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.