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 +R² 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_χ > m_ϕ /4) on the mass m_χ of the fakeon with respect to the mass m_ϕ of the inflaton. The tensor-to-scalar ratio r is predicted within less than an order of magnitude (4/2 < N²r <12 to the leading order in the number of e-foldings N). Moreover, the relation r ≃ –8n_T is not affected by the Weyl-squared term. No vector and no other scalar/tensor degree of freedom is present.