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We investigate on possible evidence from Extended Theories of Electromagnetism by looking for deviations from the Ampère-Maxwell law. The photon, main messenger for interpreting the universe, is the only free massless particle in the Standard-Model (SM). Indeed, the deviations may be due to a photon mass for the de Broglie-Proca (dBP) theory or the Lorentz-Poincaré Symmetry Violation in the SM Extension (SME), but also to non-linearities from theories as of Born-Infeld, Heisenberg-Euler. With this aim, we have analysed six years of data of the Magnetospheric Multi-Scale mission, which is a four-satellite constellation, crossing mostly turbulent regions of magnetic reconnection and collecting about 95\% of the data outside the solar wind. We examined 3.8 million data points from the solar wind, magnetosheath, and magnetosphere regions. In a minority of cases, for the highest time resolution burst data and optimal tetrahedron configurations drawn by the four spacecraft ($2.2\%$ in modulus and $4.8\%$ in Cartesian components for all regions, but un the solar wind alone $20.8\%$ in modulus and $29.7\%$ in Cartesian components and up to 45.2\% in the extreme low-mass range), deviations have been found. The deviations might be due to unaccounted experimental errors or, less likely, to non-Maxwellian terms, which we computed for the dBP and SME cases. Possibly, we are at the boundaries of measurability for non-dedicated missions. We discuss our experimental results versus more stringent but model-dependent limits., Thanks for the comments received at the MMS Boulder Conference on 5-8 June 2023

Cosmological probes at any redshift are necessary to reconstruct consistently the cosmic history. Studying properly the tension on the Hubble constant, $H_0$, obtained by Supernovae Type Ia (SNe Ia) and the Planck measurements of the Cosmic Microwave Background Radiation would require complete samples of distance indicators at any epoch. Gamma-Ray Bursts (GRBs) are necessary for the aforementioned task because of their huge luminosity that allows us to extend the cosmic ladder at very high redshifts. However, using GRBs alone as standard candles is challenging because their luminosity varies widely. To this end, we choose a reliable correlation for GRBs with a very small intrinsic scatter: the so-called fundamental plane correlation for GRB afterglows corrected for selection biases and redshift evolution. We choose a well-defined sample: the platinum sample, composed of 50 Long GRBs. To further constrain cosmological parameters, we use Baryon Acoustic Oscillations (BAOs) given their reliability as standard rulers. Thus, we have applied GRBs, SNe Ia, and BAOs in a binned analysis in redshifts so that GRBs' contribution is fully included in the last redshift bin, which reaches $z=5$. We use the fundamental plane correlation together with SNe Ia and BAOs, to constrain $H_0$ and the density matter today, $\Omega_{M}$. This methodology allows us to assess the role of GRBs combined with SNe Ia and BAOs. We have obtained results for $H_0$ and $\Omega_{M}$ using GRBs+ SNe Ia+BAOs with better precision than the SNe Ia alone for every bin, thus confirming the beneficial role of BAOs and GRBs added together. In addition, consistent results between GRBs+ SNe Ia +BAOs are obtained when compared with the SNe Ia +BAOs, showing the importance of GRBs since the distance ladder is extended up to $z=5$ with a similar precision obtained with other probes without including the GRBs., Comment: 32 Pages, 9 Figures, 7 Tables, accepted for publication by PASJ

The observed red shift $z$ might be composed by the expansion red shift $z_{\rm C}$ and an additional frequency shift $z_{\rm S}$, towards the red or the blue, by considering Extended Theories of Electromagnetism (ETE). Indeed, massive photon theories - the photon has a real mass as in the de Broglie-Proca theory or an effective mass as in the Standard-Model Extension (SME), based on Lorentz-Poincar\'e Symmetry Violation (LSV) - or Non-Linear Electro-Magnetism (NLEM) theories may induce a cosmological expansion independent frequency shift in presence of background (inter-) galactic electromagnetic fields, and where of relevance LSV fields, even when both fields are constant. We have tested this prediction considering the Pantheon Catalogue, composed by 1048 SNe Ia, and 15 BAO data, for different cosmological models characterised by the absence of a cosmological constant. From the data, we compute which values of $z_{\rm S}$ match the observations, spanning cosmological parameters ($\Omega$ densities and Hubble-Lema\^itre constant) domains. We conclude that the frequency shift $z_{\rm S}$ can support an alternative to accelerated expansion, naturally accommodating each SN Ia position in the distance-modulus versus red shift diagram, due to the light-path dependency of $z_{\rm S}$. Finally, we briefly mention laboratory test approaches to investigate the additional shift from ETE predictions., Comment: Accepted by Eur. Phys. J. Plus (Special Issue on: Tensions in cosmology from early to late universe: the value of the Hubble constant and the question of dark energy)