Universe Evolution in a 5d Ricci-flat Cosmology

We use Wetterich’s parameterization equation of state (EOS) of dark energy to a 5D Ricci-flat cosmological solution and we suppose the universe contains three major components: matter, radiation and dark energy. By using the relation between the scale factor and the redshift z, we show that the two arbitrary functions contained in the 5D solution could be solved out analytically in terms of the variable z. Thus the whole 5D solution could be constructed uniquely if the current values of the three density parameters Ωm0, Ωr0, Ωx0, the EOS w0, and the bending parameter b contained in the EOS are all known. Furthermore, we find that all the evolutions of the mass density Ωm, the radiation density Ωr, the dark energy density Ωx, and the deceleration parameter q depend on the bending parameter b sensitively. Therefore it is deserved to study observational constraints on the bending parameter b.