Context: Features in the spectra of primary cosmic rays (CRs) provide invaluable information on the propagation of these particles in the Galaxy. In the rigidity region around a few hundred GV, such features have been measured in the proton and heliu
m spectra by the PAMELA experiment and later confirmed with a higher significance by AMS-02. We investigate the implications of these datasets for the scenario in which CRs propagate under the action of self-generated waves. Aims: We show that the recent data on the spectrum of protons and helium nuclei as collected with AMS-02 and Voyager are in very good agreement with the predictions of a model in which the transport of Galactic CRs is regulated by self-generated waves. We also study the implications of the scenario for the boron-to-carbon ratio: although a good overall agreement is found, at high energy we find marginal support for a (quasi) energy independent contribution to the grammage, that we argue may come from the sources themselves Results: A break in the spectra of all nuclei is found at rigidity of a few hundred GV, as a result of a transition from self-generated waves to pre-existing waves with a Kolmogorov power spectrum. Neither the slope of the diffusion coefficient, nor its normalisation are free parameters. Moreover, at rigidities below a few GV, CRs are predicted to be advected with the self-generated waves at the local Alfven speed. This effect, predicted in our previous work, provides an excellent fit to the Voyager data on the proton and helium spectra at low energies, providing additional support to the model.
Relativistic Invariance might be modified by Quantum Gravity effects. The interesting point which emerged in the last fifteen years is that remnants of possible Lorentz Invariance Violations could be present at energies much lower than their natural
scale, and possibly affect Ultra High Energy Cosmic Rays phenomena. We discuss their status in the view of recent data from the Pierre Auger Observatory.
