Trajectories of point particles in cosmology and the Zel'dovich
  approximation
  Using a Green's function approach, we compare the trajectories of classical
Hamiltonian point particles in an expanding space-time to the effectively
inertial trajectories in the Zel'dovich approximation. It is shown that the
effective gravitational potential accelerating the particles relative to the
Zel'dovich trajectories vanishes exactly initially as a consequence of the
continuity equation, and acts only during a short, early period. The Green's
function approach suggests an iterative scheme for improving the Zel'dovich
trajectories, which can be analytically solved. We construct these trajectories
explicitly and show how they interpolate between the Zel'dovich and the exact
trajectories. The effective gravitational potential acting on the improved
trajectories is substantially smaller at late times than the potential acting
on the exact trajectories. The results may be useful for Lagrangian
perturbation theory and for numerical simulations.
