No-Boundary Wave Functional and Own Mass of the Universe.

An alternative formulation of the no-boundary initial state of the universe in the Euclidean quantum theory of gravity is proposed. Unlike the no-boundary Hartle–Hawking wave function, in which time appears together with macroscopic space–time in the semiclassical approximation, in the proposed formalism, time is present from the very beginning on an equal footing with spatial coordinates. The main element of the formalism is the wave functional, which is defined based on the world histories of the universe. This ensures formal 4D covariance of the theory. The wave functional is defined independently of the wave function as an eigenvector of the action operator. The shape of the Origin region, together with the boundary conditions, is determined by the structure of the total energy of the universe, which includes a 3D-invariant contribution of the expansion energy. The own mass of the universe arises as a non-zero value of the expansion energy in the Origin. [ABSTRACT FROM AUTHOR]