  In earlier work it was pointed out that for warped product spacetimes the
conformal (geometrical moduli) excitations of the internal compactified factor
spaces should be observable as massive scalar fields in the external spacetime.
Here we show that these scalar fields (gravitational excitons) describe weakly
interacting particles and can be considered as dark matter component. Masses of
the gravexcitons are defined by the form of the effective potential of the
theory and the stabilization scales of the internal space. This implies that
different stabilization scales result in different types of DM. An essential
role is played by the effective potential. On the one hand, its minima fix
possible stabilization scales of the internal spaces; on the other hand, they
provide possible values for the effective cosmological constant.
