Proper Time and Mass of the Universe

TL;DR

This paper proposes a modified cosmological model incorporating proper time and a rest mass analog as dynamic variables, with a variable gravitational constant, to better understand universe dynamics.

Contribution

It introduces a novel modification to the Friedman universe model by adding proper time and a rest mass analog as dynamic variables with a time-dependent gravitational constant.

Findings

Rest mass is derived as a dynamic variable.

Proper time is integrated into the universe's dynamics.

The gravitational constant depends on proper time.

Abstract

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.