  We study several quintessence models which are singular at Q=0, and use a
simple initial constraint $Q_i\ge H_{inflation}/2\pi$ to see when they enter
tracking regime, disregarding the details of inflation. We find it can give
strong constraints for the inverse power-law potential $V=V_0Q^{-\alpha}$,
which has to enter tracking regime for ${\rm ln}z \sim 10$. While for the
supergravity model $V=V_0Q^{-\alpha}{\rm exp}(kQ^2/2)$, the constraint is much
weakened. For another kind inverse power-law potential $V=V_0{\rm
exp}(\lambda/Q)$, it exhibits no constraints.

Astrophysics