This is an old idea proposed by Brans and Dicke in an alternative formulation to general relativity called the 'Scalar-Tensor Theory'. The main feature is that the Constant of Gravity was proposed to change over billions of years, but there have been many searches for this effect over the last few decades with no luck. Most recently, Stephen Thorsett at Princeton recently used neutron star masses in 5 binary neutron star systems to deduce that over the ages of these systems from 30 million to several billion years, G has not changed by more than 0.4 parts per BILLION. So, the constant of gravity is rock solid for purposes of building cosmological models. As for the other constants such as Planck's Constant and the speed of light, these too have been examined for slow changes over several billions of years and no changes have been found. I do not have the specific references for the tests but I know they were performed in the last 20 years using fossil 'haloes' of specific atoms undergoing radioactive decay.