Formulation of an Evolutionary Quantum Cosmology

We provide an evolutionary formulation of a generic quantum cosmology. Our starting point is the request that all quantities living on the slicing have to be 3-tensors. This statement, when applied to the lapse function and the shift vector, yields the no longer vanishing behavior of the super-Hamiltonian. Then, we provide the formulation of an evolutionary quantum cosmology in correspondence to a generic Universe asymptotically to the initial singularity.