# Unequal time correlators and the Zeldovich approximation

## TL;DR

This paper demonstrates that the Zeldovich approximation accurately models unequal time correlators in cosmology, validated against simulations, and discusses its implications for galaxy survey observations and intrinsic alignments.

## Contribution

It introduces a simple analytical method using the Zeldovich approximation to predict unequal time correlators, extending modeling into the nonlinear regime.

## Key findings

- Zeldovich approximation yields <10% accuracy for unequal time correlators.
- It extends accurate predictions into the nonlinear regime.
- Unequal time correlators are generally suppressed by lightcone geometry, but may matter for intrinsic alignments.

## Abstract

The modeling of cosmological observables is based on the statistics of the matter density, velocity and gravitational fields in the Universe as a function of time. Typically, calculations are restricted to equal time correlations, where any given fields are evaluated at the same redshift. For some applications, it is necessary to make accurate predictions of unequal time correlators, where the fields considered are evaluated at different redshifts. In this work, we show that the Zeldovich approximation provides an accurate (<10%) analytical prescription to model unequal time correlators, which we validate against numerical N-body simulations. The Zeldovich approximation introduces a scale-dependent exponential suppression of unequal time correlators, which depends on cosmology and the redshifts of the fields considered. Comparing the Zeldovich case to previous approximations, we show that it can yield accurate predictions for wavenumbers that extend well into the nonlinear regime. However, we also show that correlations over such scales are typically suppressed by the geometry of the lightcone, and thus should normally be negligible for cosmology with galaxy surveys. We discuss potential exceptions, such as intrinsic galaxy alignments, where unequal time correlators could play a role in the modeling of the observables.