No-boundary Wave Functional and Own Mass of the Universe

Abstract: 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 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, which includes the 3D invariant contribution of the expansion energy of the universe with a minus sign. The proper mass of the universe arises as a non-zero value of the expansion energy in the Origin and, over time, splits into a spectrum of proper masses of 3D invariant dynamic modes. 4D covariance is restored at zero own mass of the universe.