The energy of a closed universe is represented as a difference of two positive definite quantities, one of which includes the energy of matter and the energy of gravitational waves on the expanding universe background. The second quantity relates to the universe expansion and is called the energy of space. The whole energy of the universe equals zero provided the classical gravitational constraints are taken into account. In quantum theory a principle of the energy density of the matter minimum is formulated in the condition that the quantum gravitational constraints are also fulfilled in average. The states of the universe which satisfy the conditional minimal principle have different degree of the physical degrees of freedom excitation and, according to the gravitational constraints, corresponding excitation of space. The state of minimal excitation is proposed to be taken as the Beginning of the universe, and all the set of solutions, correspondingly, as admitted physical states of the universe at different moments of a cosmic time.

Citation: N.N. Gorobey, A.S. Lukyanenko, Quantization of the energy density in a closed universe, St. Petersburg Polytechnical State University Journal. PhysicsandMathematics. 11 (1) (2018) 147–156. DOI: 10.18721/JPM.11114