  The dimensional reduction of $D$-dimensional spacetimes arising in
string/M-theory, to the conformal Einstein frame, may give rise to cosmologies
with accelerated expansion. Through a complete analysis of the dynamics of
doubly warped product spacetimes, in terms of scale invariant variables, it is
demonstrated that for $D \geq 10$, eternally accelerating 4-dimensional $\kappa
= -1$ Friedmann cosmologies arise from dimensional reduction on an internal
space with negative Einstein geometry.
