Surprising phenomena in a rich new class of inflationary models
  We report on a new class of fast-roll inflationary models. In a huge part of
its parameter space, inflationary perturbations exhibit quite unusual phenomena
such as scalar and tensor modes freezing out at widely different times, as well
as scalar modes reentering the horizon during inflation. In another, narrower
range of parameters, this class of models agrees with observations. One
specific point in parameter space is characterized by extraordinary behavior of
the scalar perturbations. Freeze-out of scalar perturbations as well as
particle production at horizon crossing are absent. Also the behavior of the
perturbations around this quasi-de Sitter background is dual to a quantum field
theory in flat space-time. Finally, the form of the primordial power spectrum
is determined by the interaction between different modes of scalar
perturbations.
