  We implement EuclidEmulator (version 1), an emulator for the non-linear
correction of the matter power spectrum, into the MCMC forecasting code
MontePython. We compare the performance of Halofit, HMCode, and
EuclidEmulator1, both at the level of power spectrum prediction and at the
level of posterior probability distributions of the cosmological parameters,
for different cosmological models and different galaxy power spectrum wave
number cut-offs. We confirm that the choice of the power spectrum predictor has
a non-negligible effect on the computed sensitivities when doing cosmological
parameter forecasting, even for a conservative wave number cut-off of
$0.2\,h\,{\rm Mpc}^{-1}$. We find that EuclidEmulator1 is on average up to
$17\%$ more sensitive to the cosmological parameters than the other two codes,
with the most significant improvements being for the Hubble parameter of up to
$42\%$ and the equation of state of dark energy of up to $26\%$, depending on
the case. In addition, we point out that the choice of the power spectrum
predictor contributes to the risk of computing a significantly biased mean
cosmology when doing parameter estimations. For the four tested scenarios we
find biases, averaged over the cosmological parameters, of between 0.5 and
2$\sigma$ (from below $1\sigma$ up to $6\sigma$ for individual parameters).
This paper provides a proof of concept that this risk can be mitigated by
taking a well-tailored theoretical uncertainty into account as this allows to
reduce the bias by a factor of 2 to 5, depending on the case under
consideration, while keeping posterior credibility contours small: the standard
deviations are amplified by a factor of $\leq1.4$ in all cases.
