  We investigate the relative time scales associated with finite future
cosmological singularities, especially those classified as Big Rip cosmologies,
and the maximum predictability time of a coupled FRW-KG scalar cosmology with
chaotic regimes. Our approach is to show that by starting with a FRW-KG scalar
cosmology with a potential that admits an analytical solution resulting in a
finite time future singularity there exists a Lyapunov time scale that is
earlier than the formation of the singularity. For this singularity both the
cosmological scale parameter a(t) and the Hubble parameter H(t) become infinite
at a finite future time, the Big Rip time. We compare this time scale to the
predictability time scale for a chaotic FRW-KG scalar cosmology. We find that
there are cases where the chaotic time scale is earlier than the Big Rip
singularity calling for special care in interpreting and predicting the
formation of the future cosmological singularity.
