Finite-Range Scalar–Tensor Gravity: Constraints from Cosmology and Galaxy Dynamics

Objective: We examine whether a finite-range scalar–tensor modification of gravity can be simultaneously compatible with cosmological background data, galaxy rotation curves, and local/astrophysical consistency tests, while satisfying the luminal gravitational-wave propagation constraint (cT=1) implied by GW170817 at low redshifts. Methods: We formulate the model at the level of an explicit covariant action and derive the corresponding field equations; for cosmological inferences, we adopt an effective background closure in which the late-time dark-energy density is modulated by a smooth activation function characterized by a length scale λ and amplitude ϵ. We constrain this background model using Pantheon+, DESI Gaussian Baryon Acoustic Oscillations (BAOs), and a Planck acoustic-scale prior, including an explicit ΛCDM comparison. We then propagate the inferred characteristic length by fixing λ in the weak-field Yukawa kernel used to model 175 SPARC galaxy rotation curves with standard baryonic components and a controlled spherical approximation for the scalar response. Results: The joint background fit yields Ωm=0.293±0.007, λ=7.69−1.71+1.85Mpc, and H0=72.33±0.50kms−1Mpc−1. With λ fixed, the baryons + scalar model describes the SPARC sample with a median reduced chi-square of χν2=1.07; for a 14-galaxy subset, this model is moderately preferred over the standard baryons + NFW halo description in the finite-sample information criteria, with a mean ΔAICc outcome in favor of the baryons + scalar model (≈2.8). A Vainshtein-type screening completion with Λ=1.3×10−8 eV satisfies Cassini, Lunar Laser Ranging, and binary pulsar bounds while keeping the kpc scales effectively unscreened. For linear growth observables, we adopt a conservative General Relativity-like baseline (μ0=0) and show that current fσ8 data are consistent with μ0≃0 for our best-fit background; the model predicts S8=0.791, consistent with representative cosmic-shear constraints. Conclusions: Within the present scope (action-level weak-field dynamics for galaxy modeling plus an explicitly stated effective closure for background inference), the results support a mutually compatible characteristic length at the Mpc scale; however, a full perturbation-level implementation of the covariant theory remains an issue for future work, and the role of cold dark matter beyond galaxy scales is not ruled out.