  Assuming the existence of a 5D purely kinetic scalar field on the class of
warped product spaces we investigate the possibility of mimic both an
inflationary and a quintessential scenarios on 4D hypersurfaces, by
implementing a dynamical foliation on the fifth coordinate instead of a
constant one. We obtain that an induced chaotic inflationary scenario with a
geometrically induced scalar potential and an induced quasi-vacuum equation of
state on 4D dynamical hypersurfaces is possible. While on a constant foliation
the universe can be considered as matter dominated today, in a family of 4D
dynamical hypersurfaces the universe can be passing for a period of accelerated
expansion with a deceleration parameter nearly -1. This effect of the dynamical
foliation results negligible at the inflationary epoch allowing for a chaotic
scenario and becomes considerable at the present epoch allowing a
quintessential scenario.
