Curvature-Driven Modifications to Photon Propagation: A Kretschmann-Based Phenomenological Framework for Strong-Field Gravity

This paper presents a phenomenological model for photon propagation in curved spacetime that replaces the usual null-geodesic picture with a curvature-regularized dynamics built from the Kretschmann scalar. A bounded Lagrangian is introduced through an EFT-inspired resummation, producing modified photon trajectories that remain finite in strong-field regimes while reducing to standard general relativity in the weak-field limit. The model compares sigmoidal, exponential, and Padé regularization schemes, showing that they agree at low curvature but differ in the high-curvature domain. The framework predicts corrections to lensing, time delay, and dispersion, and the allowed parameter space is constrained by solar-system, strong-lensing, and multi-messenger data. The approach is explicitly phenomenological, with the underlying field-theoretic derivation left open.