  The future evolution of the universe suggested by the cosmological model
proposed earlier at this meeting by the authors is explored. The fundamental
role played by the positive "cosmological constant" is emphasized. Dyson's 1979
paper entitled "Time Without End" is briefly reviewed. His most optimistic
scenario requires that the universe be geometrically open and that biology is
structural in the sense that the current complexity of human society can be
reproduced by scaling up its (quantum mechanical) structure to arbitrary size.
If the recently measured "cosmological constant" is indeed a fundamental
constant of nature, then Dyson's scenario is, for various reasons, ruled out by
the finite (De Sitter) horizon due to exponential expansion of the resulting
space. However, the finite temperature of that horizon does open other
interesting options. If, as is suggested by the cosmology under consideration,
the current exponential expansion of the universe is due to a phase transition
which fixes a physical boundary condition during the early radiation dominated
era, the behavior of the universe after the relevant scale factor crosses the
De Sitter radius opens up still other possibilities. The relevance of Martin
Rees' apocalyptic eschatology recently presented in his book "Our Final Hour"
is mentioned. It is concluded that even for the far future, whether or not
cultural and scientific descendants of the current epoch will play a role in
it, an understanding (sadly, currently lacking) of community and political
evolution and control is essential for a preliminary treatment of what could be
even vaguely called scientific eschatology.
