# Assessing non-linear models for galaxy clustering I: unbiased growth forecasts from multipole expansion

## TL;DR

This paper evaluates the TNS model's effectiveness in using mildly non-linear scales of galaxy clustering data to accurately forecast the growth rate of cosmic structure, emphasizing the importance of multipole expansion.

## Contribution

It provides a detailed assessment of the TNS model's validity range and demonstrates how multipole expansion improves growth rate constraints in galaxy surveys.

## Key findings

- Including the hexadecapole improves constraints when scales are restricted.
- Unbiased growth rate estimates require a limited range of scales for the hexadecapole.
- Multipole expansion formalism effectively quantifies constraints and biases.

## Abstract

We assess the performance of the Taruya, Nishimichi and Saito (TNS) model for the halo redshift space power spectrum, focusing on utilising mildly non-linear scales to constrain the growth rate of structure f. Using simulations with volume and number density typical of forthcoming Stage IV galaxy surveys, we determine ranges of validity for the model at redshifts z = 0.5 and z = 1. We proceed to perform a Bayesian MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, followed by an exploratory Fisher matrix analysis. As previously noted in other forecasts as well as in real data analyses, we find that including the hexadecapole can significantly improve the constraints. However, a restricted range of scales is required for the hexadecapole in order for the growth parameter estimation to remain unbiased, limiting the improvement. We consistently quantify these effects by employing the multipole expansion formalism in both our Fisher and MCMC forecasts.