Varying c cosmology and Planck value constraints
  It has been suggested that by increasing the speed of light during the early universe various cosmological problems of standard big bang cosmology can be overcome, without requiring an inflationary phase. However, we find that as the Planck length and Planck time are then made correspondingly smaller, and together with the need that the universe should not re-enter a Planck epoch, the higher $c$ models have very limited ability to resolve such problems. For a constantly decreasing $c$ the universe will quickly becomes quantum gravitationally dominated as time increases: the opposite to standard cosmology where quantum behaviour is only ascribed to early times. 
D.H. Coule