A phenomenological variable speed of light theory and the secular increase of the astronomical unit

In this paper, we propose a variable speed of light (VSL) theory in which both the speed of light, c, and the inertial and gravitational masses, m, depend on the age of the universe. From a purely phenomenological standpoint, both c and m are supposed to be approximate linear functions of the form c(t) = c ₀(1 − β H ₀ t), m(t) = m ₀(1 + 2β H ₀ t), where H ₀ is the Hubble parameter at the present time, c ₀ and m ₀ are, respectively, the initial values of the speed of light and the mass of a given particle at that particular instant of time, taken as reference to the present cosmological epoch. Furthermore, β is a constant. In fact, we calculate the perturbations in the orbits of the planets in the solar system. We can deduce that β is of the order of magnitude of the fine-structure constant. This model explains both the anomalous secular increase of the astronomical unit and the recently reported anomalous increase of the Moon's orbital eccentricity.