Dark Energy Models in the w - w' Plane

Abstract

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&#39; (the derivative of w with respect to the logarithm of the scale factor). For non-phantom barotropic fluids with positive squared sound speed, we find that w&#39; < 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&#39; plane. We also derive two new bounds for quintessence models in the w - w&#39; 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&#39;) < 1+w.