Is Eternal Inflation Eternal?
  In this paper we explore the relationship between the existence of eternal inflation and the initial conditions leading to inflation. We demonstrate that past and future completion of inflation is related, in that past-incomplete inflation can not be future eternal. Bubble universes nucleating close to the initial conditions hypersurface have the largest Lorentz boosts and experience the highest anisotropy. Consequently, their probability to collide upon formation is one. Thus instead of continuing eternally inflation ends soon after it starts. The difficulty in actualizing eternal inflation originates from the breaking of two underlying symmetries: Lorentz invariance and the general covariance of the theory which lead to an inconsistency of Einstein equations. Eternal inflation may not be eternal. 
Laura Mersini-Houghton
gr-qc hep-ph hep-th