We show that under very general conditions any inhomogeneous cosmological model with a positive cosmological constant that can be described in a synchronous reference system will tend asymptotically in time towards the de Sitter solution, so making the problem of initial conditions less severe. The implications for inflationary scenarios are examined, and it is found that after inflation the Universe stays isotropic and homogeneous for a very long time.

• Received 15 August 1986

DOI:https://doi.org/10.1103/PhysRevD.35.1146