Probing the sensitivity of dark energy dynamics to equation of state parametrization flexibility

Allowing for greater low redshift flexibility through parametrizations such as CPL can lead to apparent deviations from Λ CDM. This motivates an investigation into whether such deviations reflect genuine dynamical dark energy or arise from parametrization choices. We investigate several dark energy parametrizations, including two phenomenological power law type extensions proposed here, the power law and modified power law forms, which allow greater low redshift flexibility (around z about 1) than CPL. Parametrizations permitting stronger evolution of the equation of state can exhibit enhanced phantom like behaviour at intermediate redshifts, but this feature is sensitive to the assumed functional form and its extrapolation. The statistical preference for such behaviour is modest, depends on the supernova sample, and is consistent across parametrizations, in agreement with recent analyses. The likelihood-ratio significance of this preference is 2.2 -- 3.9σ. Owing to limited data at z > 2, this is primarily driven by the equation of state in the range 1 at most z at most 2, where parametrizations with enhanced flexibility, such as power law type forms, mildly improve the fit. The Akaike Information Criterion favours the DDE parametrizations over Λ CDM for all three supernova samples. The Bayesian Information Criterion mildly favours them for + Union3 and + DESY5 but disfavours them for + PantheonPlus.