Revisiting the parametrization of Equation of State of Dark Energy via SNIa Data

TL;DR

This paper evaluates different dark energy equation of state parameterizations using SNIa data, proposing the area of the $w(z)-z$ band as a complementary figure of merit alongside $hi^2$ for better model selection.

Contribution

It introduces the area of the $w(z)-z$ band as a new figure of merit for comparing dark energy parametrizations, emphasizing the combined use with $hi^2$ for optimal model choice.

Findings

The area of the $w(z)-z$ band is effective when $hi^2$ values are similar.

Both $hi^2$ and the $w(z)-z$ band area should be used together for model evaluation.

The proposed figure of merit helps distinguish better parametrizations in dark energy studies.

Abstract

In this paper, we revisit the parameterizations of the equation of state of dark energy and point out that comparing merely the $\chi^2$ of different fittings may not be optimal for choosing the "best" parametrization. Another figure of merit for evaluating different parametrizations based on the area of the $w(z) - z$ band is proposed. In light of the analysis of some two-parameter parameterizations and models based on available SNIa data, the area of $w(z)-z$ band seems to be a good figure of merit, especially in the situation that the value of $\chi^2_{\rm min}$ for different parametrizations are very close. Therefore, we argue that both the area of the $w(z)-z$ band and $\chi^2_{\rm min}$ should be synthetically considered for choosing a better parametrization of dark energy in the future experiments.