Related papers: The GZK Bound in Discrete Space
We review the basic ideas on the origin of cosmic rays with energy in excess of $\sim 10^{19}$ eV, in the light of the most recent observational findings. The limited statistics of events detected by the two largest experiments currently…
Ultrahigh energy (UHE) extragalactic protons propagating through cosmic microwave radiation (CMB) acquire the spectrum features in the form of the dip, bump (pile-up protons) and the Greisen-Zatsepin-Kuzmin (GZK) cutoff. We have performed…
The clustering of ultra high energy (above 5\cdot 10^{19} eV) cosmic rays (UHECR) suggests that they might be emitted by compact sources. We present a statistical analysis on the source density based on the multiplicities. The propagation…
We discuss the intergalactic propagation of ultra-high-energy cosmic rays (UHECRs) with energies E \geq 10^{18.5} eV. We consider the propagation of UHECRs under the influence of the energy-dependent deflection by a weak random magnetic…
In a recently proposed model the cosmic rays spectrum at energies above 10^{18} eV can be fitted with a minimal number of unknown parameters assuming that the extragalactic cosmic rays are only protons with a power law source spectrum…
Ultra-high-energy (UHE) cosmic rays (CRs) interact with cosmic background radiation through hadronic processes, and the Universe would become `opaque' to UHE CRs of energies $\sim$($10^{18}$- $10^{20}$) eV over about several tens of Mpc,…
Ultra High Energy Cosmic Rays (UHECRs) hit the Earth's atmosphere with energies exceeding $10^{18}$ eV. This is the same energy as carried by a tennis ball moving at 100 km/h, but concentrated on a sub-atomic particle. UHECRs are so rare…
Ultra High Energy Cosmic Rays, UHECR, are charged particles with energies between $\sim10^{18}\,{\rm eV}$ and $\sim3\times10^{20}\,{\rm eV}\sim50\,{\rm J}$. They exhibit fundamental physics at energies inaccessible to terrestrial…
The rarest cosmic rays above the GZK cut'off $(E_{CR} \tilde{>} 10^{19} \div 10^{20} eV)$ are probably born at cosmic distances ($\tilde{>}$ tens Mpc) by AGNs (QSRs, BLac, Blazars...). Their puzzling survival over $2.75 K^o$ BBR radio waves…
We study the extragalactic protons with universal spectrum, which is independent of mode of propagation, when distance between sources is less than the propagation lengths, such as energy attenuation length or diffusion length (for…
If Ultra High Energy Cosmic Rays (UHECRs) with E>4 10^{19} eV originate from BL Lacertae at cosmological distances as suggested by recent studies, the absence of the GZK cutoff can not be reconciled with Standard-Model particle properties.…
We review the hypothesis that the acceleration of protons at internal shocks in Gamma Ray Bursts (GRB) could be the origin of the ultra-high energy cosmic rays (UHECR) observed at earth, E_max > 10^19 eV. We find that, even though protons…
Over the last 30 years or so, a handful of events observed in ground-based cosmic ray detectors seem to have opened a new window in the field of high-energy astrophysics. These events have energies exceeding 5x10**19 eV (the region of the…
Almost half a century ago, Greisen, Zatsepin and Kuz'min (GZK) predicted a "cosmologically meaningful termination" of the spectrum of cosmic rays at energies around $10^{20}$ eV due to their interaction with the cosmic microwave background,…
This is an introductory review about the on-going search for a signal of Lorentz Invariance Violation (LIV) in cosmic rays. We first summarise basic aspects of cosmic rays, focusing on rays of ultra high energy (UHECRs). We discuss the…
Owing to their isotropy, it is generally believed that ultrahigh energy cosmic rays (UHECRs) are extragalactic in origin. It is then expected that interactions of these cosmic rays with photons of the cosmic background radiation (CBR)…
Resonant photopion production with the cosmic microwave background predicts a suppression of extragalactic protons above the famous Greisen-Zatsepin-Kuzmin cutoff at about E_{GZK} ~ 5 x 10^10 GeV. Current cosmic ray data measured by the…
Recently the Telescope Array collaboration reported an observation of cosmic ray event with very high energy 244 EeV ($2.44 \times 10^{20}$ eV). Importantly, the event is hard to correlate with the matter distribution in the local Universe,…
The clustering of ultra high energy (above 10^20 eV) cosmic rays (UHECR) suggests that they might be emitted by compact sources. Statistical analysis of Dubovsky et al. (Phys. Rev. Lett. 85 (2000) 1154) estimated the source density. We…
The highest energy cosmic rays, above the Greisen-Zatsepin-Kuzmin cut-off of cosmic ray spectrum, may be produced in decays of superheavy long-living X-particles. We conjecture that these particles may be produced naturally in the early…