Observational Constraints and Geometric Diagnostics of Barboza-Alcaniz and Logarithmic Dark Energy Parametrizations

Abstract: This study investigates and compares two prominent two-dimensional dark energy (DE) parameterizations: Barboza-Alcaniz (BA) and Logarithmic forms by comparing them with a comprehensive set of observational data comprising Type Ia Supernovae (SNe Ia) from the Pantheon compilation, Baryon Acoustic Oscillations (DESI BAO), and Cosmic Chronometers (CC). The primary objective was to explore the constraining power and cosmological implications of each parameterization in light of the current data. After formulating the theoretical framework and background equations governing cosmic expansion, we employ Markov Chain Monte Carlo (MCMC) techniques using the emcee Python package to constrain the free parameters of each model. The best-fit values for parameters $ω_0$, $ω_a$, and $H_0$ were extracted for each model using individual and combined datasets. The results include confidence contours at the levels $1σ$ and $2σ$. Our findings demonstrate that both parameterizations are consistent with observational data, with logarithmic parameterization showing slightly better constraints in terms of parameter evolution. Furthermore, we employed a statefinder diagnostic to analyze the geometric behavior of the models, providing an effective distinction between the two DE scenarios. This study contributes to a deeper understanding of DE evolution and its constraints in light of current cosmological data.