Proper Time and Mass of the Universe

A modification of the homogeneous isotropic model of the Friedman universe with a scalar field is proposed, in which the proper time of the universe is added to the dynamic variables under the additional condition of its classical dynamics. Along with proper time, an additional parameter is included in the modified theory, which is an analog of the rest mass of a relativistic particle. Assuming the dependence of the gravitational constant on proper time, we obtain the rest mass as an additional dynamic variable.