  We point out that the solution of $(4+n)$-dimensional gravity coupled to the
dilaton and an $n$-form field strength can give rise to a flat 4-dimensional
universe (with a scale factor) of the type proposed recently under time
dependent compactifications. The compact internal spaces could be hyperbolic,
flat or spherical and the solution is identical to the space-like two brane or
S2-brane. As has been shown previously for SM2 solution with a fixed field
strength we show that for $n=7$ (where the dilaton is vanishing and with a
general field strength), 6 the corresponding SM2 and SD2 solutions can give
accelerating cosmologies in Einstein frame for both hyperbolic and flat
internal spaces, thereby meeting the challenge of obtaining such a solution
from M/String theory compactifications.
