Perturbations in Bouncing and Cyclic Models, a General Study
  Being able to reliably track perturbations across bounces and turnarounds in
cyclic and bouncing cosmology lies at the heart of being able to compare the
predictions of these models with the Cosmic Microwave Background observations.
This has been a challenging task due to the unknown nature of the physics
involved during the bounce as well as the technical challenge of matching
perturbations precisely between the expansion and contraction phases. In this
paper, we will present general techniques (analytical and numerical) that can
be applied to understand the physics of the fluctuations, especially those with
"long" wavelengths, and test its validity in some simple bouncing/cyclic toy
models where the physics is well understood. We will then apply our techniques
to more interesting cosmological models such as the bounce inflation and cyclic
inflation.
