A High-Curvature Effective Extension of Einstein Gravity via Curvature-Activated dynamics

We construct a minimal covariant extension of Einstein gravity in which extreme curvature growth is dynamically regulated by a curvature-activated scalar field. The additional field remains inactive in weakly curved regimes, ensuring exact recovery of General Relativity, but becomes dynamically relevant when curvature approaches high values. The field couples directly to the Ricci scalar and is sourced by a local scalar constructed from matter degrees of freedom. We derive the field equations from a variational principle and demonstrate, using a homogeneous collapse toy model, that the cou pled system admits solutions with bounded curvature invariants. The framework preserves locality, causality, and stress-energy conservation, providing an effective classical mechanism for avoiding singular curvature divergences.