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 $z\lesssim 1$, 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 ${\Omega }_{\Lambda }=0.8\mathrm{}$ and ${\Omega }_m=0.2\mathrm{}$ inferred from the supernovae data, one must confirm cosmic acceleration out to at least $z\simeq 1.8$ to infer that our portion of the universe is inflating. If ${\Omega }_{\Lambda }<0.736\mathrm{}$ then no present-day measurement can confirm or falsify that inference.