Finite Future Cosmological Singularity Times and Maximum Predictability Times in a Nonlinear FRW-KG Scalar Cosmology

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.