Accurate modeling for 3 times 2pt analyses in Roman and Rubin: a study of model approximations

One of the pillars of modern cosmology is the use of galaxy imaging surveys to extract information from the large-scale structure. In recent surveys, this measurement is typically performed through a 3 times 2pt analysis, which combines auto- and cross-correlations between galaxy density and galaxy weak lensing. In this paper, we carry out a systematic study of three modeling approximations commonly used in such analyses: 1) applying the Limber approximation, 2) neglecting redshift-space distortions, and 3) using less accurate models for the nonlinear matter power spectrum. We carry out the study in the context of the final data from two major Stage-IV galaxy imaging surveys: the Nancy Grace Roman Space Telescope's High Latitude Imaging Survey and the Vera C. Rubin Observatory's Legacy Survey of Space and Time. To do this, we first validate our modeling pipeline, implemented in the software package CoCoA, against an established code base, CCL. Next, we perform a simulated likelihood analysis to assess the impact of these approximations on the cosmological constraints. We find all three effects to be important; neglecting any of them can induce biases in cosmological constraints approaching or exceeding 1 sigma, and exceeding 2 sigma for Rubin in several cases. Moreover, we explore how the lens-galaxy sample configuration and scale-cut choice can influence the constraints.