Challenging the $ω_0ω_a$CDM parametrization through rational expansions in view of DESI data release

TL;DR

This work challenges the DESI-preferred $\omega_0\omega_a$CDM parametrization by exploring Padé rational expansions as alternative dark-energy backgrounds. Through MCMC analyses with CLASS against Pantheon+ SN Ia, DESI DR2 BAO, CMB shift parameters, and OHD, the authors compare Padé$^{\omega}$ (0,1), Padé$^{\omega}$ (1,1), Padé$^{q}$ (0,1), $\omega_0\omega_a$CDM, and $\Lambda$CDM. They find that Padé cosmologies are not statistically excluded and, depending on the criterion, can outperform $\omega_0\omega_a$CDM (AIC) or even be preferred (DIC), with the Padé$^{q}$ (0,1) model achieving the best AIC and Padé (1,1) the strongest DIC support. The analysis also shows improved late-time stability against unphysical negative sound speeds for Padé$^{q}$ (0,1) and Padé$^{\omega}$ (0,1) relative to other parameterizations. Overall, the work advocates rational Padé expansions as robust, physically viable alternatives for describing the cosmological background and highlights the need for broader data combinations to robustly discern dark-energy dynamics.

Abstract

In view of the new Dark Energy Spectroscopic Instrument (DESI) 2025 results, we analyze three types of \emph{Padé cosmology}, based on rational series making use of Padé approximants over the equations of state, namely Padé$^ω$ (0,1) and Padé$^ω$ (1,1), plus a Padé$^{q}$ (0,1), i.e., a rational expansion on the dark energy deceleration parameter, in which where the numerator and denominator orders are incorporated into the above brackets. These scenarios appear alternative dark energy parameterizations with respect to the well-known $ω_0ω_a$CDM model, claimed as the most viable model by DESI. Accordingly, we perform Monte Carlo Markov chain (MCMC) analyses with the publicly available \texttt{CLASS} Boltzmann code, including the three Padé cosmology, along with the $ω_0ω_a$CDM and $Λ$CDM standard pictures. To this end, we combine independent probes from high to low redshifts to obtain reliable constraints on the cosmological parameters of these models and compare them using statistical selection criteria. \emph{Our results show that Padé cosmology is neither statistically excluded nor worse than the $ω_0ω_a$CDM parametrization}. On the contrary, the Akaike Information Criterion (AIC) identifies Padé$^{q}$ (0,1) as \emph{the best-fit model}, with weak evidence against the $ω_0ω_a$CDM parameterization, while the Deviance Information Criterion (DIC) provides \emph{strong evidence against the $ω_0ω_a$CDM model, favoring Padé (1,1)}. Based on our bounds, we further investigate the evolution of the squared sound speed, revealing that the Padé$^{q}$ (0,1) and Padé$^ω$ (0,1) parameterizations exhibit enhanced stability compared with the other cases here considered and, therefore, describe robust alternatives for the cosmological background.

Figures (3)

• Figure 1: Sound speed as a function of redshift, obtained from the MCMC analysis of the proposed Padé dark energy parameterization, compared with the $\Lambda$CDM and $\omega_0\omega_a$CDM models. The shaded regions denote the 1$\sigma$ confidence intervals.
• Figure 2: Contour plots of the cosmological parameters for the three dark energy parameterizations considered in this work, obtained with GetDist. The top row corresponds to Padé$^{\omega}$ (0,1) and Padé (1,1), while the bottom panel shows $\omega_0\omega_a$CDM and Padé$^{q}$ (0,1).
• Figure 3: Reconstructed evolution of the deceleration parameter $q(z)$ based on the MCMC constraints for the proposed Padé dark energy parameterizations, compared to the $\Lambda$CDM and $\omega_0\omega_a$CDM models. The shaded bands indicate the $1\sigma$ uncertainty ranges around the mean.