Assessing observational constraints on dark energy

Observational constraints on time-varying dark energy ({\it e.g.}, quintessence) are commonly presented on a $w_0$-$w_a$ plot that assumes the equation of state of dark energy strictly satisfies $w(z)= w_0+ w_a z/(1+z)$ as a function of the redshift $z$. Recent observations favor a sector of the $w_0$-$w_a$ plane in which $w_0 > -1$ and $w_0+w_a< -1$, suggesting that the equation of state underwent a transition from violating the null energy condition (NEC) at large $z$ to obeying it at small $z$. In this paper, we demonstrate that this impression is misleading by showing that simple quintessence models satisfying the NEC for all $z$ predict an observational preference for the same sector. We also find that quintessence models that best fit observational data can predict a value for the dark energy equation of state at present that is significantly different from the best-fit value of $w_0$ obtained assuming the parameterization above. In addition, the analysis reveals an approximate degeneracy of the $w_0$-$w_a$ parameterization that explains the eccentricity and orientation of the likelihood contours presented in recent observational studies.