Current evidence suggests that the cosmological constant is not zero, or that
we live in an open universe. We examine the implications for the future under
these assumptions, and find that they are striking. If the Universe is
cosmological constant-dominated, our ability to probe the evolution of large
scale structure will decrease with time ---presently observable distant sources
will disappear on a time-scale comparable to the period of stellar burning.
Moreover, while the Universe might expand forever, the integrated conscious
lifetime of any civilization will be finite, although it can be astronomically
long. We find that this latter result is far more general. In the absence of
possible exotic and uncertain strong gravitational effects, the total
information recoverable by any civilization over the entire history of our
universe is finite, and assuming that consciousness has a physical
computational basis, life cannot be eternal.Comment: 23 pages, latex, submitted to Ap.