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

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 $\Lambda$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 $\Lambda$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 ($\Delta\chi^2\simeq-6$ to $-12$ for PantheonPlus and Union3, and $\simeq-38$ for DESY5). Statistical consistency with $\Lambda$CDM, quantified via the Mahalanobis distance in one, two, and three dimensional parameter subspaces, reveals mild to moderate deviations, $\sim2$--$2.5\sigma$ for $+$PantheonPlus, $2$--$3\sigma$ for $+$Union3, and up to $4$--$5\sigma$ 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 $\Lambda$CDM and well behaved parameter correlations. Overall, these results indicate consistent evidence for departures from $\Lambda$CDM.