Diagnostics of dark energy evolution using logarithmic Om(z) parameterization

Abstract

In this study, we explore the logarithmic $Om\left(z\right)$ parameterization as a tool for diagnosing the nature and evolution of dark energy. We propose the form $Om\left(z\right)=\alpha \ln (1+z)+\beta$, where α and β are free parameters, and analyze its behavior for different values of α. When $\alpha =0$, the model reduces to a constant, consistent with the cosmological constant, while $\alpha \ne 0$ indicates dynamical dark energy, with $\alpha >0$ suggesting phantom-like behavior and $\alpha <0$ indicating quintessence-like dynamics. By constraining the model parameters using observational datasets such as OHD, the Pantheon+ sample, and the combined dataset (OHD+SNe+BAO), we obtain tight constraints on the cosmic evolution. Our results suggest a mild deviation from the standard ΛCDM model, with a slight preference for phantom-like behavior at low redshifts. The deceleration parameter and equation of state parameter were analyzed to understand the cosmic transition from deceleration to acceleration, with a transition redshift around $z_{tr}\approx 0.6-0.8$. The present-day deceleration parameter was found to range from $q_0=-0.55$ to $q_0=-0.60$, and the EoS parameter values varied between ${\omega }_0=-0.70$ and ${\omega }_0=-0.73$. The inferred Hubble constant values exhibit dataset-dependent variations, highlighting the persistent Hubble tension. Our analysis suggests that the logarithmic $Om\left(z\right)$ parameterization offers a flexible framework for studying cosmic acceleration.