorrects a large fraction of the biases with only a few parameters whilepreserving the constraining power.

Cosmology from Clustering, Cosmic Shear, CMB Lensing, and Cross Correlations: Combining Rubin Observatory and Simons Observatory