Cosmological Implications of the Supergravity Tracking Potential

It is demonstrated that any realistic model of quintessence should be based on Supergravity since, when the scalar field is on tracks today, $Q\approx m_{\rm Pl}$. This improves the agreement between theoretical predictions and the current observations. In particular, a generic property is that ratio $\omega_{\rm Q}\equiv p_{\rm Q}/\rho_{\rm Q}$ is pushed towards -1. A string-inspired model is proposed where the potential is given by $V(Q)= \frac{\Lambda ^{4+\alpha}}{Q^{\alpha}}e^{\frac{\kappa}{2}Q^2}$. The model predicts $\omega_{\rm Q}\approx -0.82$, a value less that one sigma from the current likehood value.