On the cosmic convergence mechanism of the massless dilaton

The converging mechanism discussed in Damour and Nordtvedt (1993) [10] for scalar-tensor theories has been applied to dilaton-like theories in several subsequent papers. In the present communication, we show that an unfortunate assumption in those studies led to a scalar-field equation unsuitable for the study of the dilaton field. The corrected scalar-field equation turns to change the numerical outcome of those studies in general, but even sometimes their qualitative aftermath. Therefore, the present result call for new investigations of the subject. On the other hand, our result shows that the string-inspired theory presented in Minazzoli and Hees (2013) [13] is naturally solution to the problem of the effective constancy of the fundamental coupling constants at late cosmic times, while it requires less fine-tuning than other massless dilaton or usual scalar-tensor theories