Reconstructing dark energy potentials from parameterized deceleration parameters

In this paper, the properties of dark energy are investigated according to the parameterized deceleration parameter q(z), which is used to describe the extent of the accelerating expansion of the universe. The potential of dark energy V() and the cosmological parameters, such as the dimensionless energy density ωo, Ωm, and the state parameter w, are connected to it. Concretely, by giving two kinds of parameterized deceleration parameters q(z) = a + bz/(1 + z) and q(z) = 1/2 + (az + b)/(1 + z)2, the evolution of these parameters and the reconstructed potentials V() are plotted and analysed. It is found that the potentials run away with the evolution of universe.