Dynamical Dark Energy and the Unresolved Hubble Tension: Multi-model Constraints from DESI 2025 and Other Probes

TL;DR

The paper confronts the Hubble tension and the nature of dark energy by comparing ΛCDM, wCDM, w0w_aCDM, φCDM, and ξ-index interacting models against DESI DR2 BAO, Pantheon+ SNIa, and Planck 2018 + ACT DR6 CMB+lensing data using Bayesian model comparison. It finds that no model decisively outperforms ΛCDM across all data, yet there is robust evidence for dynamical dark energy: high-redshift CMB data favor a phantom state ($w(z)<-1$) while low-redshift distances prefer quintessence ($w(z)>-1$), with a Quintom-like crossing in $w_0w_a$CDM. The ξ-index model shows tentative late-time DE–matter interactions, with energy transfer from DE to matter suggested by full data, though results are dataset-dependent. Across all models, the Hubble constant remains anchored near early-Universe Planck inferences, leaving the Hubble tension unresolved and highlighting possible systematics or new physics beyond current dark energy parameterizations. These findings motivate next-generation, multi-probe surveys and more sophisticated theories to pin down the mechanism of cosmic acceleration.

Abstract

We present a Bayesian comparative analysis of five cosmological models: $Λ$CDM, $w$CDM, $w_0w_a$CDM, $φ$CDM (with scalar-field dark energy), and an interacting dark energy scenario (the $ξ$-index model), to investigate dark energy evolution and the Hubble tension. Utilizing the latest data from the Dark Energy Spectroscopic Instrument (DESI) DR2 (Baryon Acoustic Oscillations, BAO), Pantheon+ (Type Ia Supernovae, SNIa), and Cosmic Microwave Background (CMB) data (including lensing) from \textit{Planck} and the Atacama Cosmology Telescope (ACT), we report three key findings. First, the Hubble constant ($H_0$) inferred from the combined data consistently aligns with early-universe measurements across all models, indicating a persistent Hubble tension. Second, we find compelling evidence for dynamical dark energy: early-universe (CMB) constraints favor a phantom phase (with an equation-of-state parameter $w < -1$), while late-universe (BAO/SNIa) data prefer quintessence ($w > -1$). Third, the full dataset suggests a late-time interaction between dark energy and matter. Our results demonstrate that dark energy evolves with cosmic time, challenging the cosmological constant paradigm.

Figures (4)

• Figure 1: Bayesian evidence comparison reveals strong dataset dependence. The $\ln B$ values for the five cosmological models are shown for four data combinations. No alternative model achieves decisive evidence ($\Delta\ln B > 2.5$) over $\Lambda$CDM (black) across all datasets. Error bars show 1$\sigma$ uncertainties.
• Figure 2: Constraints on $\Omega_m$ and $H_0$ highlight the persistent Hubble tension. Joint 68% CL constraints are shown for the five models (same color scheme as Fig. 1) across four data combinations. The purple dashed and gray dot-dashed lines indicate the SH0ES and Planck 2018 measurements, respectively. All models converge to the lower $H_0$ value with constraining datasets.
• Figure 3: Redshift evolution of $w(z)$ provides evidence for dynamical dark energy. The 1$\sigma$ constraints on $w(z)$ are shown for the five models (same style and color as previous figures) across four data combinations. A clear evolutionary trend is observed: high-$z$ CMB data prefer phantom behavior ($w < -1$), while low-$z$ BAO and SNIa data favor quintessence ($w > -1$).
• Figure 4: Constraints on interacting dark energy from the $\xi$-index model. (Left) Joint 68% and 95% CL constraints in the $w_X$-$\xi$ plane. The black solid and dashed lines mark the non-interacting and $\Lambda$CDM limits, respectively. (Right) Posterior distributions of the interaction strength $\xi + 3w_X$. A negative value indicates energy transfer from dark energy to matter. The full dataset (CMB+lensing+BAO+SNIa) favors a negative coupling at 68% CL (gray band).