Cosmology and the massive photon frequency shift in the Standard-Model Extension

Understand

The total red shift $z$ might be recast as a combination of the expansion red shift and a static shift due to the energy-momentum tensor non-conservation of a photon propagating through Electro-Magnetic (EM) fields.

• If massive, the photon may be described by the de Broglie-Proca (dBP) theory which satisfies the Lorentz(-Poincar\'e) Symmetry (LoSy) but not gauge-invariance.
• The latter is regained in the Standard-Model Extension (SME), associated with LoSy Violation (LSV) that naturally dresses photons of a mass.
• The non-conservation stems from the vacuum expectation value of the vector and tensor LSV fields.