We model the transport of cosmic ray nuclei in the Galaxy by means of a new numerical code. Differently from previous numerical models we account for a generic spatial distribution of the diffusion coefficient. We found that in the case of radially uniform diffusion, the main secondary/primary ratios (B/C, N/O and sub-Fe/Fe) and the modulated antiproton spectrum match consistently the available observations. Convection and re-acceleration do not seem to be required in the energy range we consider: 1 ≤ E ≤ 10 3 GeV/nucleon. We generalize these results accounting for radial dependence of the diffusion coefficient, which is assumed to trace that of the cosmic ray sources. While this does not affect the prediction of secondary/primary ratios, the simulated longitude profile of the diffuse γ-ray emission is significantly different from the uniform case and may agree with EGRET measurements without invoking ad hoc assumptions on the galactic gas density distribution. ‡ This unit of measure corresponds to the energy E competing on average to each nucleon within a nucleus with A nucleons and energy A × E.

We review the main theoretical motivations and observational constraints on Planck scale suppressed violations of Lorentz invariance. After introducing the problems related to the phenomenological study of quantum gravitational effects, we discuss the main theoretical frameworks within which possible departures from Lorentz invariance can be described. In particular, we focus on the framework of Effective Field Theory, describing several possible ways of including Lorentz violation therein and discussing their theoretical viability. We review the main low energy effects that are expected in this framework. We discuss the current observational constraints on such a framework, focusing on those achievable through high-energy astrophysics observations. In this context we present a summary of the most recent and strongest constraints on QED with Lorentz violating non-renormalizable operators. Finally, we discuss the present status of the field and its future perspectives.

The latest years have seen steady progresses in WIMP dark matter (DM) searches, with hints of possible signals suggested both in direct and indirect detection. Antiprotons play a key role in this context, since WIMP annihilations can be a copious source of antiprotons, and the antiproton flux from conventional astrophysical sources is predicted with fair accuracy and matches the measured cosmic ray (CR) spectrum very well. Using the publicly available numerical DRAGON code, we reconsider antiprotons as a tool to set constraints on DM models; we compare against the most upto-datep measurements, taking also into account the latest spectral information on the p and He CR fluxes. In particular, we probe carefully the uncertainties associated to both standard astrophysical and DM originated antiprotons, by using a variety of distinctively different assumptions for the propagation of CRs and for the DM distribution in the Galaxy. We find that the impact of the astrophysical uncertainties on constraining the DM properties of a wide class of annihilating DM models can be much stronger, up to a factor of ∼ 50, than the one due to uncertainties on the DM distribution (∼ 2 − 6). Remarkably, even reducing the uncertainties on the propagation parameters derived by local observables, non-local effects can change our predictions for the constraints even by 50%. Nevertheless, currentp data can place tight constraints on DM models, excluding some of those suggested in connection with indirect and direct searches. Finally we discuss the impact of upcoming CR spectral data from the AMS-02 instrument on DM model constraints.