Evidence for the dynamical dark energy with evolving Hubble constant

TL;DR

This paper tackles the $H_0$ tension and possible dynamical dark energy by performing a model-independent, non-parametric reconstruction of the dark-energy EoS $w(z)$ and an evolving Hubble constant $H_0(z)$ using DESI DR2 BAO and multiple SNe Ia datasets. It employs Gaussian Process priors with different covariance forms to infer $w(z)$ and $H_0(z)$ across 29 redshift bins up to $z=2.5$, without assuming a specific functional form. The results indicate a redshift-evolving $w(z)$ with two phantom-crossings at $z \nsim 0.5$ and $z sim 1.5$, and a smoothly decreasing $H_0(z)$ that mitigates the tension with early-Universe measurements. Bayesian evidence favors the joint $w(z)$-$H_0(z)$ model over conventional $w$CDM and $ m Lambda$CDM scenarios across dataset/prior combinations, with the strongest support when including PantheonPlus data, suggesting that dynamical dark energy and $H_0$ evolution may play a key role in cosmic expansion. The conclusions highlight robustness to kernel choices and Horndeski priors, while noting degeneracies with the sound horizon $r_d$ that future surveys will help resolve.

Abstract

Hubble constant tension, together with the recent indications of dynamical dark energy proposed from the Dark Energy Spectroscopic Instrument (DESI) baryon acoustic oscillation (BAO) measurements, poses significant challenges to the standard cosmological model. In this work, we perform a model-independent reconstruction of the dark-energy equation of state $w(z)$, jointly with an evolving Hubble constant $H_0(z)$. Using the DESI DR2 data combined with multiple type Ia supernova samples, we find that $w(z)$ varies with redshift and exhibits two potential phantom crossings at $z\sim0.5$ and $z\sim1.5$. Meanwhile, $H_0$ decreases continually from local to high redshift, alleviating the Hubble constant tension effectively. The joint $w(z)$-$H_0(z)$ model is strongly favored over the $w$CDM ($Λ$CDM) framework, with a logarithmic Bayes factor $\ln \boldsymbol{\mathcal B}= 5.04~(8.53)$. Across various prior assumptions and dataset combinations, we obtain consistent, data-driven reconstructions of both $w(z)$ and $H_0(z)$. Future BAO measurements from Euclid and next-generation CMB experiments will provide critical tests of these results and bring deeper insights into the nature of dark energy and the evolution of cosmic expansion.

Figures (5)

• Figure 1: Reconstructed dark-energy EoS $w(z)$ and Hubble constant $H_0(z)$ from multiple datasets. The GP for $w(z)$ and $H_0(z)$ use $\rm Mat \acute{e} rn$-3/2 and Gaussian kernels, respectively. Panels in each column correspond to using the same datasets. Solid blue lines show the mean values of the $w(z)$ and $H_0(z)$ distributions. The shaded blue regions indicate the corresponding $68\%$ credible intervals. The dashed black lines marks $w=-1$. The orange and green bands denote $H_0$ estimations from SNe Ia 2022ApJ...934L...7R and CMB 2020AA...641A...6P, respectively.
• Figure 2: Similar with \ref{['fig:1']}, but using the Gaussian kernel for the $w(z)$ prior. In the right panel, the blue region represents the results with a maximum Bayes factor with $l=0.05$. The purple region corresponds to $l=0.2$, assuming the same scale length as in the left and middle panels. A smaller $l$ ($l<0.01$) in the DESI + Union case may yield a higher Bayesian evidence, but the resulting $w(z)$ becomes too flexible to provide clear constraint. Therefore, the right panel only shows the results for $l=0.05$ and $l=0.2$.
• Figure 3: Similar with \ref{['fig:1']}, but using the Horndeski theory to derive the $w(z)$ prior. The results in the left panel use a Gaussian kernel with $l=2.0$ to derive the $H_0(z)$ priors, while the others use $l=1.0$ to obtain the maximum bayes factors.
• Figure 4: Comparisons with different scale length under various prior assumptions. The red, orange, and blue scatters represent the Bayes factors relative to $w$CDM models using DESI combined with PantheonPlus, DESY5, and Union3 datasets, respectively.
• Figure 5: The reconstructions of $w(z)$ and $H_0(z)$ using the DESI + PantheonPlus datasets. The prior of $H_0(z)$ uses the Gaussian kernel with $l=1.5$. The red, orange and blue regions correspond to $w(z)$ priors generated from the $\rm Mat \acute{e} rn$-3/2 kernel ($l=2.5$), the Gaussian kernel ($l=0.2$), and the Horndeski theory, respectively.