  We investigate aspects of quantum cosmology in relation to string cosmology
systems that are described in terms of the Dirac-Born-Infeld action. Using the
Silverstein-Tong model, we analyze the Wheeler-DeWitt equation for the rolling
scalar and gravity as well for $R\times{S^3}$ universe, by obtaining the wave
functions for all dynamical degrees of freedom of the system. We show, that in
some cases one can construct a time dependent version of the Wheeler-DeWitt
(WDW) equation for the moduli field $\phi$. We also explore in detail the
minisuperspace description of the rolling tachyon when non-minimal gravity
tachyon couplings are inserted into the tachyon action.
