Dynamics of empty homogeneous isotropic three-dimensional spaces
  It is shown that there are seven types of solutions described in the framework of general relativity theory (GRT), the dynamics of empty homogeneous isotropic three-dimensional spaces. Solution of the equations of GRT, which describes the dynamics of a homogeneous isotropic universe, in the limiting case of vanishingly small effect of matter on the metric properties of space must go to one of them. 
A. V. Klimenko and V. A. Klimenko
physics.gen-ph