In any approach to qunatum gravity, it is crucial to look for observational effects. In my talk, I discuss how quantum gravitational contributions to the anisotropy spectrum of the cosmic microwave background arise in the framework of quantum geometrodynamics (Wheeler-DeWitt equation). From the present non-observation of these contributions, one finds a constraint on the Hubble parameter of inflation. I finally compare these results with the corresponding predictions from loop quantum cosmology.
Ref.: C. Kiefer and M. Krämer, Phys. Rev. Lett. 108, 021301 (2012).