Early tracking behavior in small-field quintessence models

We study several quintessence models which are exotic at Q = 0, and use a simple constraint Q greater than or equal to H/2pi to check when they enter the tracking regime, disregarding the details of inflation. We find that it can also give strong constraints for V = V(0)Q(-alpha), which has to enter the tracking regime after In z similar to 10, while for the supergravity model V = V(0)Q(-alpha)exp(kQ(2)/2), the constraint is much weaker. For the exponential form of inverse power-law potential V = V(0)exp(lambda/Q), it exhibits no constraints.