Safe Phantom Divide Crossing from Unscreened Non-Minimal Coupling to Gravity

Abstract

Recent hints of dynamical dark energy, including a possible crossing of the phantom divide, have motivated the search for viable theoretical explanations. Scalar fields non-minimally coupled to gravity with a coupling of the form $F(φ)=1+αφ^2$ have emerged as promising candidates, providing an improved fit to the data compared to $Λ$CDM and even the $w_0w_a$CDM parametrization. However, in the absence of a screening mechanism, the regions of parameter space examined exhaustively so far (with $α<0$) violate stringent local constraints on the strength and time variation of gravity and enhance the matter growth rate at low redshifts, thereby compromising the viability of these solutions. In this work, we investigate a largely unexplored region of parameter space (with $α>0$) that realizes the crossing while remaining consistent with local constraints. This setup, which is subject to some fine-tuning, respects the BBN constraints and leads only to deviations of the effective gravitational coupling from Newton's constant below $0.3%$ in the past. We review the background and linear perturbation dynamics of the model, deriving analytical results that provide physical insight into its behavior, and update the constraints on the model using the latest cosmological data, including the DES-Dovekie supernova sample. We perform for the first time a full-fledged Monte Carlo analysis with $α>0$, studying the impact of the variation of $G$ on the supernovae absolute luminosity, and compare the results with those obtained for $α<0$, using in both cases a linear potential. In the context of the model with non-minimal coupling and $α<0$, the standard model is excluded at the $2.50σ$ CL, whereas for $α>0$, the exclusion significance decreases to $\sim 2σ$ CL, indicating a moderate preference for these models over $Λ$CDM. [abridged]