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

Abstract

Recent cosmological data, including DESI DR2, highlight significant tensions within the $\Lambda$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, ${\mu }_G(z)\equiv G_{eff}/G_N$, and the DDE equation of state, $w(z)$. This MG framework significantly alleviates the tension, leading to a higher inferred value of $H_0=70.6\pm 1.4{\text{km s}}^{-1}{\text{Mpc}}^{-1}$. 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 $F(\Phi )=1+\xi {\Phi }^2{e}^{n\Phi }$ and the scalar potential $U(\Phi )=U_0+a{e}^{b{\Phi }^2}$, which well-describe the reconstructed functions.

This version contains 32 pages and 13 figures. The manuscript matches the version accepted for publication in Physical Review D. The numerical analysis file used for the construction of the figures may be found at https://github.com/Dimitrios1993/Reconstructing-Scalar-Tensor-Theories (Python and Mathematica v13)

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