Parametrization Framework for the Deceleration Parameter in Scalar Field Dark Energy Model

The universe is currently experiencing acceleration. One way to explain this is via matter with negative energy, called dark energy. We propose a Friedmann-Lemaitre-Robertson-Walker cosmological model with a scalar field that represents dark energy. The deceleration parameter measures this acceleration. A novelty of this work is that a new parametrization of the deceleration parameter is introduced of the form q = -1 + eta /(1 + mu a eta) where eta and mu are model parameters, and a is the scale factor or radius of the universe. We find the values of the parameters of the model by means of best-fit to recent observations, including cosmic chronometers, Pantheon+ and Baryon Acoustic Observations, using the Markov Chain Monte Carlo method. We address the expansion history of the universe and provide a viable description of the transition from deceleration to acceleration. A comparison is then made with the Lambda Cold Dark Matter (Lambda CDM) model of general relativity. We examine the evolution of the main key cosmological parameters, such as the deceleration parameter, jerk parameter, snap parameter, density parameter, and equation-of-state parameter. By interpreting them, we obtain insights into what has been dubbed "dynamical dark energy" under the assumptions made above. Our method provides a framework that is independent of the model to explore dark energy. This leads to a deeper and more subtle understanding of the mechanisms driving late-time cosmic acceleration.