Quintessence models of H ( t ) in the light of DESI DR2

In this paper, we study the parametrization of the Hubble parameter [Formula: see text], known as Pacif’s scheme of parametrization. This approach naturally gives rise to two quintessence dark energy models, namely the linearly varying deceleration parameter (LVDP) and the quadratically varying deceleration parameter (QVDP) models, in light of the latest Baryon Acoustic Oscillation data from the Dark Energy Spectroscopic Instrument (DESI) Data Release 2, together with Pantheon[Formula: see text] and Cosmic Chronometer measurements. To constrain the parameters of each model, we use the nested sampling algorithm via the dynesty package. We further analyze the present-day deceleration parameter ([Formula: see text]) and the transition redshift ([Formula: see text]), identifying the epoch when the Universe shifted from deceleration to acceleration. Our results show that the inferred values of [Formula: see text] for both models agree closely with Planck 2018 findings. Importantly, LVDP predicts [Formula: see text], consistent with DESI DR2 results, thereby supporting the possibility of dynamical dark energy rather than a cosmological constant. In contrast, QVDP exhibits quintessence-like behavior at higher redshifts ([Formula: see text]) but subsequently crosses the phantom divide, entering the [Formula: see text] regime. Bayesian evidence further reveals that LVDP is strongly favored, while QVDP provides a better fit than [Formula: see text]CDM but with weaker support.