Shear-free rotating inflation
  We demonstrate the existence of shear-free cosmological models with rotation and expansion which support the inflationary scenarios. The corresponding metrics belong to the family of spatially homogeneous models with the geometry of the closed universe (Bianchi type IX). We show that the global vorticity does not prevent the inflation and even can accelerate it. 
Yuri N. Obukhov, Thoralf Chrobok, and Mike Scherfner