Diagnostic and Comparative Analysis of Dark Energy Models with $q(z)$ Parametrizations

This manuscript presents a diagnostic analysis of three dark energy models resulting from the parametrization of the deceleration parameter. These models exhibit intriguing features, including late-time acceleration and a cosmological phase transition from early deceleration to late acceleration. The analysis utilizes parametrizations of the deceleration parameter, $q(z)$, and employs Cosmic Chronometers (CC), Type Ia supernovae (SNIa), Gamma Ray Bursts (GRB), Quasar (Q) and Baryon Acoustic Oscillations (BAO) datasets to constrain the models and determine the best-fitting values of the model parameters. Additionally, the evolution of kinematic cosmographic parameters is investigated. The study focuses on discussing the statefinder and Om diagnostic analyses of the considered models, comparing them with the well-established $\Lambda$CDM and SCDM models. By utilizing information criteria, the viability of the models is examined, assessing their goodness of fit and their ability to explain the observed data. The results provide valuable insights into the behavior and characteristics of the dark energy models. The comparison with the standard models sheds light on the similarities and differences, while the information criteria analysis offers a quantitative assessment of their suitability. This analysis contributes to our understanding of the dynamics and evolution of the universe, furthering our knowledge of dark energy and its role in shaping the cosmos.