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 H/2π to check when they enter the tracking regime, disregarding the details of inflation. We find that it can also give strong constraints for V = VoQ-α, which has to enter the tracking regime after Inz - 10, while for the supergravity model V = V0Q-αexp(kQ2/2), the constraint is much weaker. For the exponential form of inverse power-law potential V = V0exp(λ/Q), it exhibits no constraints.