Reconstruction of $5D$ Cosmological Models From Equation of State of Dark Energy

Abstract

We consider a class of five-dimensional cosmological solutions which contains two arbitrary function $μ(t)$ and $ν(t)$. We found that the arbitrary function $μ(t)$ contained in the solutions can be rewritten in terms of the redshift $z$ as a new arbitrary function $f(z)$. We further showed that this new arbitrary function $f(z)$ could be solved out for four known parameterized equations of state of dark energy. Then the $5D$ models can be reconstructed and the evolution of the density and deceleration parameters of the universe can be determined.