Perturbative Noncommutative Quantum Gravity
  We study perturbative noncommutative quantum gravity by expanding the gravitational field about a fixed classical background. A calculation of the one loop gravitational self-energy graph reveals that only the non-planar graviton loops are damped by oscillating internal momentum dependent factors. The noncommutative quantum gravity perturbation theory is not renormalizable beyond one loop for matter-free gravity and all loops for matter interactions. Comments are made about the nonlocal gravitational interactions produced by the noncommutative spacetime geometry. 
J. W. Moffat