Initial State in Quantum Cosmology and the Proper Mass of the Universe

Abstract

In the Euclidean form of the theory of gravity, where there is no dedicated time parameter, a generalized canonical form of the principle of least action is proposed. On its basis, the quantum principle of least action is formulated, in which the “dynamics” of the universe in the Origin is described by the eigenvector of the action operator—the wave functional on the space of 4D Riemannian geometries and configurations of matter fields in some compact region of 4D space. The corresponding eigenvalue of the action operator determines the initial state for the world history of the universe outside this region, where the metric signature is Lorentzian and, thus, the time parameter exists. The boundary of the Origin region is determined by the condition that the rate of change of the determinant of the 3D metric tensor is zero on it. The size of the Origin is interpreted as a reciprocal temperature of the universe in the initial state. It has been suggested that in the initial state, the universe contains a certain distribution of its own mass, which is not directly related to the fields of matter.