We consider the inverse mean curvature flow in Robertson-Walker spacetimes that satisfy the Einstein equations and have a big crunch singularity and prove that under natural conditions the rescaled inverse mean curvature flow provides a smooth transition from big crunch to big bang. We also construct an example showing that in general the transition flow is only of class $C^3$.
"The Inverse Mean Curvature Flow in Robertson-Walker Spaces and its Application." Methods Appl. Anal. 13 (1) 19 - 28, March 2006.