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 $\mathrm{\Lambda }$, and (ii) an inhomogeneous inflaton field $\mathrm{\Phi }$ with a potential $\frac{1}{2}{m}^2{\mathrm{\Phi }}^2$. For the 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 do not prevent the onset of inflation. As for the 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 Planck mass), the field is soon homogenized and the universe always evolves into de Sitter spacetime. These support the cosmic no hair conjecture in a planar universe. We also discuss the effects of an additional massless scalar field, which is introduced to set initial data in usual analysis.