6X2pt: Forecasting Gains from Joint Weak Lensing and Galaxy Clustering Analyses with Spectroscopic-Photometric Galaxy Cross-Correlations

We explore the enhanced self-calibration of photometric galaxy redshift distributions, n(z), through the combination of up to six two-point functions. Our 3×2pt configuration is comprised of photometric shear, spectroscopic galaxy clustering, and spectroscopic-photometric galaxy-galaxy lensing (GGL). We further include spectroscopic-photometric cross-clustering; photometric GGL; and photometric auto-clustering, using the photometric shear sample as density tracer. We perform simulated likelihood forecasts of the cosmological and nuisance parameter constraints for Stage-III- and Stage-IV-like surveys. For the Stage-III-like case, we employ realistic but perturbed redshift distributions, and distinguish between "coherent" shifting in one direction, versus more internal scattering and full-shape errors. For perfectly known n(z), a 6×2pt analysis gains ∼40% in Figure of Merit (FoM) in the S_8≡σ_8√(Ω_ m/0.3) and Ω_ m plane relative to the 3×2pt analysis. If untreated, coherent and incoherent redshift errors lead to inaccurate inferences of S_8 and Ω_ m, respectively. Employing bin-wise scalar shifts δz_i in the tomographic mean redshifts reduces cosmological parameter biases, with a 6x2pt analysis constraining the shift parameters with 2-4 times the precision of a photometric 3^ph×2pt analysis. For the Stage-IV-like survey, a 6×2pt analysis doubles the FoM(σ_8-Ω_ m) compared to any 3×2pt or 3^ph×2pt analysis, and is only 8% less constraining than if the n(z) were perfectly known. A Gaussian mixture model for the n(z) reduces mean-redshift errors and preserves the n(z) shape. It also yields the most accurate and precise cosmological constraints for any N×2pt configuration given n(z) biases.