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