Assessing non-linear models for galaxy clustering III: Theoretical
  accuracy for Stage IV surveys
  We provide in depth MCMC comparisons of two different models for the halo
redshift space power spectrum, namely a variant of the commonly applied
Taruya-Nishimichi-Saito (TNS) model and an effective field theory of large
scale structure (EFTofLSS) inspired model. Using many simulation realisations
and Stage IV survey-like specifications for the covariance matrix, we check
each model's range of validity by testing for bias in the recovery of the
fiducial growth rate of structure formation. The robustness of the determined
range of validity is then tested by performing additional MCMC analyses using
higher order multipoles, a larger survey volume and a more highly biased tracer
catalogue. We find that under all tests, the TNS model's range of validity
remains robust and is found to be much higher than previous estimates. The
EFTofLSS model fails to capture the spectra for highly biased tracers as well
as becoming biased at higher wavenumbers when considering a very large survey
volume. Further, we find that the marginalised constraints on $f$ for all
analyses are stronger when using the TNS model.
