The Dirac Field at the Future Conformal Singularity
  We examine in detail the effect of the conformal factor associated with the Friedmann-Robertson-Walker spacetimes on the discrete symmetries usually present in the Dirac theory and analyze the behavior of the Dirac wavefunction near the future conformal singularity. We find that only two of the 4 bi-spinor components survive to the boundary, one effect of which is to cause the geodesics to experience a drag towards the Hubble frame. We then present arguments for the existence of a genuine boundary condition on the wavefunction at the future conformal singularity based upon the assumption there is no redundant copy of the universe in the post-conformal singularity era. This future boundary condition affects the spectral decomposition of the wavefunction, and this maybe locally testable at the present time. 
Michael Ibison
physics.gen-ph