Mapping the Chevallier-Polarski-Linder parametrization onto Physical Dark Energy Models

TL;DR

This paper investigates how well the Chevallier-Polarski-Linder (CPL) parametrization models dark energy in quintessence and barotropic models, revealing limitations in its ability to represent the full range of physical behaviors.

Contribution

It maps the CPL parametrization onto physical dark energy models, identifying the specific conditions under which it accurately describes their potentials and dynamics.

Findings

CPL maps onto a narrow potential form in quintessence models.

A specific linear relation in parameters corresponds to diverse potential forms.

CPL may not be optimal for testing certain dark energy models.

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 $V(\phi)$, while a one-dimensional subset of parameter space, for which $w_a = \kappa (1+w_0)$, with $\kappa$ constant, corresponds to a wide range of functional forms for $V(\phi)$. 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.