Early Tracking Behavior in Small-field Quintessence Models

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We study several quintessence models which are singular at Q=0, and use a simple initial constraint Qᵢ≥ Hinflation/2π 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.