  In the framework of Kaluza-Klein theory, we investigate a $(4+1)$-dimensional
universe consisting of a $(4+1)$ dimensional Robertson-Walker type metric
coupled with a $(4+1)$ dimensional energy-momentum tensor. The matter part
consists of an energy density together with a pressure subject to 4D part of
the $(4+1)$ dimensional energy-momentum tensor. The dark part consists of just
a dark pressure $\bar{p}$, corresponding to the extra-dimension endowed by a
scalar field, with no element of dark energy. It is shown that the reduced
Einstein field equations are free of 4D pressure and are just affected by an
effective pressure produced by the 4D energy density and dark pressure. It is
then proposed that the expansion of the universe may be controlled by the
equation of state in higher dimension rather than four dimensions. This may
account for the emergence of unexpected current acceleration in the middle of
matter dominant era.
