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 $H_0 = 71.02 \pm 0.66~\text{kms}^{-1}\text{Mpc}^{-1}$, $Ω_m = 0.2863 \pm 0.0080,$ $w_0 = -0.875 \pm 0.066,$ $w_a = -0.69^{+0.37}_{-0.32},$ 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.

Figures (8)

• Figure 1: Distance modulus $\mu(z)$ as a function of redshift for the Pantheon Plus Type Ia supernova sample. The purple data points with error bars represent the observed $\mu(z)$ measurements. The solid red curve corresponds to the best-fit $w_{\log}$CDM model based on the logarithmic parameterization of the dark-energy equation of state, while the dashed black curve denotes the standard $\Lambda$CDM prediction.
• Figure 2: Best-fit reconstruction of the Hubble parameter $H(z)$ for the logarithmic dark-energy model using observational Hubble data. The orange points with error bars represent the measured $H(z)$ values from cosmic chronometer observations. The solid red curve corresponds to the best-fit $w_{\log}$CDM model, while the dashed black curve shows the standard $\Lambda$CDM prediction for comparison.
• Figure 3: One-D posterior distributions and Two-D marginalized confidence regions ($68\%$ CL and $95\%$ CL) for $\Omega_{\rm m}$, $M_B$, $w_0$, $w_a$$10^{-2}\omega_{b}$ and $H_0$ obtained from the DESI BAO+BBN+CC ,DESI BAO+BBN+CC+PP and DESI BAO+BBN+CC+PPS for the $w_{log}$CDM model. The parameter $H_0$ is in units of $km/s/Mpc$.
• Figure 4: Two–dimensional marginalized confidence contours in the $w_{0}$–$H_{0}$ plane for the $w_{log}$CDM model using the DESI BAO+BBN+CC, DESI BAO+BBN+CC+PP, and DESI BAO+BBN+CC+PPS dataset combinations. The shaded horizontal band shows the SH0ES local determination of the Hubble constant, $H_{0}=73.04 \pm 1.04~\mathrm{km\,s^{-1}\,Mpc^{-1}}$.
• Figure 5: Two–dimensional marginalized confidence contours in the $w_{a}$–$H_{0}$ plane for the $w_{log}$CDM model using the DESI BAO+BBN+CC, DESI BAO+BBN+CC+PP, and DESI BAO+BBN+CC+PPS dataset combinations. The shaded horizontal band shows the SH0ES local determination of the Hubble constant, $H_{0}=73.04 \pm 1.04~\mathrm{km\,s^{-1}\,Mpc^{-1}}$.