On the time variation of c, G, and h and the dynamics of the cosmic expansion

Several authors have recently explored the idea that physical constants such as c and G might vary over time and have formulated theories describing this variation that can address a range of cosmological problems. Such work typically invokes a generic parameterization which assumes a power-law variation with the expansion scale factor, R. This work offers alternative, physically motivated definitions for the parameters c, G, and h based on the Machian premise that these dimensional quantities reflect global dynamics of the expansion geometry. Together with a postulated conservation law and equations of motion, the implications of this theory for Friedmann models are examined, and found to yield several interesting conclusions including: (1) natural solutions to the horizon, flatness, and lambda problems, (2) the prediction of a flat, Omega_0 = 1 universe, (3) different forms for some cosmological scaling laws, (4) an apparent fit to observations of Type Ia supernovae without invoking a cosmological constant, (5) equivalence between our Universe and a black hole and apparent consistency of the model with the Holographic Principle, and (6) potentially testable predictions for the time variation of physical parameters, including values for c_dot and h_dot that are small but non-zero today and a value for G_dot that was negative and nonzero during radiation domination and decayed to effectively zero upon the epoch of matter domination. While this work does not attempt to provide the complete theoretical foundation that must ultimately underlie any theory that could naturally marry traditional physics with the notion of time-varying physical parameters, it is written in the hope that it might stimulate further progress towards this end.