Minimal Infrared Running of the Gravitational Coupling

We investigate a minimal infrared modification of General Relativity induced by a nonlocal curvature operator of the form Rμν□−1RμνR_{\mu\nu} \Box^{-1} R^{\mu\nu}Rμν□−1Rμν. Near an infrared marginal direction, the effective gravitational coupling acquires a mild logarithmic scale dependence. The resulting framework preserves the tensor structure of General Relativity, introduces no additional propagating degrees of freedom at the linearized level, and remains stable in a cosmological background. The model is formulated as an effective infrared extension consistent with standard gravitational phenomenology for small running parameter ∣α∣≪1|\alpha| \ll 1∣α∣≪1.