A Bianchi type-IX cosmological model has been found as a solution of Einstien’s vacuum field equations with a cosmological constant. The solution represents a rotating generalziation fo the de Sitter universe. This universe shows a transition to exponential expansion and the vorticity begins to decay exponentially at the grand-unified-theory time. The point of time for this transition is independent of the magnitude of the vorticity. During the Guth inflationary era the vorticity decays by a factor of the order ${10}^{\mathrm{-}142}$.

• Received 3 September 1986

DOI:https://doi.org/10.1103/PhysRevD.33.1204