Observation of Cosmic Acceleration and Determining the Fate of the Universe

Current observations of Type Ia supernovae provide evidence for cosmic acceleration out to a redshift of $z \lsim 1$, leading to the possibility that the universe is entering an inflationary epoch. However, inflation can take place only if vacuum-energy (or other sufficiently slowly redshifting source of energy density) dominates the energy density of a region of physical radius 1/H. We argue that for the best-fit values of $\Omega_\Lambda$ and $\Omega_m$ inferred from the supernovae data, one must confirm cosmic acceleration out to at least $z \simeq 1.8$ to infer that the universe is inflating.