Bekenstein model and the time variation of the strong coupling constant

We propose to generalize Bekenstein model for the time variation of the fine structure “constant” αem to QCD strong coupling constant αS. We find that, except for a “fine tuned” choice of the free parameters, the extension cannot be performed trivially without being in conflict with experimental constraints and this rules out αS variability. This is due largely to the huge numerical value of the QCD vacuum gluon condensate when compared to the matter density of the universe.