  We study the cosmology of a Lee-Wick type scalar field theory. First, we
consider homogeneous and isotropic background solutions and find that they are
nonsingular, leading to cosmological bounces. Next, we analyze the spectrum of
cosmological perturbations which result from this model. Unless either the
potential of the Lee-Wick theory or the initial conditions are finely tuned, it
is impossible to obtain background solutions which have a sufficiently long
period of inflation after the bounce. More interestingly, however, we find that
in the generic non-inflationary bouncing cosmology, perturbations created from
quantum vacuum fluctuations in the contracting phase have the correct form to
lead to a scale-invariant spectrum of metric inhomogeneities in the expanding
phase. Since the background is non-singular, the evolution of the fluctuations
is defined unambiguously through the bounce. We also analyze the evolution of
fluctuations which emerge from thermal initial conditions in the contracting
phase. The spectrum of gravitational waves stemming for quantum vacuum
fluctuations in the contracting phase is also scale-invariant, and the tensor
to scalar ratio is not suppressed.
