  We extend the monumental result of Christodoulou-Klainerman on the global
nonlinear stability of the Minkowski spacetime to the global nonlinear
stability of a class of large dispersive spacetimes. More precisely, we show
that any regular future causally geodesically complete, asymptotically flat
solution to the Einstein-scalar field system which approaches the Minkowski
spacetime sufficiently fast for large times is future globally nonlinearly
stable. Combining our main theorem with results of Luk-Oh, Luk-Oh-Yang and
Kilgore, we prove that a class of large data spherically symmetric dispersive
solutions to the Einstein-scalar field system are globally nonlinearly stable
with respect to small non-spherically symmetric perturbations. This in
particular gives the first construction of an open set of large asymptotically
flat initial data for which the solutions to the Einstein-scalar field system
are future causally geodesically complete.
