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

TL;DR

This work evaluates two two-parameter dark energy parameterizations, Barboza–Alcaniz and a Logarithmic form, against the latest background cosmology data. Using MCMC with the emcee package, the authors constrain H0, w0, and wa from Pantheon SNe Ia, DESI BAO, and cosmic chronometers, and employ statefinder diagnostics to contrast the geometric evolution of the models. The BA and Logarithmic parameterizations both fit the data well, with the Logarithmic form yielding tighter evolution constraints and a phantom-like future, while BA remains closer to quintessence and tends toward a de Sitter phase; neither is decisively preferred over CPL according to AIC/BIC, though the models offer distinct late-time implications. The study demonstrates how high-precision data and geometric diagnostics jointly illuminate the potential dynamics of dark energy and their impact on the cosmic fate and the H0 tension.

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.

Figures (6)

• Figure 1: The plot of Hubble parameter $H(z)$, and $\mu(z)$ versus $z$ for BA parameterization
• Figure 2: The best fit plots for 1-D marginalized distribution, and 2-D contours with $68\%$ CL and $95\%$ CL for the model parameters with the combined CC + DESI BAO + Pantheon datasets.
• Figure 3: The plot of Hubble parameter $H(z)$, and $\mu(z)$ versus z for Logarithmic parameterization
• Figure 4: The best fit plots for 1-D marginalized distribution, and 2-D contours with $68\%$ CL and $95\%$ CL for the model parameters with the combined CC + DESI BAO + Pantheon datasets.
• Figure 5: The plot displays the evolution of the effective Deceleration $(q)$ and EoS $(w_{eff})$ parameters with respect to the redshift $z$ using the values constrained from the Pantheon+DESI BAO+CC datasets.