Exponential Potentials and Attractor Solution of Dilatonic Cosmology

We present the scalar-tensor gravitational theory with an exponential potential in which pauli metric is regarded as the physical space-time metric. We show that it is essentially equivalent to coupled quintessence(CQ) model. However for baryotropic fluid being radiation there are in fact no coupling between dilatonic scalar field and radiation. We present the critical points for baryotropic fluid and investigate the properties of critical points when the baryotropic matter is specified to ordinary matter. It is possible for all the critical points to be attractors as long as the parameters $\lambda$ and $\beta$ satisfy certain conditions. To demonstrate the attractor behaviors of these critical points, We numerically plot the phase plane for each critical point. Finally with the bound on $\beta$ from the observation and the fact that our universe is undergoing an accelerating expansion, we conclude that present accelerating expansion is not the eventual stage of universe. Moreover, we numerically describe the evolution of the density parameters $\Omega$ and the decelerating factor $q$, and computer the present values of some cosmological parameters, which are consistent with current observational data.