Recently , we find that the correction for the EdS assumption on the one-loop matter power spectrum for general dark energy models using the standard perturbation theory is not negligible ( ( 1 ) ) .
Thus , we investigate the same problem by obtaining the exact displacement vector and kernels up to the third order for the general dark energy models in the Lagrangian perturbation theory ( LPT ) .
Using these exact solutions , we investigate the present one-loop matter power spectrum in the \Lambda CDM model with \Omega _ { m 0 } = 0.25 ( 0.3 ) to obtain about 0.2 ( 0.18 ) % error correction compared to that obtained from the EdS assumption for k = 0.1 h Mpc ^ { -1 } mode .
If we consider the total matter power spectrum , the correction is only 0.05 ( 0.03 ) % for the same mode .
It means that EdS assumption is a good approximation for \Lambda CDM model in LPT theory .
However , one can use this method for general models where EdS assumption is improper .