Scale-invariant perturbations in ekpyrotic cosmologies without
  fine-tuning of initial conditions
  Ekpyrotic bouncing cosmologies have been proposed as alternatives to
inflation. In these scenarios, the universe is smoothed and flattened during a
period of slow contraction preceding the bounce while quantum fluctuations
generate nearly scale-invariant super-horizon perturbations that seed structure
in the post-bounce universe. An analysis by Tolley and Wesley (2007) showed
that, for a wide range of ekpyrotic models, generating a scale-invariant
spectrum of adiabatic or entropic fluctuations is only possible if the
cosmological background is unstable, in which case the scenario is highly
sensitive to initial conditions. In this paper, we analyze an important
counterexample: a simple action that generates a Gaussian, scale-invariant
spectrum of entropic perturbations during ekpyrotic contraction without
requiring fine-tuned initial conditions. Based on this example, we discuss some
generalizations.
