Potentials of Coupled Quintessence Based on a Dilaton

In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as coupled Quintessence, which is called DCQ model by us. Parametrization of the dark energy model is a good method by which we can construct the scalar potential directly from the effective equation of state function $omega_sigma(z)$ describing the properties of the dark energy. Applying this method to the DCQ model, we consider four parametrizations of $omega(z)$ and investigate the features of the constructed DCQ potentials, which possess two different evolutive behaviors called O mode and E mode. Lastly, we comprise the results of the constructed DCQ model with those of quintessence model numerically.