Informationally Modified Gravity as a Scalar–Vector–Tensor Effective Field Theory

We present an exploratory scalar–vector–tensor Effective Field Theory (EFT) aimed at modeling modified gravitational dynamics in the infrared regime. The framework introduces a covariant coupling between a scalar vacuum configuration and a Proca-type vector field, yielding an effective modification of gravity while preserving luminal propagation of tensor modes ($c_T = 1$) and a consistent counting of physical degrees of freedom. The theory is formulated in a Jordan-frame covariant action with non-minimal scalar–curvature coupling and derivative interactions between scalar and vector sectors. We analyze the resulting field equations, establish stability conditions via Stückelberg decomposition, and identify parameter regimes free from ghost instabilities at the EFT level. In the weak-field limit, the model admits infrared configurations that generate modified Poisson dynamics capable of reproducing effective scaling behaviors relevant to galactic rotation curves. At the cosmological level, the framework introduces a time-dependent effective gravitational coupling that can lead to a suppression of late-time structure growth, providing a possible phenomenological connection to observed tensions in the $S_8$ parameter. This work is a first EFT-level construction and does not claim a complete UV or phenomenological closure.