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 Newton's 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 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 conclusive and undisputed evidence has been presented to show that any changes have been found over the last 5-10 billion years.

Here's an abstract from the journal Physics Today describing one such search and outcome:

IS THE FINE STRUCTURE CONSTANT CHANGING? The inherent strength of the electromagnetic force is characterized by a parameter called the fine structure constant (denoted by the Greek letter alpha), defined as the charge of the electron squared divided by the product of Planck's constant and the speed of light. The size of alpha determines how well atoms hold together and what types of light atoms will emit when heated up. And just as the elastic band keeping a swimsuit snug will gradually relax with time, so it is reasonable to ask whether an atoms' elasticity (or alpha) might also vary with time, an idea broached by Paul Dirac in 1937. A group of scientists at the University of New South Wales in Australia (John Webb, jkw@edwin.phys.unsw.edu.au) test this proposition by sampling ancient light emitted by ancient atoms, and comparing them to modern light from modern atoms. In particular they looked at the relative spacing of doublets of absorption lines in the spectra of several types of atoms in distant gas clouds lying in front of still more distant quasars. The spacings, not easy to tease out from the faint spectra, are proportional to alpha squared. After taking into account Doppler effects owing to the expansion of the universe, the Australian scientists find that there is a consistent change in alpha with increasing redshift (z), especially above a z of one. Owing to the caution needed in claiming a "measurement" of alpha change, the researchers prefer to think of their result as constituting a new upper limit on the fractional alpha change for z>1 of about 2 parts in 10,000. (Webb et al., Physical Review Letters, 1 February 1999.)

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