  The role of the dilaton field and its coupling to matter may result to a
dilution of Dark Matter (DM) relic densities. This is to be contrasted with
quintessence scenarios in which relic densities are augmented, due to
modification of the expansion rate, since Universe is not radiation dominated
at DM decoupling. Dilaton field, besides this, affects relic densities through
its coupling to dust which tends to decrease relic abundances. Thus two
separate mechanisms compete each other resulting, in general, to a decrease of
the relic density. This feature may be welcome and can rescue the situation if
Direct Dark Matter experiments point towards small neutralino-nucleon cross
sections, implying small neutralino annihilation rates and hence large relic
densities, at least in the popular supersymmetric scenarios. In the presence of
a diluting mechanism both experimental constraints can be met. The role of the
dilaton for this mechanism has been studied in the context of the non-critical
string theory but in this work we follow a rather general approach assuming
that the dilaton dominates only at early eras long before Big Bang
Nucleosynthesis.
