In cyclic universe models based on a single scalar field (e.g., the radion determining the distance between branes in M theory), virtually the entire Universe makes it through the ekpyrotic smoothing and flattening phase, bounces, and enters a new epoch of expansion and cooling. This stable evolution cannot occur, however, if scale-invariant curvature perturbations are produced by the entropic mechanism because it requires two scalar fields (e.g., the radion and the Calabi-Yau dilaton) evolving along an unstable classical trajectory. In fact, we show here that an overwhelming fraction of the Universe fails to make it through the ekpyrotic phase; nevertheless, a sufficient volume survives and cycling continues forever provided the dark energy phase of the cycle lasts long enough, of order a trillion years. Two consequences are a new role for dark energy and a global structure of the Universe radically different from that of eternal inflation.

• Received 15 January 2009

DOI:https://doi.org/10.1103/PhysRevD.79.063503