AbstractWe propose a QFT-motivated effective framework for the vacuum sector of Vacuum–Energonic Relativity (VER), in which the causal limit c (x) and the axion-like phase of the vacuum are unified as the modulusand phase of a single complex order parameter, Ψ=√φeiϑ. In VER, the physical frame of matter is defined by the unique operational metric ˜gµν, while the energonicityfield φ > 0 determines the local causal limit c (x) = φ (x) and enters the conformal relation ˜gµν = φ−1gµν (realization I), where gµν is the variational metric of the vacuum–gravitational sector. Universality of matteris implemented through minimal coupling Smψm, ˜g and the absence of direct couplings to φ, ϑ at fixed˜g, which removes the standard units-based criticism of VSL approaches and suppresses any direct fifth-forcechannel from ϑ. Weformulate a covariant vacuum EFT action, derive the universal source of φ from matter through the trace˜T, and fix a minimal working model (Model-0), in which the canonical kinetic term of Ψ rigidly determinesZ (φ) = 1/ (2φ) and K (φ) = 2φ, while regime 3 couples ϑ to φ through the potentialV (φ, ϑ) = U (φ) +Λ4 (φ) 1−cosϑ. Wethenshowhowthefunction Λ (φ) naturally arises in QFT from hidden confinement and RG transmutationthrough a φ-dependent gauge kinetic function, thereby turning VER–I–ϑ into a compact unified theory of thevacuum in the EFT sense. Finally, we analyze the radiative structure of the model, the weak-field Yukawachannel, dimensionless anti-units invariants, and formulate a map of viability gates without developing fullcosmology.
Ренат Гафаров (Tue,) studied this question.