The End of Eternal Inflation
  We propose a new measure for eternal inflation that includes both conditions, large field fluctuations and smooth homogeneous domains, in the self reproducing probability estimate. We show that due to the increasing inhomogeneities in the background spacetime fractal, self-reproduction stops within a finite time t_f, thus inflation can not be eternal. 
Laura Mersini-Houghton and Malcolm J Perry
hep-th gr-qc hep-ph