The Quantum Vacuum Composite Stiffness Response: A Covariant Field Theory of Low-Acceleration Environments and the Emergence of Gravitational Solitons

This paper develops the fully covariant field-theoretic formulation of the Quantum Vacuum Composite Stiffness Response (QVCSR), in which low-acceleration departures from Newtonian gravity arise from a nonlinear stiffness response of the quantum vacuum rather than from particulate dark matter. The theory is formulated as a minimal Einstein–scalar system involving a single vacuum stiffness field \chi, constructed exclusively from first-derivative composite invariants to ensure ghost-free dynamics and a well-posed Cauchy problem. The interaction sector introduces a unique infrared acceleration scale, a_{\rm QV}, which emerges as the only dimensionally consistent scale in the minimal covariant action and governs the onset of the nonlinear vacuum response.