  The concept of expanding space has come under fire recently as being
inadequate and even misleading in describing the motion of test particles in
the universe. Previous investigations have suffered from a number of
shortcomings, which we seek to correct. We study the motion of test particles
in the universe in detail, solving the geodesic equations of General Relativity
for a number of cosmological models. In particular, we use analytic methods to
examine whether particles removed from the Hubble flow asymptotically rejoin
the Hubble flow, a topic that has caused confusion because of differing
definitions and invalid reasoning. We conclude that particles in eternally
expanding but otherwise arbitrary universes do not in general rejoin the Hubble
flow.
