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

摘要

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.