A Covariant Scalar Extension of General Relativity with Curvature-Dependent Activation

We propose a covariant extension of General Relativity in which the growth of spacetime curvature dynamically activates an additional scalar degree of freedom. The activation is generated by a curvature–dependent coupling term of the form α R φ², which modifies the effective mass of the scalar field and causes it to become dynamical only when the curvature approaches a critical scale. As a result, the scalar field backreacts on the Einstein equations and produces a self–regulating behavior that prevents the divergence of curvature invariants. The theory remains local, covariant, and second order in derivatives, and therefore avoids the higher–derivative instabilities that occur in many modified gravity models. We derive the field equations from a variational principle, analyze conservation laws, and study the behavior of the theory in cosmology, gravitational collapse, and static spherically symmetric spacetimes. In homogeneous cosmology the model allows finite–curvature bounce solutions, while in gravitational collapse the scalar field generates an effective pressure that can prevent the formation of curvature singularities. Black hole interiors may approach a regular finite–curvature core while the weak–field limit remains consistent with General Relativity. The curvature–activated mechanism provides a minimal classical framework in which singularities are avoided through dynamical backreaction rather than through higher–derivative corrections or nonlocal modifications. The model can be interpreted as an effective theory valid below a finite curvature scale and may be relevant for the study of the strong–gravity regime and the conceptual foundations of spacetime singularities.