  We study the impact of setting initial conditions in numerical simulations
using the standard procedure based on the Zel'dovich approximation (ZA). As it
is well known from perturbation theory, ZA initial conditions have incorrect
second and higher-order growth and therefore excite long-lived transients in
the evolution of the statistical properties of density and velocity fields. We
also study the improvement brought by using more accurate initial conditions
based on second-order Lagrangian perturbation theory (2LPT). We show that 2LPT
initial conditions reduce transients significantly and thus are much more
appropriate for numerical simulations devoted to precision cosmology. Using
controlled numerical experiments with ZA and 2LPT initial conditions we show
that simulations started at redshift z_i=49 using the ZA underestimate the
power spectrum in the nonlinear regime by about 2,4,8 % at z=0,1,3
respectively, whereas the mass function of dark matter halos is underestimated
by 5% at m=10^15 M_sun/h (z=0) and 10% at m=2x10^14M_sun/h (z=1). The
clustering of halos is also affected to the few percent level at z=0. These
systematics effects are typically larger than statistical uncertainties in
recent mass function and power spectrum fitting formulae extracted from
numerical simulations. At large scales, the measured transients in higher-order
correlations can be understood from first principle calculations based on
perturbation theory.
