Fermi acceleration mechanisms beyond Lorentz symmetry

Abstract We construct models for first- and second-order Fermi acceleration of particles, incorporating generic frame transformations, dispersion relations, and conservation laws. Within this framework, we study deformations of Lorentz symmetry via the $$\kappa $$ κ -Poincaré algebra in the bicrossproduct and classical bases, which, respectively, deform and preserve the relativistic dispersion relation. We also examine explicit Lorentz symmetry violation and compare the results with deformed relativity and special relativity. The energy spectra present different shapes when one considers deformation or violation of Lorentz symmetry in superluminal or subluminal scenarios. One of the possible outcomes is an intense decay of the spectrum for higher energies. We also gather the predictions of all the scenarios considered, comparing the spectra produced at the source in the energy domain, which is the variable in which cosmic ray observatories report their measurements.