Correspondence Between $5D$ Ricci-Flat Cosmological Models and Quintessence Dark Energy Models

Abstract

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 $V(\varphi )$ 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 $V(\varphi )$.

arXiv commentws-mpla.cls, 10 pages, 4 figures, to be published in MPLA, one reference added, four eps figures changed

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Cited by in corpus (3)

• Statefinder Parameters for Five-Dimensional Cosmology
• Exact solutions of embedding the 4D Universe in a 5D Einstein manifold
• Thermodynamics of Apparent Horizon and Friedmann Equations in Big Bounce Universe