Correspondence between 5D Ricci-flat cosmological models and quintessence dark energy models

We study the accelerating expansion and the induced dark energy of the 5D Ricci-flat universe which is characterized by having a big bounce as opposed to a big bang. We show that the arbitrary function mu(t) contained in the 5D solutions can be rewritten in terms of the redshift z as a new arbitrary function f (z), and we find that there is a correspondence between this f (z) and the potential V(phi) of the 4D quintessence models. Using this correspondence, the arbitrary function f (z) and the 5D solution could be specified for a given form of the potential V(phi).