On the Quantum Creation of Matter in the Expanding Universe
  Quantum Action Principle which has been used as a ground for a probabilistic interpretation of one-particle relativistic quantum mechanics \cite{GLL} is applied to quantum cosmology. The quantum creation of matter in a minisuperspace model with one homogeneous scalar field is considered. The initial state of the universe is defined as a stationary ground state of the Hamiltonian with the Euclidean signature in which the mean value of the universe radius is equal to the Plank length and the number of the scalar field quanta is equal zero. We interpret the change of the signature as the universe "birth". From this moment of time the dynamics of the scale factor is considered as classical. The real phase of the amplitude of the creation process is taken as a quantum action. The balance between matter and gravitation energies in the creation process is fulfilled by the condition of the stationarity of the quantum action with respect to the internal time of the universe. 
Natalia Gorobey and Alexander Lukyanenko
gr-qc quant-ph