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 $\Lambda$CDM, with the latter lying at roughly the $2\sigma$ level from the best-fit model. 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 new phenomenological models proposed here, the power-law and modified power-law forms, which allow greater low-redshift flexibility (around $z \sim 1$) than CPL. We find that parametrizations permitting stronger evolution of the equation of state can exhibit enhanced phantom-like behaviour at intermediate redshifts, however, this feature is sensitive to the assumed functional form and its extrapolation. The statistical preference for such behaviour remains modest, typically at the $\sim 2\sigma$ level, but is consistently observed across different parametrizations, in agreement with recent analyses. Owing to limited data at $z > 2$, this conclusion is primarily driven by the behaviour of the equation of state in the redshift range $1 \leq z \leq 2$. We show that parametrizations with enhanced redshift flexibility, such as power-law-type forms, can mildly improve the fit. Although the statistical significance, quantified using the Akaike and Bayesian information criteria, remains modest, our results indicate that current data favour dynamical dark energy with phantom-like features, although the strength and detailed evolution of this behaviour are not robustly constrained.