  Next generation large scale surveys probe the nonlinear regime with high
resolution. Making viable cosmological inferences based on these observations
requires accurate theoretical modeling of the mildly nonlinear regime. In this
work we investigate the sensitivity of cosmological parameter measurements from
future probes of galaxy clustering to the choice of nonlinear prescription up
to $k_{\rm max}=0.3~h~\rm{Mpc}^{-1}$. In particular, we calculate the induced
parameter bias when the mildly nonlinear regime is modeled by the Halofit
fitting scheme. We find significant ($\sim5\sigma$) bias for some parameters
with a future Euclid-like survey. We also explore the contribution of different
scales to the parameter estimation for different observational setups and
cosmological scenarios, compared for the two nonlinear prescriptions of Halofit
and EFTofLSS. We include in the analysis the free parameters of the nonlinear
theory and a blind parametrization for the galaxy bias. We find that
marginalization over these nuisance parameters significantly boosts the errors
of the standard cosmological parameters. This renders the differences in the
predictions of the various nonlinear prescriptions less effective when
transferred to the parameter space. More accurate modeling of these nuisance
parameters would therefore greatly enhance the cosmological gain from the
mildly nonlinear regime.
