Alleviating the $H_0$ tension through the interacting dark energy model from quantum gravitational field theory in light of DESI DR2

Technical Summary: Alleviating the H0 Tension via Interacting Dark Energy in Quantum Gravitational Field Theory

Problem Statement
The standard cosmological model ($\Lambda$CDM) faces a significant crisis known as the $H_0$ tension, a discrepancy exceeding $5\sigma$ between the Hubble constant inferred from Cosmic Microwave Background (CMB) data ($H_0 \approx 67.4$ km s$^{-1}$ Mpc$^{-1}$) and local distance ladder measurements from SH0ES ($H_0 \approx 73.0$ km s$^{-1}$ Mpc$^{-1}$). Recent data releases, particularly the second data release (DR2) from the Dark Energy Spectroscopic Instrument (DESI), have further complicated this landscape. While DESI DR2 BAO data combined with CMB and Supernova (SN) data show a strong preference for dynamical dark energy (specifically the $w_0w_a$CDM model), this preference paradoxically exacerbates the $H_0$ tension, pushing the discrepancy to the $4.2\sigma$ level. The authors posit that the tension may be alleviated not by standard dynamical dark energy, but by interacting dark energy models derived from the asymptotic safety framework of quantum gravitational field theory.

Methodology
The study investigates two interacting dark energy models motivated by the asymptotic safety scenario, where the gravitational constant $G$ and the cosmological constant $\Lambda$ are not fixed but evolve with the energy scale (redshift $z$):

1. $e\Lambda$CDM: A one-parameter extension where the critical indices $\delta_G$ (governing $G$) and $\delta_\Lambda$ (governing $\Lambda$) are related by a low-redshift constraint ($\delta_\Lambda \simeq 0.47 \delta_G$).
2. $ee\Lambda$CDM: A two-parameter extension where $\delta_G$ and $\delta_\Lambda$ are treated as independent free parameters.

The background evolution is modified such that $G(z) = G_0(1+z)^{-\delta_G}$ and $\Lambda(z) = \Lambda_0(1+z)^{\delta_\Lambda}$. The authors perform observational constraints using a comprehensive dataset combination:

• CMB: Planck and ACT DR6 data.
• BAO: DESI DR2 data (galaxies, quasars, and Lyman-$\alpha$ forest).
• Supernovae: DESY5 and PantheonPlus compilations.
• Local Hubble: SH0ES prior ($H_0 = 73.04 \pm 1.04$ km s$^{-1}$ Mpc$^{-1}$).

Parameter estimation is conducted via Markov Chain Monte Carlo (MCMC) analysis using the Cobaya framework interfaced with a modified version of the Boltzmann solver CAMB. Model performance is evaluated using $\Delta\chi^2_{min}$ and the Deviance Information Criterion (DIC) relative to the standard $\Lambda$CDM model.

Key Results

• $ee\Lambda$CDM Performance: The two-parameter $ee\Lambda$CDM model demonstrates a significant ability to alleviate the $H_0$ tension, particularly when SH0ES data is included. In the CMB+DESI+SH0ES combination, the model yields $H_0 = 70.84 \pm 0.74$ km s$^{-1}$ Mpc$^{-1}$, reducing the tension to $1.7\sigma$.
• Parameter Constraints: This higher $H_0$ value is driven by a negative deviation in the cosmological constant scaling parameter, $\delta_\Lambda = -0.270 \pm 0.100$, which deviates from zero at the $2.7\sigma$ level. The analysis reveals a strong anti-correlation between $\delta_\Lambda$ and $H_0$; a negative $\delta_\Lambda$ implies a dynamical evolution that enhances the effective cosmological constant, thereby increasing the inferred expansion rate.
• Comparison with $w_0w_a$CDM: While DESI data favors the $w_0w_a$CDM model, the authors find that this model worsens the $H_0$ tension (reaching $4.2\sigma$ with CMB+DESI). In contrast, the $ee\Lambda$CDM model provides a mild alleviation even without SH0ES (reducing tension to $2.9\sigma$ with CMB+DESI alone) and a substantial alleviation when SH0ES is included.
• Statistical Preference: The $ee\Lambda$CDM model shows a marked improvement in fit quality over $\Lambda$CDM for specific dataset combinations. For CMB+DESI+SH0ES, the study reports $\Delta\chi^2_{min} = -14.14$ and $\Delta DIC = -9.18$, indicating a strong statistical preference for the interacting model even after penalizing for the additional free parameter.
• $e\Lambda$CDM Limitations: The one-parameter $e\Lambda$CDM model shows only modest improvements over $\Lambda$CDM, with $\delta_G$ remaining consistent with zero at low significance levels, suggesting that the independent evolution of $\Lambda$ (captured by $\delta_\Lambda$) is crucial for alleviating the tension.

Significance and Claims
The paper claims that the $ee\Lambda$CDM model, rooted in the asymptotic safety of quantum gravity, offers a compelling alternative to the standard $\Lambda$CDM paradigm. Its primary significance lies in its capacity to simultaneously accommodate the preference for dynamical behavior suggested by DESI DR2 data while resolving the $H_0$ tension, a feat that standard dynamical dark energy models fail to achieve. The authors conclude that the interacting dark energy scenario, specifically the two-parameter extension, not only fits the observational data better but also provides a theoretical mechanism (via the anti-correlation of $\delta_\Lambda$ and $H_0$) to reconcile the discrepancy between early-universe and late-universe measurements of the Hubble constant. The work suggests that future combinations of DESI, CMB, and SN data will further test the existence of such interactions and the nature of dark energy.