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In modern cosmology, the precision of the theoretical prediction isincreasingly required. In cosmological $N$-body simulations, the effect ofhigher-order Lagrangian perturbation on the initial conditions appears in termsof statistical quantities of matter density field. We have considered theeffect of third-order Lagrangian perturbation (3LPT) on the initial conditions,which can be applied to Gadget-2 code. Then, as statistical quantities,non-Gaussianity of matter density field has been compared between cases ofdifferent order perturbations for the initial conditions. Then, we demonstratethe validity of the initial conditions with second-order Lagrangianperturbation (2LPT).

Transients from Initial Conditions Based on Lagrangian Perturbation Theory in $N$-body Simulations III: The Case of GADGET-2 Code