Curvature-Controlled Vacuum Response and the Cosmological Constant Problem

This note proposes a phenomenological framework for the cosmological constant problem based on curvature-controlled vacuum response. The central assumption is that the flat-space component of the quantum vacuum stress tensor is dynamically screened, while curvature-dependent residual components remain gravitationally active. Under locality and analyticity assumptions, the leading curvature-dependent residual response naturally gives a vacuum energy scale proportional to MPl² R, corresponding to H₀² MPl² in the present universe. The framework does not assume a cancellation of large independent vacuum energy contributions. Instead, the observed hierarchy is interpreted as a consequence of the extremely small curvature scale of the present universe. This idea is related in spirit to vacuum adjustment and self-sustained vacuum approaches, where the vacuum is regarded as a dynamical medium. However, the present framework does not attempt to tune the total vacuum energy exactly to zero; instead, it focuses on the suppression of the flat-space component and the remaining curvature-controlled residual response. A possible high-curvature extension is also discussed, where a weakly screened vacuum-response regime may lead to an inflation-like phase. The transition toward the screened phase may provide a phenomenological route toward reheating through relaxation of the vacuum response. The proposal is intended as a phenomenological framework. The microscopic origin of the vacuum-response function, its covariant formulation, reheating dynamics, and cosmological perturbations remain open problems.