  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.
