Constant-Curvature Fixed Points and Ultraviolet Regulation in Cubic f(R) Gravity with Exact Infrared General Relativity Limit

This work presents a complete metric variation, explicit trace reduction, and nonlinear dynamical characterization of the cubic polynomial gravity model f(R) = R + aR² + bR³. All constant-curvature vacuum branches are derived algebraically from the trace equation. The scalar perturbation operator is constructed explicitly, and hyperbolicity, ghost freedom, and linear stability are demonstrated under explicit parameter constraints. A compact dynamical flow formulation clarifies the ultraviolet curvature saturation mechanism. The model admits nonzero constant-curvature vacuum branches generated purely by cubic self-interaction. Under simultaneous stability conditions, curvature invariants remain finite on the regulated branch. In the infrared limit R → 0, the theory reduces exactly to Einstein’s General Relativity without generating a residual cosmological constant. The mechanism is classical and arises solely from nonlinear curvature self-interaction.