Dark energy models in the w-w' plane

We examine the behavior of dark energy models in the plane defined by w (the equation of state parameter for the dark energy) and w' (the derivative of w with respect to the logarithm of the scale factor). For nonphantom barotropic fluids with positive squared sound speed, we find that w'<3w(w+1), the opposite of the bound on quintessence models previously derived by Caldwell and Linder. Thus, these barotropic models and quintessence models for the dark energy occupy disjoint regions in the w-w' plane. We also derive two new bounds for quintessence models in the w-w' plane: the first is a general bound for any scalar field with a monotonic potential, while the second improves on the Caldwell-Linder bound for tracker quintessence models. Observationally distinguishing barotropic models from quintessence models requires σ(w') < or approx. 1+w