Generality of inflation in a planar universe

We study a generality of an inflationary scenario by integrating the Einstein equations numerically in a plane-symmetric spacetime. We consider the inhomogeneous spacetimes due to (i) localized gravitational waves with a positive cosmological constant Λ and (ii) an inhomogeneous inflation field Φ with a potential 12m2Φ2. For case (i), we find that any initial inhomogeneities are smoothed out even if waves collide, so that we conclude that inhomogeneity due to gravitational waves does not prevent the onset of inflation. As for case (ii), if the mean value of the inflaton field is initially as large as the condition in an isotropic and homogeneous inflationary model (i.e., the mean value is larger than several times the Planck mass), the field is soon homogenized and the universe always evolves into de Sitter spacetime. This supports the cosmic no hair conjecture in a planar universe. We also discuss the effects of an additional massless scalar field, which are introduced to set initial data in the usual analysis.