  Precanonical quantization is based on the mathematical structures of the De
Donder-Weyl Hamiltonization of field theories. The resulting formulation of
quantum gravity describes the quantum geometry of space-time in terms of
operator-valued distances and the transition amplitudes between the values of
spin connection at different points of space-time, which obey the covariant
precanonical analogue of the Schr\"odinger equation. In the context of quantum
cosmology the theory predicts a probability distribution of a cosmological
spin-connection field, which may have an observable impact on the large scale
structures in the universe.
