Energy Conservation Law in the Closed Universe and a Concept of the Proper Time

Abstract

To define time in the homogeneous anisotropic Bianchi-IX model of the universe, we propose a classical equation of motion of the proper time of the universe as an additional gauge condition. This equation is the law of conservation of energy. As a result, a new parameter, called a “mass” of the universe, appears. This parameter is added to the anisotropy energy and regarded as an observed quantity. The “mass” of the universe is decisive when it comes to the dynamics of its origin.

Editorial to the Special Issue “Selected Papers from the 17th Russian Gravitational Conference—International Conference on Gravitation, Cosmology and Astrophysics (RUSGRAV-17)”

“…In this connection, article [17] discusses a question: Is the axionic dark matter an equilibrium system? Several articles investigate gravitational radiation as the bremsstrahlung of superheavy particles in the early Universe [18], energy conservation law in the closed Universe in connection with a concept of the proper time [19], and the possibility of applying the Copenhagen interpretation to quantum cosmology [20]. The cosmological constant problem in the super-early Universe and the collision of relativistic shock waves and its impact on the large scale structure of the Universe are considered in [21,22], respectively.…”