john-edward-holland

We examine the theoretical consistency of a minimal Standard Model extension featuring a real scalar field Φ, singlet under all gauge interactions, coupled to the Higgs doublet through a density-modulated Higgs-portal interaction. The scalar sector employs the most general renormalizable potential consistent with gauge invariance and discrete ℤ₂ symmetry, with the portal coupling rescaled by a dimensionless function S(Σ) of coarse-grained macroscopic energy density. For any fixed density, the theory reduces to conventional singlet-Higgs extension with effective portal coupling λ̃ΦH = S(Σ)λΦH, maintaining local, polynomial, and renormalizable structure.