Quantum Gravitational Spectroscopy

We report that one of the main goals for improving the accuracy of quantum gravitational spectroscopy with neutrons is searches for extra short-range fundamental forces. We discuss also any progress in all competing nonneutron methods as well as constraints at other characteristic distances. Among major methodical developments related to the phenomenon of gravitational quantum states are the detailed theoretical analysis and the planning experiments on observation of gravitational quantum states of antihydrogen atoms.