  We test the ability of the numerical action method (NAM) to recover the
individual orbit histories of mass tracers in an expanding universe in a region
of radius 26Mpc/h, given the masses and redshift-space coordinates at the
present epoch. The mass tracers are represented by dark matter haloes
identified in a high resolution N-body simulation of the standard LCDM
cosmology. Since previous tests of NAM at this scale have traced the underlying
distribution of dark matter particles rather than extended haloes, our study
offers an assessment of the accuracy of NAM in a scenario which more closely
approximates the complex dynamics of actual galaxy haloes. We show that NAM can
recover present-day halo distances with typical errors of less than 3 per cent,
compared to 5 per cent errors assuming Hubble flow distances. The total halo
mass and the linear bias were both found to be constained at the 50 per cent
level. The accuracy of individual orbit reconstructions was limited by the
inability of NAM, in some instances, to correctly model the positions of haloes
at early times solely on the basis of the redshifts, angular positions, and
masses of the haloes at the present epoch. Improvements in the quality of NAM
reconstructions may be possible using the present-day three-dimensional halo
velocities and distances to further constrain the dynamics. This velocity data
is expected to become available for nearby galaxies in the coming generations
of observations by SIM and GAIA.
