Photons are the sole free massless particles in the Standard-Model (SM) and light-waves are still studied with the linear Maxwellian theory. But, if we refer to massive formalisms, started by de Broglie-Proca, or non-linear by Euler-Heisenberg (for second order quantum electrodynamics) and Born-Infeld (to normalise the infinitesimal charge), and followers, surprising options emerge for our reading of the universe, including dark energy or compact objects as magnetars. A collaboration (CERN, London, Napoli, Rio de Janeiro, Tenerife) has found an effective mass for the photon proportional to the Lorentz(-Poincaré) Symmetry Violation (LSV), a group velocity differing from c and birefringence within the SM Extension (SME). Further, it determined three experimental or observational upper limits for the photon mass, published by the Particle Data Group, using solar wind satellite data and Fast Radio Bursts.
In the SME, we have determined a frequency (red or blue) shift for a photon propagating in vacuo - possibly in presence of a magnetic field - to be added to the expansion red-shift. A non-zero vacuum expectation value due to the LSV might explain the discrepancy between the red-shift and luminosity distances for Supernovae without recurring to an accelerated expansion. We also obtain frequency shifts in case of a generalised non-linear electromagnetism described by a Lagrangian in the powers of the electromagnetic field and its dual.
Finally, time permitting, the application of the Heisenberg uncertainty principle to the photon mass shallbe mentioned with respect to the Hubble tension and the observable universe.