Beyond CPL: Evidence for dynamical dark energy in three-parameter models

TL;DR

The paper addresses persistent tensions in ΛCDM by testing two three-parameter dynamical dark energy models, MmAH1 and MmAH2, built as extensions of the Akhtar-Hossain framework. Using a joint analysis of Planck 2018 CMB priors, DESI DR2 BAO, H(z), RSD, and SNeIa samples (PantheonPlus, Union3, DESY5) with MCMC, the authors compare ΛCDM, wCDM, CPL, CPL-$w_{ m b}$, mAH, and the two MmAH variants, employing AIC/BIC and Mahalanobis-distance tensions to assess statistical preference and consistency. They find CPL, MmAH1, and MmAH2 to offer the best combinations of fit quality and physical coherence, with MmAH1/2 delivering substantial improvements in $\chi^2$ especially when DESY5 is included, and notable but dataset-dependent tensions with ΛCDM. Overall, the results indicate consistent departures from a pure cosmological constant, with MmAH1 and MmAH2 providing robust, flexible descriptions of DDE that remain physically meaningful across data combinations, signaling a potential dynamical component to dark energy that warrants future high-precision surveys.

Abstract

We introduce two three-parameter extensions of the minimal Akhtar-Hossain (mAH) dark energy parametrization, termed modified minimal AH (MmAH1 and MmAH2), which provide a smooth and bounded evolution of the dark energy equation of state while retaining $Λ$CDM as a limiting case. Using a joint analysis of the CMB compressed likelihood, DESI DR2 BAO, $H(z)$, redshift space distortions, and three SNeIa samples (PantheonPlus, Union3, and DESY5), we compare these models with $Λ$CDM, $w$CDM, mAH, CPL, and the three-parameter CPL-$w_{\rm b}$ extension. The standard cosmological parameters remain stable across all models, while CPL, MmAH1 and MmAH2 parametrizations yield modest but consistent improvements in fit ($Δχ^2\simeq-6$ to $-12$ for PantheonPlus and Union3, and $\simeq-38$ for DESY5). Statistical consistency with $Λ$CDM, quantified via the Mahalanobis distance in one, two, and three dimensional parameter subspaces, reveals mild to moderate deviations, $\sim2$--$2.5σ$ for $+$PantheonPlus, $2$--$3σ$ for $+$Union3, and up to $4$--$5σ$ for $+$DESY5 combination, depending on model complexity. Among all extensions CPL, MmAH1 and MmAH2 provide the most stable and physically coherent representations of dynamical dark energy, maintaining moderate tensions with $Λ$CDM and well behaved parameter correlations. Overall, these results indicate consistent evidence for departures from $Λ$CDM.

Figures (5)

• Figure 1: Top left: Energy density $\rho$ is plotted against redshift $z$ in $log$ scale for mAH, MmAH1, MmAH2 and CPL.Top right: Evolution of density parameter ($\Omega$) is shown in for MmAH1 and MmAH2 parametrizations along with the evolution of matter and radiation. Bottom left: EoS ($w(z)$) is plotted against $z$. Bottom right: Comparison with CPl in the evolution of EoS is shown for very small redshifts .
• Figure 2: Lensed CMB temperature (top) and E-mode polarization (middle) power spectra ($\mathcal{D}_\ell^{TT}$ and $\mathcal{D}_\ell^{EE}$) and their differences with respect to the $\Lambda$CDM, using lensed $C_\ell$ data. Bottom: Matter power spectrum $P(k)$ and its difference with respect to the $\Lambda$CDM baseline.
• Figure 3: Evolution of the EoS for the CPL (top left), CPL-$w_{\rm b}$ (top right), MmAH1 (bottom left) and MmAH2 (bottom right) models. The solid blue curves correspond to the median value of the EoS. The dark colour and light colour shaded regions show the corresponding $1\sigma$ and $2\sigma$ errors.
• Figure 4: $1\sigma$ and $2\sigma$ confidence contours for the parameters $w_0$, $w_a$, and $w_b$ in the CPL, MmAH1, and MmAH2 models (left), and in the CPL-$w_{\rm b}$ model (right).
• Figure 5: $1\sigma$ and $2\sigma$ confidence contours for the parameters $z_{\rm t}$, $\alpha$, and $\beta$ in the MmAH1 (left) and MmAH2 (right) models. The contours for $z_{\rm eq}$ and $\gamma$ are also shown for the MmAH1 model.