Mapping the Chevallier-Polarski-Linder parametrization onto physical dark energy Models

Robert J. Scherrer

Phys. Rev. D 92, 043001 – Published 5 August 2015

Abstract

We examine the Chevallier–Polarski–Linder (CPL) parametrization, in the context of quintessence and barotropic dark energy models, to determine the subset of such models to which it can provide a good fit. The CPL parametrization gives the equation of state parameter $w$ for the dark energy as a linear function of the scale factor $a$ , namely $w = w_{0} + w_{a} (1 - a)$ . In the case of quintessence models, we find that over most of the $w_{0}$ , $w_{a}$ parameter space the CPL parametrization maps onto a fairly narrow form of behavior for the potential $V (ϕ)$ , while a one-dimensional subset of parameter space, for which $w_{a} = κ (1 + w_{0})$ , with $κ$ constant, corresponds to a wide range of functional forms for $V (ϕ)$ . For barotropic models, we show that the functional dependence of the pressure on the density, up to a multiplicative constant, depends only on $w_{i} = w_{a} + w_{0}$ and not on $w_{0}$ and $w_{a}$ separately. Our results suggest that the CPL parametrization may not be optimal for testing either type of model.