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

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 ΛCDM 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 ΛCDM, wCDM, mAH, CPL, and the three-parameter CPL- w 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 ≃ -6 to -12 for PantheonPlus and Union3, and ≃ -38 for DESY5). Statistical consistency with ΛCDM, quantified via the Mahalanobis distance in one, two, and three dimensional parameter subspaces, reveals mild to moderate deviations, ∼ 2–2.5 σ for +PantheonPlus, 2–3 σ for +Union3, and up to 4–5 σ 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 ΛCDM and well behaved parameter correlations. Overall, these results indicate consistent evidence for departures from ΛCDM.