Testing approximate predictions of displacements of cosmological dark
  matter halos
  We present a test to quantify how well some approximate methods, designed to
reproduce the mildly non-linear evolution of perturbations, are able to
reproduce the clustering of DM halos once the grouping of particles into halos
is defined and kept fixed. The following methods have been considered:
Lagrangian Perturbation Theory (LPT) up to third order, Truncated LPT,
Augmented LPT, MUSCLE and COLA. The test runs as follows: halos are defined by
applying a friends-of-friends (FoF) halo finder to the output of an N-body
simulation. The approximate methods are then applied to the same initial
conditions of the simulation, producing for all particles displacements from
their starting position and velocities. The position and velocity of each halo
are computed by averaging over the particles that belong to that halo,
according to the FoF halo finder. This procedure allows us to perform a
well-posed test of how clustering of the matter density and halo density fields
are recovered, without asking to the approximate method an accurate
reconstruction of halos. We have considered the results at $z=0,0.5,1$, and we
have analysed power spectrum in real and redshift space, object-by-object
difference in position and velocity, density Probability Distribution Function
(PDF) and its moments, phase difference of Fourier modes. We find that higher
LPT orders are generally able to better reproduce the clustering of halos,
while little or no improvement is found for the matter density field when going
to 2LPT and 3LPT. Augmentation provides some improvement when coupled with
2LPT, while its effect is limited when coupled with 3LPT. Little improvement is
brought by MUSCLE with respect to Augmentation. The more expensive
particle-mesh code COLA outperforms all LPT methods [abridged]
