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We numerically investigate the propagation of plane gravitational waves inthe form of an initial boundary value problem with de Sitter initial data. Thefull non-linear Einstein equations with positive cosmological constant$\lambda$ are written in the Friedrich-Nagy gauge which yields a wellposedsystem. The propagation of a single wave and the collision of two with colinearpolarization are studied and contrasted with their Minkowskian analogues.Unlike with $\lambda=0$, critical behaviours are found with $\lambda>0$ and arebased on the relationship between the wave profile and $\lambda$. We find thatchoosing boundary data close to one of these bifurcations results in a "false"steady state which violates the constraints. Simulations containing(approximate) impulsive wave profiles are run and general features arediscussed. Analytic results of Woodard and Tsamis, which describe howgravitational waves could affect an expansion rate at an initial instance oftime, are explored and generalized to the entire space-time. Finally we putforward boundary conditions that, at least locally, slow down the expansionconsiderably for a time.

Can gravitational waves halt the expansion of the universe?