On precanonical quantization of gravity in spin connection variables

The basics of precanonical quantization and its relation to the functional Schr\"odinger picture in QFT are briefly outlined. The approach is applied to quantization of Einstein's gravity in vielbein and spin connection variables and leads to a quantum dynamics described by the covariant Schr\"odinger equation for the transition amplitudes on the bundle of spin connection coefficients over the space-time, that yields a novel quantum description of space-time geometry. A toy model of precanonical quantum cosmology based on the example of flat FLRW universe is considered.