Variation of the Gravitational Constant in the Radiation-Dominated Universe

The unification of classical electrodynamics and general relativity within the context of five-dimensional general relativity (Kaluza, 1921, and Thiry, 1948) contains a scalar field which may be identified with the gravitational constant, G. The field equations of this theory are solved under conditions of the Robertson-Walker metric for flat space, for a radiation-dominated universe—a model appropriate for the early history of our universe. This leads to a cosmology wherein G is inversely proportional to the Robertson-Walker scale factor. This result is discussed in the context of the Dirac large number hypothesis and in the context of an expression for G in terms of atomic constants.