https://doi.org/10.1140/epjc/s10052-020-08703-3
Regular Article – Theoretical Physics
Cosmology and the massive photon frequency shift in the Standard-Model Extension
1
Observatoire des Sciences de l’Univers en région Centre (OSUC) UMS 3116, Université d’Orléans, 1A rue de la Férollerie, 45071, Orléans, France
2
Pôle de Physique, Collegium Sciences et Techniques (CoST), Université d’Orléans, Rue de Chartres, 45100, Orléans, France
3
Laboratoire de Physique et Chimie de l’Environnement et de l’Espace (LPC2E) UMR 7328, Centre National de la Recherche Scientifique (CNRS), Campus CNRS, 3A Avenue de la Recherche Scientifique, 45071, Orléans, France
4
Departamento de Física Teórica, Instituto de Física, Universidade do Estado do Rio de Janeiro (UERJ), Rua São Francisco Xavier 524, Maracanã, 20550-013, Rio de Janeiro, RJ, Brazil
5
Departamento de Astrofísica, Cosmologia e Interações Fundamentais (COSMO), Centro Brasileiro de Pesquisas Físicas (CBPF), Rua Xavier Sigaud 150, 22290-180, Rio de Janeiro, Urca, RJ, Brazil
6
Instituto de Astrofísica de Canarias (IAC), C/ Vía Láctea s/n, 38205, San Cristóbal de La Laguna, Tenerife, Spain
7
Departamento de Astrofísica, Sección de Física, Facultad de Ciencias, Universidad de La Laguna, Avenida Astrofísico Francisco Sánchez s/n, Apartado 456, 38200, San Cristóbal de La Laguna, Tenerife, Spain
8
Dipartimento di Fisica Ettore Pancini, Università degli Studi di Napoli, Federico II (UNINA), Via Cinthia 9, 80126, Napoli, Italy
9
Laboratory for Theoretical Cosmology, Tomsk State University of Control Systems and Radioelectronics (TUSUR), 40 prospect Lenina, 634050, Tomsk, Russia
Received:
22
May
2020
Accepted:
24
November
2020
Published online:
5
January
2021
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(-Poincaré) 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. The final colour (red or blue) and size of the static shift depend on the orientations and strength of the LSV and EM multiple fields encountered along the path of the photon. Turning to cosmology, for a zero 
energy density, the discrepancy between luminosity and red shift distances of SNeIa disappears thanks to the recasting of z. Massive photons induce an effective dark energy acting ‘optically’ but not dynamically.
© The Author(s) 2020
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