Predictions of quantum gravity in inflationary cosmology: effects of the
  Weyl-squared term
  We derive the predictions of quantum gravity with fakeons on the amplitudes
and spectral indices of the scalar and tensor fluctuations in inflationary
cosmology. The action is $R+R^{2}$ plus the Weyl-squared term. The ghost is
eliminated by turning it into a fakeon, that is to say a purely virtual
particle. We work to the next-to-leading order of the expansion around the de
Sitter background. The consistency of the approach puts a lower bound ($
m_{\chi }>m_{\phi }/4$) on the mass $m_{\chi }$ of the fakeon with respect to
the mass $m_{\phi }$ of the inflaton. The tensor-to-scalar ratio $r$ is
predicted within less than an order of magnitude ($4/3<N^{2}r<12$ to the
leading order in the number of $e$-foldings $N$). Moreover, the relation
$r\simeq -8n_{T}$ is not affected by the Weyl-squared term. No vector and no
other scalar/tensor degree of freedom is present.
