w and w' of Scalar Field Models of Dark Energy

Abstract

Important observables to reveal the nature of dark energy are the equation of state $w$ and its time derivative in units of the Hubble time $w^{\prime }$. Recently, it is shown that the simplest scalar field models of dark energy (quintessence) occupy rather narrow regions in the $w-w^{\prime }$ plane. We extend the $w-w^{\prime }$ plane to $w<-1$ and derive bounds on $w^{\prime }$ as a function of $w$ for tracker phantom dark energy. We also derive bounds on tracker k-essence.

Comments: 7 pages, 2 figures, errors corrected