Cosmology with a light ghost
  We study the creation and evolution of cosmological perturbations in
renormalizable quadratic gravity with a Weyl term. We adopt a prescription that
implies the stability of the vacuum at the price of introducing a massive
spin-two ghost state, leading to the loss of unitarity. The theory may still be
predictive regardless the interpretation of non-unitary processes provided that
their rate is negligible compared to the Universe expansion rate. This implies
that the ghost is effectively stable. In such a setup, there are two scalar
degrees of freedom excited during inflation. The first one is the usual
curvature perturbation whose power spectrum appears to coincide with that of
single-field inflation. The second one is a scalar component of the ghost
encoded in the shift vector of the metric in the uniform inflaton gauge. The
amplitudes of primordial tensor and vector perturbations are strongly
suppressed. After inflation the ghost field starts to oscillate and its energy
density shortly becomes dominant in the Universe. For all ghost masses allowed
by laboratory constraints ghosts should have "overclosed" the Universe at
temperatures higher than that of primordial nucleosynthesis. Thus, the model
with the light Weyl ghost is ruled out.
