Dilaton Coupled Quintessence Model in the $\ddot{I}‰-\ddot{I}{‰}^{\prime }$ Plane

Abstract

In this paper, we regard dilaton in Weyl-scaled induced gravitational theory as a coupled quintessence. Based on this consideration, we investigate the dilaton coupled quintessence(DCQ) model in $\ddot{I}‰-\ddot{I}{‰}^{\prime }$ plane, which is defined by the equation of state parameter for the dark energy and its derivative with respect to $N$(the logarithm of the scale factor $a$). We find the scalar field equation of motion in $\ddot{I}‰-\ddot{I}{‰}^{\prime }$ plane, and show mathematically the property of attractor solutions which correspond to $\ddot{I}{‰}_{\ddot{I}}ƒ\sim -1$, $\hat{I}{\text{c◯}}_{\ddot{I}}ƒ=1$. Finally, we find that our model is a tracking one which belongs to "freezing" type model classified in $\ddot{I}‰-\ddot{I}{‰}^{\prime }$ plane.

7 pages, 4 figures, some references added