Dark pressure in a non-compact and non-Ricci flat 5D Kaluza-Klein cosmology

In the framework of noncompact Kaluza-Klein theory, we investigate a $(4+1)$-dimensional universe consisting of a $(4+1)$ dimensional Robertson-Walker type metric coupled to 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 for a flat universe, coupled with the non-vacuum states of the scalar field, the reduced field equations subject to suitable equations of state for matter and dark part may reveal inflationary behavior at early universe, deceleration for radiation dominant era and then acceleration in matter dominant era.