  Inflation has been the leading early universe scenario for two decades, and
has become an accepted element of the successful `cosmic concordance' model.
However, there are many puzzling features of the resulting theory. It requires
both high energy and low energy inflation, with energy densities differing by a
hundred orders of magnitude. The questions of why the universe started out
undergoing high energy inflation, and why it will end up in low energy
inflation, are unanswered. Rather than resort to anthropic arguments, we have
developed an alternative cosmology, the Cyclic universe, in which the universe
exists in a very long-lived attractor state determined by the laws of physics.
The model shares inflation's phenomenological successes without requiring an
epoch of high energy inflation. Instead, the universe is made homogeneous and
flat, and scale-invariant adiabatic perturbations are generated during an epoch
of low energy acceleration like that seen today, but preceding the last big
bang. Unlike inflation, the model requires low energy acceleration in order for
a periodic attractor state to exist. The key challenge facing the scenario is
that of passing through the cosmic singularity at t=0. Substantial progress has
been made at the level of linearised gravity, which is reviewed here. The
challenge of extending this to nonlinear gravity and string theory remains.
