Examining the Linear and Quadratic Dark Energy Parameterizations with DESI DR2 via AIC and BIC Selection

Abstract

We examine whether or not the current observational preference for a dynamical dark energy(DE), as reported by DESI, is an artifact of the chosen functional form of dark energy equation of state (EoS) parameter $w(z)$ by considering a higher-order quadratic extension in EoS. We explore three distinct parameterizations of the DE models: the two-parameter (linear) Chevallier-Polarski-Linder (CPL) and Wang models, alongside a three-parameter parabolic (quadratic) formulation. Using a joint dataset of CMB measurements from Planck and ACT DR6, baryon acoustic oscillations of DESI DR2, and Type Ia supernovae from Pantheon+ and DES-SN5YR, we constrain the model parameters and observe a maximum frequentist preference of up to $\sim 4\sigma$ for these dynamical models. Specifically, the joint CMB + DESI + DES-SN5YR combination yields a substantial improvement in fit over $\Lambda\text{CDM}$, with $\Delta\chi^2_{\text{min}}$ values of $-20.5$, $-19.4$, and $-21.7$ for CPL, Wang, and Parabolic models, respectively. In addition, the Akaike Information Criterion (AIC) provides weak to no evidence for $\Lambda$CDM, consistently favoring the dynamical DE models instead. On the other hand, the Bayesian Information Criterion (BIC) imposes a heavy penalty on all the three models, reflecting its high sensitivity to dataset size and model complexity. We find at best a mild support for CPL and Wang models but the Parabolic model is strongly disfavored ($\Delta \text{BIC} \sim +6.4$ to $+15.6$). Furthermore, due to its expanded parameter space, the Parabolic model exhibits a significant reduction in the Figure of Merit (FoM) compared to the two-parameter counterparts, demonstrating that the current cosmological datasets do not yet justify an introduction of the higher-order DE models. So, as a result, the two-parameter descriptions of $w(z)$ remain the optimal choice for testing the dynamical DE signatures.