Cosmological Signatures of Curvature-Coupled Dark Energy

We study a curvature-coupled dark energy model that can modify cosmological evolution both before recombination and during the late-time accelerated era. The model belongs to the class of scalar-tensor theories, in which a quintessence field is non-minimally coupled to the Ricci scalar. We specify the model through a shifted quartic coupling, f(φ)=α(φ 2-φ today 2) squared, and an inverse power-law potential, V(φ)=Λφ-σ, where φ today is a constant fixed by requiring the effective Planck mass to recover its present-day normalization. We implement the model in a modified version of and compute its background and linear cosmological predictions. This specific form of non-minimal coupling allows an effective crossing of the phantom divide at late times while naturally suppressing deviations from standard gravity today and satisfying local gravity constraints. At the same time, the scalar field can modify the expansion history before recombination, shifting the acoustic scale in the direction required to alleviate the H 0 tension, while remaining dynamically relevant as dark energy at low redshift. For the parameter choices studied here, we find tens-of-percent deviations from Λ CDM in the expansion history, matter clustering, and metric-potential spectra. The modified evolution of the gravitational potentials leaves characteristic signatures in relativistic observables, with weak-lensing power suppressed by O(20 - 40%) at low multipoles and order-unity changes in the late Integrated Sachs-Wolfe signal. Together, these results reveal a broad, scale-dependent phenomenology that motivates both a full parameter-space analysis and an extension of the present linear treatment to a dedicated non-linear N-body implementation.