Observational Diagnostics of a Parametrized Deceleration Parameter in FRW Cosmology

The evolution of the deceleration parameter q(z) plays a crucial role in understanding the dynamics of dark energy within the framework of modern cosmology. In this study, we perform a parametric reconstruction of q(z) in a spatially flat Friedmann–Robertson–Walker (FRW) Universe composed of radiation, pressureless dark matter, and dark energy. We consider a physically motivated form of q(z) that effectively describes the transition of the Universe from a decelerating to an accelerating expansion phase. This parametrization is incorporated into the Friedmann equations to derive the corresponding Hubble parameter, which is then confronted with a comprehensive set of observational data, including Hubble parameter measurements H(z), Type Ia supernovae (SNIa), and Baryon Acoustic Oscillations (BAO) data. Employing the Markov Chain Monte Carlo (MCMC) approach, we constrain the model parameters using the combined H(z) + SNIa + BAO dataset. The best-fit parameters are subsequently used to reconstruct the cosmographic quantities, such as the deceleration, jerk, and snap parameters, which provide deeper insight into the expansion history of the Universe. Finally, a comparative analysis with the standard ΛCDM model is carried out to assess the compatibility and effectiveness of the proposed parametrization.