 
Summary: ASYMPTOTIC BEHAVIOR OF FUTURECOMPLETE COSMOLOGICAL
SPACETIMES
MICHAEL T. ANDERSON
Dedicated to Vince Moncrief on his 60 th Birthday
Abstract. This work discusses the apriori possible asymptotic behavior to the future, for (vacuum)
spacetimes which are geodesically complete to the future, and which admit a foliation by constant
mean curvature compact Cauchy surfaces.
1. Introduction.
Let (M, g) be a CMC cosmological spacetime, i.e. a spacetime with a compact constant mean
curvature Cauchy surface (; g; K). The main focus will be on the vacuum case in 3+1 dimensions
although we will occasionally consider generalizations to nonnegative energy conditions and higher
dimensions.
A fundamental issue in general relativity is to understand the global structure of (M, g), and
in particular the evolution of the geometry of the CMC foliation generated by the CMC slice
: Singularities of (M, g) will generally form in nite proper time, both to the future and to the
past of . Roughly, these may correspond either to big bang or big crunch singularities of the
spacetime as a whole, or to localized gravitational collapse within only parts of the spacetime.
The understanding of the mechanism and structure of such singularity formation is of course a
central issue in general relativity.
Here we concentrate instead on the simpler situation where there is no singularity formation (in
