Alleviating the Hubble Tension with Logarithmic Dark Energy: Constraints on the $w_{log}$CDM Model

Abstract: Observational constraints are considered on a $w_{log}$CDM model of the dark energy equation of state, $w_{d}(z) = w_{0} + w_{a}\left( \frac{\ln(2+z)}{1+z} - \ln 2 \right)$, using the most recent cosmological datasets including DESI Baryon Acoustic Oscillation (BAO) measurements, Big Bang Nucleosynthesis (BBN) priors, Cosmic Chronometer (CC) observations, and Pantheon Plus (PPS) Type Ia supernovae. From the combined DESI BAO+BBN+CC+PPS dataset, we obtain $H_0 = 71.02 \pm 0.66~\text{kms}^{-1}\text{Mpc}^{-1}$, $Ωm = 0.2863 \pm 0.0080,$ $w_0 = -0.875 \pm 0.066,$ $w_a = -0.69^{+0.37}{-0.32},$ at the 68\% and 95\% confidence levels, indicating a preference for phantom dark energy with mild evidence for temporal evolution. The Hubble constant obtained from our model is closer to the local SH0ES measurement than the standard $Λ$CDM prediction, partially easing the Hubble tension. We perform extensive parameter-space exploration revealing correlations between $w_0$, $w_a$, and $H_0$, showing that dynamical dark energy models can fit higher values of the Hubble constant. The reconstructed deceleration parameter $q(z)$ shows the transition from deceleration to acceleration at $z \sim 0.6$--$0.7$, while the equation-of-state reconstruction remains consistent with a cosmological constant across the observed redshift range. A model comparison using information criteria indicates that the $w_{log}$CDM model remains statistically competitive with $Λ$CDM.