  We compare the non-linear matter power spectrum in real space calculated
analytically from 3rd-order perturbation theory with N-body simulations at
1<z<6. We find that the perturbation theory prediction agrees with the
simulations to better than 1% accuracy in the weakly non-linear regime where
the dimensionless power spectrum, Delta^2(k)=k^3P(k)/2pi^2, which approximately
gives variance of matter density field at a given k, is less than 0.4. While
the baryonic acoustic oscillation features are preserved in the weakly
non-linear regime at z>1, the shape of oscillations is distorted from the
linear theory prediction. Nevertheless, our results suggest that one can
correct the distortion caused by non-linearity almost exactly. We also find
that perturbation theory, which does not contain any free parameters, provides
a significantly better fit to the simulations than the conventional approaches
based on empirical fitting functions to simulations. The future work would
include perturbation theory calculations of non-linearity in redshift space
distortion and halo biasing in the weakly non-linear regime.
