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 ^ { 3 } P ( k ) / 2 \pi ^ { 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 .