Transients from initial conditions based on Lagrangian perturbation
  theory in $N$-body simulations II: the effect of the transverse mode
  We study the initial conditions for cosmological $N$-body simulations for
precision cosmology. In general, Zel'dovich approximation has been applied for
the initial conditions of $N$-body simulations for a long time. These initial
conditions provide incorrect higher-order growth. These error caused by setting
up the initial conditions by perturbation theory is called transients. We
investigated the impact of transient on non-Gaussianity of density field by
performing cosmological $N$-body simulations with initial conditions based on
first-, second-, and third-order Lagrangian perturbation theory in previous
paper. In this paper, we evaluates the effect of the transverse mode in the
third-order Lagrangian perturbation theory for several statistical quantities
such as power spectrum, non-Gaussianty, and multifractal dimensions. Then we
clarified that the effect of the transverse mode in the third-order Lagrangian
perturbation theory is quite small.
