# Wide-angle redshift-space distortions at quasi-linear scales: cross-correlation functions from Zel'dovich approximation

## TL;DR

This paper develops a quasi-linear model for wide-angle redshift-space distortions using the Zel'dovich approximation, improving upon linear theory and enabling future inclusion of relativistic effects in galaxy survey analyses.

## Contribution

It introduces a novel quasi-linear approach based on the Zel'dovich approximation for modeling wide-angle RSD in galaxy surveys, extending beyond linear perturbation theory.

## Key findings

- Reproduces linear theory results accurately
- Provides a framework for incorporating relativistic corrections
- Enhances modeling of wide-angle RSD in future surveys

## Abstract

Redshift-space distortions (RSD) in galaxy redshift surveys generally break both the isotropy and homogeneity of galaxy distribution. While the former aspect is particularly highlighted as a probe of growth of structure induced by gravity, the latter aspect, often quoted as wide-angle RSD but ignored in most of the cases, will become important and critical to account for as increasing the statistical precision in next-generation surveys. However, the impact of wide-angle RSD has been mostly studied using linear perturbation theory. In this paper, employing the Zel'dovich approximation, i.e., first-order Lagrangian perturbation theory for gravitational evolution of matter fluctuations, we present a quasi-linear treatment of wide-angle RSD, and compute the cross-correlation function. The present formalism consistently reproduces linear theory results, and can be easily extended to incorporate relativistic corrections (e.g., gravitational redshift).