# The Full-Sky Angular Bispectrum in Redshift Space

## TL;DR

This paper presents a comprehensive calculation of the full-sky angular bispectrum of galaxy counts in redshift space, incorporating nonlinear bias and redshift space distortions, with implications for future large-scale structure analyses.

## Contribution

It introduces a novel formalism for computing the full-sky angular bispectrum including RSD and nonlinear bias, extending previous flat-sky and simplified models.

## Key findings

- Nonlinear RSD effects are comparable to matter density perturbations in narrow redshift bins.
- The formalism accurately models the bispectrum without flat-sky approximation.
- Differences between galaxy number counts and CMB bispectra are highlighted.

## Abstract

We compute the redshift-dependent angular bispectrum of galaxy number counts at tree-level, including nonlinear clustering bias and estimating numerically for the first time the effect of redshift space distortions (RSD). We show that for narrow redshift bins the amplitude of nonlinear RSD is comparable with the matter density perturbations. While our numerical results only include terms relevant on sub-horizon scales, the formalism can readily be extended to the full tree-level bispectrum. Our approach does not rely on the flat-sky approximation and it can be easily generalized to different sources by including the appropriate bias expansion. We test the accuracy of Limber approximation for different z-bins. We highlight the subtle but relevant differences in the angular bispectrum of galaxy number counts with respect to CMB, due to the different scale dependence of perturbations. Our formalism can also be directly applied to the angular HI intensity mapping bispectrum.