Inflation in a spatially closed anisotropic universe

Abstract

The effects of shear on the occurrence of inflation are studied on the basis of a simple model for a spatially closed universe which enters an inflationary era. It is assumed that the universe enters a vacuum-dominated phase in an abrupt transition that occurs everywhere at the same time. The space-time geometries, before and after the phase transition, are matched to each other via the Lichnerowicz junction conditions. The Einstein field equations are solved exactly for a viscous universe of the Kantowski–Sachs type. It is found that the inclusion of (positive) shear retards the occurrence of the vacuum phase transition. The magnitude of this effect depends on the mass of the universe at the time of the phase transition. For a universe with a mass of about 10 kg (which is a value usually associated with the mass of the region from which our universe originated), it is found that the inclusion of shear does not really have a large effect on the time at which the vacuum phase transition occurs. The generality of the results is also discussed.