Title: Theoretical Accuracy in Cosmological Growth Estimation,
Abstract: We elucidate the importance of the consistent treatment of gravity-model
specific non-linearities when estimating the growth of cosmological structures
from redshift space distortions (RSD). Within the context of standard
perturbation theory (SPT), we compare the predictions of two theoretical
templates with redshift space data from COLA (COmoving Lagrangian Acceleration)
simulations in the normal branch of DGP gravity (nDGP) and General Relativity
(GR). Using COLA for these comparisons is validated using a suite of full
N-body simulations for the same theories. The two theoretical templates
correspond to the standard general relativistic perturbation equations and
those same equations modelled within nDGP. Gravitational clustering non-linear
effects are accounted for by modelling the power spectrum up to one loop order
and redshift space clustering anisotropy is modelled using the Taruya,
Nishimichi and Saito (TNS) RSD model. Using this approach, we attempt to
recover the simulation's fiducial logarithmic growth parameter $f$. By
assigning the simulation data with errors representing an idealised survey with
a volume of $10\mbox{Gpc}^3/h^3$, we find the GR template is unable to recover
fiducial $f$ to within 1$\sigma$ at $z=1$ when we match the data up to $k_{\rm
max}=0.195h$/Mpc. On the other hand, the DGP template recovers the fiducial
value within $1\sigma$. Further, we conduct the same analysis for sets of mock
data generated for generalised models of modified gravity using SPT, where
again we analyse the GR template's ability to recover the fiducial value. We
find that for models with enhanced gravitational non-linearity, the theoretical
bias of the GR template becomes significant for stage IV surveys. Thus, we show
that for the future large data volume galaxy surveys, the self-consistent
modelling of non-GR gravity scenarios will be crucial in constraining theory
parameters.