  A theory of quantum gravity has been recently proposed by means of a novel
quantization prescription, which is able to turn the poles of the free
propagators that are due to the higher derivatives into fakeons. The classical
Lagrangian contains the cosmological term, the Hilbert term, $\sqrt{-g}R_{\mu
\nu }R^{\mu \nu }$ and $\sqrt{-g}R^{2}$. In this paper, we compute the one-loop
renormalization of the theory and the absorptive part of the graviton self
energy. The results illustrate the mechanism that makes renormalizability
compatible with unitarity. The fakeons disentangle the real part of the self
energy from the imaginary part. The former obeys a renormalizable power
counting, while the latter obeys the nonrenormalizable power counting of the
low energy expansion and is consistent with unitarity in the limit of vanishing
cosmological constant. The value of the absorptive part is related to the
central charge $c$ of the matter fields coupled to gravity.
