Emergent Non-Local Gravity from Cosmic Connectivity: A BAO-Scale Spectral Enhancement Test with the Roman Space Telescope

This project presents a covariant, causal non‑local scalar–tensor framework in which largescale gravitational phenomena emerge from baryonic connectivity encoded through the operator η ≡ ξ F(□)□𝑒T. A topographic weight E(x), derived from cosmic‑web classifiers, enhances highly connected environments (filaments/nodes) relative to voids. The model predicts (i) a narrowband spectral enhancement (“knee” or peak) near k ≃ ℓ⁻¹ with ℓ ≃ 20–30 h⁻¹ Mpc, and (ii) a robust environment split. We identify a decisive observable for the Nancy Grace Roman Space Telescope: the cross-spectrum Cκη(k) between weak-lensing convergence and a reconstructed connectivity field using HLWAS/HLSS data. A binary pass/fail criterion is defined: (1) S/N_enh > 5 for the spectral enhancement; (2) ΔC(k) > 3σ for the environment split. A detection supports connectivity-driven non-local gravity. A null result supports Einsteinian locality at Roman sensitivity.