6x2pt: Forecasting gains from joint weak lensing and galaxy clustering analyses with spectroscopic-photometric galaxy cross-correlations

Abstract

We explore the enhanced self-calibration of photometric galaxy redshift distributions, $n(z)$, through the combination of up to six two-point functions. Our $3\times 2pt$ 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 $6\times 2pt$ analysis gains $\sim 40\%$ in Figure of Merit (FoM) in the $S_8\equiv \ddot{I}{ƒ}_8\sqrt{\hat{I}{\text{c◯}}_{\mathrm{m}}/0.3}$ and $\hat{I}{\text{c◯}}_{\mathrm{m}}$ plane relative to the $3\times 2pt$ analysis. If untreated, coherent and incoherent redshift errors lead to inaccurate inferences of $S_8$ and $\hat{I}{\text{c◯}}_{\mathrm{m}}$, respectively. Employing bin-wise scalar shifts $\hat{I}´z_i$ 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 $3^{\mathrm{ph}}\times 2pt$ analysis. For the Stage-IV-like survey, a $6\times 2pt$ analysis doubles the FoM($\ddot{I}{ƒ}_8-\hat{I}{\text{c◯}}_{\mathrm{m}}$) compared to any $3\times 2pt$ or $3^{\mathrm{ph}}\times 2pt$ 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 $N\times 2pt$ configuration given $n(z)$ biases.

38 pages, 20 figures, to be submitted to A&A