A parameterized equation of state for dark energy and Hubble Tension

TL;DR

The paper proposes a parameterized dark-energy equation of state with $w(z) = -1/(1+\alpha(1+z)^6)$ and derives the corresponding expansion history $H^2(z) = H_0^2[\Omega_m(1+z)^3 + (1-\Omega_m) f(z)]$ where $f(z) = \sqrt{(1+\alpha(1+z)^6)/(1+\alpha)}$. Using MCMC with emcee, the authors constrain $H_0$, $\Omega_m$, and $\alpha$ from four datasets: observational Hubble data, Pantheon+, BAO, and DESI DR2 F data, analyzing progressively larger combinations. The joint analyses yield best-fit values around $H_0 \sim 74$ km s$^{-1}$ Mpc$^{-1}$, $\Omega_m \sim 0.23$–$0.24$, and $\alpha$ near zero but slightly negative (phantom behavior) in the full data combination, indicating consistency with late-time observations and an alleviation of the Planck-inferred Hubble tension. The results demonstrate robustness to dataset choice and show that including DESI DR2 F data tightens constraints, supporting phantom-like dark energy within this parameterization and highlighting the potential for future data to further refine or challenge the model.

Abstract

We propose a parameterized equation of state for dark energy and perform observational tests with the Hubble parameter measurements, the Pantheon supernova sample, baryon acoustic oscillations, and DESI DR2 data. We obtain the best-fit values for the parameters as: $H_0=73.96\pm 0.16$, $Ω_{\rm m}=0.2434\pm 0.0079$, and $α=-0.00049\pm 0.00092$, demonstrating that the model exhibits a high degree of consistency with astronomical observations and provides a promising parameterized method for addressing the Hubble tension.

Figures (6)

• Figure 1: The inferred best-fit model parameters along with their $1\sigma$ and $2\sigma$ confidence regions based on the Hubble datasets.
• Figure 2: The reconstructed Hubble function $H(z)$ as a function of redshift inferred from observational Hubble data. The dotted lines shows the prediction of our model, while the solid black curve denotes the $\Lambda$CDM scenario.
• Figure 3: Best-fit parameter estimates together with their $1\sigma$ and $2\sigma$ confidence regions derived from the combined Hubble and Pantheon$+$ observational samples.
• Figure 4: The predicted distance modulus $\mu_{z}$ as a function of redshift $z$ for both our model and the $\Lambda$CDM model, using parameter constraints obtained from the combined Hubble and Pantheon$+$ data.
• Figure 5: The inferred best-fit model parameters, along with the corresponding $1\sigma$ and $2\sigma$ confidence contours, as constrained by the combined Hubble, Pantheon$+$, and BAO observational samples.