  We consider open globally hyperbolic spacetimes $N$ of dimension $n+1$, $n\ge
3$, which are spatially asymptotic to a Robertson-Walker spacetime or an open
Friedmann universe with spatial curvature $\tilde\kappa = 0,-1$ and prove,
under reasonable assumptions, that there exists a unique foliation by
hypersurfaces of constant mean curvature and that the mean curvature function
$\tau$ is a smooth time function if $N$ is smooth. Moreover, among the
Friedmann universes which satisfy the necessary conditions are those that
reflect the present assumptions of the development of the universe.
