The aim of this section is to present a picture of the dynamics
of forever-expanding cosmological models, by which we mean
spacetimes that are maximal globally hyperbolic developments and
which can be covered by a foliation by Cauchy surfaces whose mean
is strictly negative. In contrast to the approach to the big
bang considered in Section
8, the spatial topology can be expected to play an important role
in the present considerations. Intuitively, it may well happen
that gravitational waves have time to propagate all the way
around the universe. It will be assumed, as the simplest case,
that the spacetimes considered admit a compact Cauchy surface.
Then the hypersurfaces of negative mean curvature introduced
above have finite volume and this volume is a strictly increasing
function of time.