Linear Response of the de Sitter Vacuum to Accelerated Matter: A Kubo-Formalism Proof that MOND Requires Non-Equilibrium Physics

Abstract

Recent attempts to derive Modified Newtonian Dynamics (MOND) and its characteristic acceleration scale a0 rely on the interaction between accelerated matter and the cosmological horizon. A persistent conjecture is that the vacuum response in de Sitter spacetime modifies inertia at low accelerations. In this work, we formalize this conjecture using Kubo linear response theory. We postulate that the modification to inertia is dictated by a causal memory kernel K(t), derived as the inverse Fourier transform of the retarded susceptibility of the de Sitter vacuum. By computing this susceptibility for a massive scalar field in the Bunch-Davies vacuum, we show exactly that the equilibrium de Sitter vacuum is thermodynamically passive (it satisfies the Kubo-Martin-Schwinger condition). Consequently, the spectral density is non-negative, and the resulting inertia correction is strictly positive. The linear response of the de Sitter vacuum therefore raises inertia, an "anti-MOND" effect. We conclude that any derivation of MOND from vacuum dynamics strictly forbids the use of dynamical memory kernels (influence functionals). Instead, we demonstrate that Modified Inertia must be formulated as a Category-2 thermodynamic Equation of State (EOS). By defining inertia as the excess response above the de Sitter thermal floor, the EOS approach bypasses the passivity wall entirely, yielding a causal, ghost-free relation that reproduces the exact MOND phenomenology without requiring non-equilibrium physics. All numerical claims are reproduced by the self-checking script included in this record, which evaluates the worldline Wightman function directly to extract the susceptibility and mass correction.