Though the arrival directions of ultra-high-energy cosmic rays (UHECRs) are distributed in a relatively isotropic manner, there is evidence of small-scale anisotropy. This, combined with the detection of cosmic rays with energies above the GZK cut-off, has motivated us to further investigate the idea that UHECRs are the result of a top-down mechanism involving the annihilation of superheavy dark matter particles in our galactic halo. To more precisely characterize the nature of dark matter, we have endeavoured to apply two different models to the leading UHECR spectra, namely those from the AGASA, High Resolution Flys Eye, and Pierre Auger Collaborations. First, we attempt a non-linear, least-squares fit of the particle physics fragmentation function to the spectra. Second, we propose that the observed cosmic ray spectrum above 3.5 × 10E+18 eV is the superposition of flux from two different sources: bottom-up acceleration via a simple power-law relation at lower energies and scattered particles from dark matter annihilation governed by fragmentation functions at higher energies. We find that while the former model does not provide a satisfactory fit to observatory data, the latter yields reduced χ2 values between 1.14 and 2.6. From the fragmentation function component of our second model, we are able to extract estimates of dark matter particle mass. We find values of (1.2 ± 0.6) 10E+21 eV, (5.0 ± 4.3) 10E+20 eV, and (2.6 ± 1.5) 10E+21 eV respectively for the AGASA, HiRes, and Pierre Auger data, which agree with earlier predictions based on a cosmological analysis of non-thermal particle production in an inflationary universe. Furthermore, we verify that the dark matter particle densities required by our two-source model are in line with current CDM theory.

Though the arrival directions of ultra-high-energy cosmic rays (UHECRs) are distributed in a relatively isotropic manner, there is evidence of small-scale anisotropy. This, combined with the detection of cosmic rays with energies above the GZK cut-off, has motivated us to further investigate the idea that UHECRs are the result of a top-down mechanism involving the annihilation of superheavy dark matter particles in our galactic halo. To more precisely characterize the nature of dark matter, we have endeavoured to apply two different models to the leading UHECR spectra, namely those from the AGASA, High Resolution Flys Eye, and Pierre Auger Collaborations. First, we attempt a non-linear, least-squares fit of the particle physics fragmentation function to the spectra. Second, we propose that the observed cosmic ray spectrum above 3.5 × 10E+18 eV is the superposition of flux from two different sources: bottom-up acceleration via a simple power-law relation at lower energies and scattered particles from dark matter annihilation governed by fragmentation functions at higher energies. We find that while the former model does not provide a satisfactory fit to observatory data, the latter yields reduced χ2 values between 1.14 and 2.6. From the fragmentation function component of our second model, we are able to extract estimates of dark matter particle mass. We find values of (1.2 ± 0.6) 10E+21 eV, (5.0 ± 4.3) 10E+20 eV, and (2.6 ± 1.5) 10E+21 eV respectively for the AGASA, HiRes, and Pierre Auger data, which agree with earlier predictions based on a cosmological analysis of non-thermal particle production in an inflationary universe. Furthermore, we verify that the dark matter particle densities required by our two-source model are in line with current CDM theory.

Relativity is one of the most important and well tested theories and Lorentz invariance is one of its pillars. Lorentz invariance violation (LIV), however, has been discussed in several quantum gravity and high energy models. For this reason, it is crucial to test it. Several tests, both terrestrial and astrophysical, have been performed in the last years and provide limits on the violation. This work takes part in these efforts and discuss the possibility of testing LIV with ultra-high energy cosmic rays (UHECRs). The effects of LIV in their propagation and the resulting changes in the spectrum of UHECRs are obtained and compared to the experimental data from the Pierre Auger Observatory. An analytical calculation for the inelasticity in the laboratory frame with LIV of any a + b → c + d interaction is presented and used to obtain the phase space and the energy losses of the pion production for protons, the photodisintegration for nuclei and the pair production for photons with LIV. A parametrization for the threshold energy of the photodisintegration with LIV is also proposed. The main effect seen is a decrease in the phase space and a resulting decrease in the energy loss. These changes have been implemented in Monte Carlo propagation codes and the resulting spectra of protons, nuclei and photons on Earth have been obtained and fitted to the data from the Pierre Auger Observatory. It is shown that upper limits on the photon LIV coefficient can be derived from the upper limits on the photon flux from the Pierre Auger Observatory. / Relatividade é uma das mais importantes e bem testadas teorias e a invariância de Lorentz é um de seus pilares. A violação da invariância de Lorentz (VIL), todavia, tem sido discutida em diversos modelos de gravidade quântica e altas energias. Por tal motivo, é crucial testá-la. Diversos testes, tanto terrestres quanto astrofísicos, foram realizados nos últimos anos e fornecem limites na violação. Este trabalho se insere nesses esforços e discute a possibilidade de testar VIL com raios cósmicos de altíssima energia. Os efeitos da VIL em sua propagação e as consequentes mudanças no espectro de raios cósmicos de altíssima energia são obtidos e comparados com os dados experimentais do Observatório Pierre Auger. Um cálculo analítico para a inelasticidade no referencial do laboratório com VIL para qualquer interação da forma a + b → c + d é apresentado e usado para obter o espaço de fase e as perdas de energia para a produção de píons para prótons, a fotodesintegração para núcleos e a produção de pares para fótons com VIL. Uma parametrização para o limiar de energia da fotodesintegração com VIL também é proposta. O principal efeito observado é uma diminuição no espaço de fase e uma consequente diminuição nas perdas de energia. Tais mudanças foram implementadas em códigos de Monte Carlo para a propagação e os espectros resultantes para prótons, núcleos e fótons na Terra foram obtidos e ajustados aos dados do Observatório Pierre Auger. É mostrado que limites superiores nos coeficientes de VIL para o fóton podem ser deduzidos dos limites superiores para o fluxo de fótons do Observatório Pierre Auger.

Relativity is one of the most important and well tested theories and Lorentz invariance is one of its pillars. Lorentz invariance violation (LIV), however, has been discussed in several quantum gravity and high energy models. For this reason, it is crucial to test it. Several tests, both terrestrial and astrophysical, have been performed in the last years and provide limits on the violation. This work takes part in these efforts and discuss the possibility of testing LIV with ultra-high energy cosmic rays (UHECRs). The effects of LIV in their propagation and the resulting changes in the spectrum of UHECRs are obtained and compared to the experimental data from the Pierre Auger Observatory. An analytical calculation for the inelasticity in the laboratory frame with LIV of any a + b → c + d interaction is presented and used to obtain the phase space and the energy losses of the pion production for protons, the photodisintegration for nuclei and the pair production for photons with LIV. A parametrization for the threshold energy of the photodisintegration with LIV is also proposed. The main effect seen is a decrease in the phase space and a resulting decrease in the energy loss. These changes have been implemented in Monte Carlo propagation codes and the resulting spectra of protons, nuclei and photons on Earth have been obtained and fitted to the data from the Pierre Auger Observatory. It is shown that upper limits on the photon LIV coefficient can be derived from the upper limits on the photon flux from the Pierre Auger Observatory. / Relatividade é uma das mais importantes e bem testadas teorias e a invariância de Lorentz é um de seus pilares. A violação da invariância de Lorentz (VIL), todavia, tem sido discutida em diversos modelos de gravidade quântica e altas energias. Por tal motivo, é crucial testá-la. Diversos testes, tanto terrestres quanto astrofísicos, foram realizados nos últimos anos e fornecem limites na violação. Este trabalho se insere nesses esforços e discute a possibilidade de testar VIL com raios cósmicos de altíssima energia. Os efeitos da VIL em sua propagação e as consequentes mudanças no espectro de raios cósmicos de altíssima energia são obtidos e comparados com os dados experimentais do Observatório Pierre Auger. Um cálculo analítico para a inelasticidade no referencial do laboratório com VIL para qualquer interação da forma a + b → c + d é apresentado e usado para obter o espaço de fase e as perdas de energia para a produção de píons para prótons, a fotodesintegração para núcleos e a produção de pares para fótons com VIL. Uma parametrização para o limiar de energia da fotodesintegração com VIL também é proposta. O principal efeito observado é uma diminuição no espaço de fase e uma consequente diminuição nas perdas de energia. Tais mudanças foram implementadas em códigos de Monte Carlo para a propagação e os espectros resultantes para prótons, núcleos e fótons na Terra foram obtidos e ajustados aos dados do Observatório Pierre Auger. É mostrado que limites superiores nos coeficientes de VIL para o fóton podem ser deduzidos dos limites superiores para o fluxo de fótons do Observatório Pierre Auger.