Joining the Hubble Flow: Implications for Expanding Space
  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. 
Luke A. Barnes, Matthew J. Francis, J. Berian James, Geraint F. Lewis