Addressing the DESI DR2 Phantom-Crossing Anomaly and Enhanced $H_0$ Tension with Reconstructed Scalar-Tensor Gravity

TL;DR

DESI DR2 data hint evolving dark energy with phantom-crossing behavior and a higher inferred $H_0$ that is difficult to accommodate in GR. The authors show that scalar–tensor gravity with a scale-independent modification to gravity, characterized by $\\mu_G(z)$, can reconcile the DESI signal with a dynamical $w(z)$, raising $H_0$ to about $H_0 \\approx 70.6 \,\\pm \,1.7$ km s$^{-1}$ Mpc$^{-1}$ and alleviating the $H_0$ tension, while also softening the $S_8$ tension to $S_8 \\approx 0.76 \\\pm \\\sim0.05$. They reconstruct the underlying ST Lagrangian by deriving $F(\\Phi)$ and $U(\\Phi)$ from the data, finding analytic fits $F(\\Phi)=1+\\xi\\Phi^2 e^{n\\Phi}$ and $U(\\Phi)=U_0+a e^{b\\Phi^2}$ that reproduce the recovered histories within $0\lesssim z\lesssim2$. The framework relies on the quasi-static, unscreened, scale-independent approximation for $G_{eff}$ and yields a consistent mapping between background evolution and growth, providing a data-driven route to test MG as a solution to cosmological tensions. Overall, the work highlights a viable Modified Gravity pathway to address phantom-crossing dark energy and $H_0$/$S_8$ tensions, while emphasizing the need to test broader MG classes and higher-redshift validity.

Abstract

Recent cosmological data, including DESI DR2, highlight significant tensions within the $Λ$CDM paradigm. When analyzed in the context of General Relativity (GR), the latest DESI data favor a dynamical dark energy (DDE) equation of state, $w(z)$, that crosses the phantom divide line $w=-1$. However, this framework prefers a lower Hubble constant, $H_0$, than Planck 2018, thereby worsening the tension with local measurements. This phantom crossing is a key feature that cannot be achieved by minimally coupled scalar fields (quintessence) within GR. This suggests the need for a new degree of freedom that can simultaneously: (A) increase the best-fit value of $H_0$ in the context of the DESI DR2 data, and (B) allow the crossing of the $w=-1$ line within a new theoretical approach. We argue that both of these goals may be achieved in the context of Modified Gravity (MG), and in particular, Scalar-Tensor (ST) theories, where phantom crossing is a natural and viable feature. We demonstrate these facts by analyzing a joint dataset including DESI DR2, Pantheon+, CMB, and growth-rate (RSD) data in the context of simple parametrizations for the effective gravitational constant, $μ_G(z) \equiv G_{eff}/G_N$, and the DDE equation of state, $w(z)$. This MG framework significantly alleviates the tension, leading to a higher inferred value of $H_0 = 70.6 \pm 1.7 \, \text{km s}^{-1} \text{Mpc}^{-1}$. We also present a systematic, data-driven reconstruction of the required underlying ST Lagrangian and provide simple, generic analytical expressions for both the non-minimal coupling $F(Φ) = 1+ξΦ^{2}e^{nΦ}$ and the scalar potential $U(Φ) = U_{0}+ae^{bΦ^{2}}$, which well-describe the reconstructed functions.

Figures (13)

• Figure 1: Evolution of the effective gravitational constant $\mu_G(z) = G_{\rm eff}(z)/G_N$ for different values of the parameter $g_a$ with $n = 2$ [Eq.\ref{['pantazisparam']}]. The parametrization exhibits a transient modification to gravity that peaks at intermediate redshifts ($z \sim 2$) and vanishes at both early times and today, ensuring consistency with BBN and local gravity tests. The horizontal dashed line indicates General Relativity ($\mu_G = 1$).
• Figure 2: Contour plots showing the 1$\sigma$ and 2$\sigma$ confidence regions in the $(g_a, \sigma_8)$ parameter space, obtained from the profile likelihood with all other parameters fixed at their best-fit values.
• Figure 3: Triangle plot showing the posterior distributions for the CPL cosmological model parameters, assuming a multivariate Gaussian likelihood $P(\theta|{\rm data}) \propto \exp\left(-\frac{1}{2}(\theta - \mu)^T \Sigma^{-1} (\theta - \mu)\right)$ with uniform priors (see Appendix \ref{['appB']}). Unlike direct $\chi^2$ mapping, this approach marginalizes over all parameters simultaneously but assumes Gaussianity. The minimum $\chi^2 = 1571.2$ for the best-fit model is indicated.
• Figure 4: Evolution of the effective gravitational constant for the four dark energy parametrizations, shown as functions of (a) redshift $z$ and (b) scale factor $a$. Shaded regions represent $1\sigma$ confidence bands of CPL. The transient enhancement of gravity at intermediate times is a robust prediction across all parametrizations, driven by the positive best-fit values $g_a > 0$.
• Figure 5: The equation of state $w(z)$ plotted for all four models selected in panel (a) and in three cases of the CPL parametrization in panel (b).