# Assessing non-linear models for galaxy clustering II: model validation and forecasts for Stage IV surveys

## TL;DR

This paper compares two non-linear galaxy clustering models, the TNS and EFTofLSS, using simulations and statistical analyses to determine their validity and forecast their effectiveness for future galaxy surveys.

## Contribution

It provides a comprehensive validation and comparison of the TNS and EFTofLSS models for galaxy clustering, including forecasts for Stage IV surveys and a novel comparison of Fisher and MCMC methods.

## Key findings

- TNS model with Lorentzian damping performs best among variants.
- EFTofLSS model may yield tighter constraints on growth rate $f$ at certain redshifts.
- Good agreement found between Fisher matrix and MCMC forecasts.

## Abstract

Accurate modelling of non-linear scales in galaxy clustering will be crucial for data analysis of Stage IV galaxy surveys. A selection of competing non-linear models must be made based on validation studies. We provide a comprehensive set of forecasts of two different models for the halo redshift space power spectrum, namely the commonly applied TNS model and an effective field theory of large scale structure (EFTofLSS) inspired model. Using simulation data and a least-$\chi^2$ analysis, we determine ranges of validity for the models. We then conduct an exploratory Fisher analysis using the full anisotropic power spectrum to investigate parameter degeneracies. We proceed to perform an MCMC analysis utilising the monopole, quadrupole, and hexadecapole spectra, with a restricted range of scales for the latter in order to avoid biasing our growth rate, $f$, constraint. We find that the TNS model with a Lorentzian damping and standard Eulerian perturbative modelling outperforms other variants of the TNS model. Our MCMC analysis finds that the EFTofLSS-based model may provide tighter marginalised constraints on $f$ at $z=0.5$ and $z=1$ than the TNS model, despite having additional nuisance parameters. However this depends on the range of scales used as well as the fiducial values and priors on the EFT nuisance parameters. Finally, we extend previous work to provide a consistent comparison between the Fisher matrix and MCMC forecasts using the multipole expansion formalism, and find good agreement between them.