Investigating the $H_0$ Tension and Expansion-History Mismatch with Diverse Dark Energy Parametrization Frameworks
In this work, we investigate whether the mismatch between early- and late-Universe inferences of the cosmic expansion history is associated with a particular redshift range, and whether models that alleviate the $H_0$ tension also provide a consistent description of $H(z)$ across cosmic time. We consider four late-time cosmological frameworks: $Λ$CDM, a dark energy (DE) equation-of-state parametrization, a DE pressure parametrization, and a generalized scale-factor parametrization. Using Planck CMB data as an early-Universe anchor and Pantheon+ with SH0ES calibration as a late-Universe probe, together with DESI DR2 BAO measurements, we first assess the $H_0$ tension in each framework and then reconstruct the expansion history through $H(z)$. We further compare these parametric reconstructions with non-parametric reconstruction employing Gaussian process regression. We find that the expansion histories inferred within $Λ$CDM remain significantly discrepant over the full redshift range considered, whereas the alternative phenomenological parametrizations largely localize the mismatch to lower redshifts. Among these models, the pressure parametrization gives the strongest reduction of the $H_0$ tension, to approximately $2.6σ$, while still exhibiting significant discrepancies in the reconstructed $H(z)$ at intermediate redshifts. Both the parametric and model-independent reconstructions identify the strongest deviations around $z=0.51$ and $z=0.706$ consistently, indicating robust late-time tensions in the cosmic expansion rate.