  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.
