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arXiv · 2606.26427

Stueckelberg Gauge Invariant Formulation of MOG

John W. Moffat
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Abstract

We develop a Stueckelberg gauge-invariant formulation of modified gravity (MOG). The massive vector field is made gauge-invariant by introducing a compensating scalar field, without requiring a Higgs field, spontaneous symmetry breaking, or a vacuum expectation value to fix the effective Newtonian gravitational coupling. This separates the gauge-invariant origin of the vector mass from the cosmological evolution of the gravitational coupling. The formulation preserves the finite-range vector interaction of MOG, while allowing the effective gravitational coupling to be treated as an independent scalar or scale-dependent quantity. This distinction is important for cosmological tests, since early-universe constraints and late-time large-scale gravitational phenomena need not be tied to a symmetry-breaking vacuum. The Stueckelberg formulation provides a gauge-invariant framework for comparing MOG with nucleosynthesis, cosmic microwave background, large-scale structure, lensing, and distance data.

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John W. Moffat. 2026-06-24. Stueckelberg Gauge Invariant Formulation of MOG. https://arxiv.org/abs/2606.26427

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