Bekenstein model and the time variation of the strong coupling constant

We propose to generalize Bekenstein model for the time variation of the fin e structure "constant" cue, to QCD strong coupling constant alpha (S) We fi nd that, except for a "fine tuned" choice of the free parameters, the exten sion cannot be performed trivially without being in conflict with experimen tal constraints and this rules out alpha (S) variability. This is due large ly to the huge numerical value of the QCD vacuum gluon condensate when comp ared to the matter density of the universe. (C) 2001 Published by Elsevier Science B.V.