Improving Photometric Galaxy Clustering Constraints With Cross-Bin Correlations

Clustering studies in current photometric galaxy surveys focus solely on auto-correlations, neglecting cross-correlations between redshift bins. We evaluate the potential advantages and drawbacks of incorporating cross-bin correlations in Fisher forecasts for the Dark Energy Survey (DES) and the forthcoming Rubin Observatory Legacy Survey of Space and Time (LSST). Our analysis considers the impact of including redshift space distortions (RSD) and magnification in model predictions, as well as systematic uncertainties in photometric redshift distributions (photo-$z$). While auto-correlations alone suffer from a degeneracy between the amplitude of matter fluctuations ($\sigma_8$) and galaxy bias parameters, accounting for RSD and magnification in cross-correlations helps break this degeneracy - although more weakly than the degeneracy breaking expected from a combined analysis with other observables. Incorporating cross-bin correlations does not significantly increase sensitivity to photo-$z$ systematics, addressing previous concerns, and self-calibrates photo-$z$ systematics, reducing errors on photo-$z$ nuisance parameters. We suggest that the benefits of including cross-correlations in future photometric galaxy clustering analyses outweigh the risks, but caution that careful evaluation is necessary as more realistic pictures of surveys' precision and systematic error budgets develop.