Leading order effective operators in quantum gravity

We explore the nature of higher dimensional operators generated by quantum gravity. Calculating the tree-level and one-loop effective operators generated by graviton exchange between fields of the standard model and those of a hidden sector, we show that the leading order operators generated by quantum gravity are non-local dimension 6 operators. Dimension 5 operators are not generated by perturbative (weak field) effects, although they might be generated by strong field effects such as Planck-scale fluctuations in spacetime. We investigate the consequences of our findings for models of ultralight scalar dark matter.