Bouncing Galileon Cosmologies
  We present nonsingular, homogeneous and isotropic bouncing solutions of the
conformal Galileon model. We show that such solutions necessarily begin with a
radiation-dominated contracting phase. This is followed by a quintom scenario
in which the background equation of state crosses the cosmological constant
boundary allowing for a nonsingular bounce which in turn is followed by
Galilean Genesis. We analyze the spectrum of cosmological perturbations in this
background. Our results show that the fluctuations evolve smoothly and without
any pathology, but the adiabatic modes form a blue tilted spectrum. In order to
achieve a scale-invariant primordial power spectrum as required by current
observations, we introduce a light scalar field coupling to the Galileon
kinetically. We find two couplings which yield a scale-invariant spectrum, one
of which requires a fine tuning of the initial conditions. This model also
predicts a blue tilted spectrum of gravitational waves stemming from quantum
vacuum fluctuations in the contracting phase.
