Gravity can be embedded into a renormalizable theory by means of adding quadratic in curvature terms.
However, this at first leads to the presence of the Weyl ghost. It is possible to get rid of this ghost if the
locality assumption is weakened and the propagator of the graviton is represented by an entire function
of the d'Alembertian operator without new poles and zeros. Models of this type admit a cosmological
solution describing the R^2, or Starobinsky, inflation. We study graviton production after inflation in
this model and show that it is negligible despite the presence of the higher derivative operators which
could potentially cause instabilities.