Lagrangian Perturbation Theory : Exact One-Loop Power Spectrum in
  General Dark Energy Models
  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 \cite{LPB}. 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 $\Omega_{m0} = 0.25 (0.3)$ to
obtain about 0.2 (0.18) \% error correction compared to that obtained from the
EdS assumption for $k = 0.1 \rm{h\, Mpc}^{-1}$ 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.
