Abstract
We numerically investigate the propagation of plane gravitational waves in the form of an initial boundary value problem with de Sitter initial data. The full non-linear Einstein equations with positive cosmological constant lambda are written in the Friedrich-Nagy gauge which yields a well-posed system. The propagation of a single wave and the collision of two with colinear polarization are studied and contrasted with their Minkowskian analogues. Unlike with lambda = 0, critical behaviours are found with lambda > 0 and are based on the relationship between the wave profile and l. We find that choosing 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 are discussed. Analytic results of Tsamis and Woodard, which describe how gravitational waves could affect an expansion rate at an initial instance of time, are explored and generalized to the entire space-time. Finally we put forward boundary conditions that, at least locally, slow down the expansion considerably for a time.