Early Tracking Behavior in Small-field Quintessence Models

We study several quintessence models which are singular at Q=0, and use a simple initial constraint Qᵢ\≥ Hinflation/2\π 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=V₀Q-\α, which has to enter tracking regime for \ lnz \~ 10. While for the supergravity model V=V₀Q-\α\ exp(kQ²/2), the constraint is much weakened. For another kind inverse power-law potential V=V₀\ exp(\λ/Q), it exhibits no constraints.