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Register a new userLorentz Invariance Violation and the Observed Spectrum of Ultrahigh Energy Cosmic Rays
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S. T. Scully
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There has been much interest in possible violations of Lorentz invariance, particularly motivated by quantum gravity theories. It has been suggested that a small amount of Lorentz invariance violation (LIV) could turn off photomeson interactions of ultrahigh energy cosmic rays (UHECRs) with photons of the cosmic background radiation and thereby eliminate the resulting sharp steepening in the spectrum of the highest energy CRs predicted by Greisen Zatsepin and Kuzmin (GZK). Recent measurements of the UHECR spectrum reported by the HiRes and Auger collaborations, however, indicate the presence of the GZK effect. We present the results of a detailed calculation of the modification of the UHECR spectrum caused by LIV using the formalism of Coleman and Glashow. We then compare these results with the experimental UHECR data from Auger and HiRes. Based on these data, we find a best fit amount of LIV of $4.5^{+1.5}_{-4.5} times 10^{-23}$,consistent with an upper limit of $6 times 10^{-23}$. This possible amount of LIV can lead to a recovery of the cosmic ray spectrum at higher energies than presently observed. Such an LIV recovery effect can be tested observationally using future detectors.
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The assumption of Lorentz invariance is one of the founding principles of Modern Physics and violation of it would have profound implications to our understanding of the universe. For instance, certain theories attempting a unified theory of quantum gravity predict there could be an effective refractive index of the vacuum; the introduction of an energy dependent dispersion to photons could in turn lead to an observable Lorentz invariance violation signature. Whilst a very small effect on local scales the effect will be cumulative, and so for very high energy particles that travel very large distances the difference in arrival times could become sufficiently large to be detectable. This proceedings will look at testing for such Lorentz invariance violation (LIV) signatures in the astronomical lightcurves of gamma-ray emitting objects, with particular notice being given to the prospects for LIV testing with, the next generation observatory, the Cherenkov Telescope Array.
The propagation of photons, electrons and positrons at ultra-high energies above 10^{19} eV can be changed considerably if the dispersion relations of these particles are modified by terms suppressed by powers of the Planck scale. We recently pointed out that the current non-observation of photons in the ultra-high energy cosmic ray flux at such energies can put strong constraints on such modified dispersion relations. In the present work we generalize these constraints to all three Lorentz invariance breaking parameters that can occur in the dispersion relations for photons, electrons and positrons at first and second order suppression with the Planck scale. We also show how the excluded regions in these three-dimensional parameter ranges would be extended if ultra-high energy photons were detected in the future.
Lorentz symmetry breaking at very high energies may lead to photon dispersion relations of the form omega^2=k^2+xi_n k^2(k/M_Pl)^n with new terms suppressed by a power n of the Planck mass M_Pl. We show that first and second order terms of size xi_1 > 10^(-14) and xi_2 < -10^(-6), respectively, would lead to a photon component in cosmic rays above 10^(19) eV that should already have been detected, if corresponding terms for electrons and positrons are significantly smaller. This suggests that Lorentz invariance breakings suppressed up to second order in the Planck scale are unlikely to be phenomenologically viable for photons.
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 Greisen-Zatsepin-Kuzmin (GZK) energy cutoff for cosmic protons, which is predicted due to photopion production in the Cosmic Microwave Background (CMB). This is a process of modest energy in the proton rest frame. It can be investigated to a high precision in the laboratory, if Lorentz transformations apply even at factors $gamma sim O(10^{11})$. For heavier nuclei the energy attenuation is even faster due to photo-disintegration, again if this process is Lorentz invariant. Hence the viability of Lorentz symmetry up to tremendous gamma-factors - far beyond accelerator tests - is a central issue. Next we comment on conceptual aspects of Lorentz Invariance and the possibility of its spontaneous breaking. This could lead to slightly particle dependent ``Maximal Attainable Velocities. We discuss their effect in decays, Cerenkov radiation, the GZK cutoff and neutrino oscillation in cosmic rays. We also review the search for LIV in cosmic gamma-rays. For multi TeV gamma-rays we possibly encounter another puzzle related to the transparency of the CMB, similar to the GZK cutoff. The photons emitted in a Gamma Ray Burst occur at lower energies, but their very long path provides access to information not far from the Planck scale. No LIV has been observed so far. However, even extremely tiny LIV effects could change the predictions for cosmic ray physics drastically. An Appendix is devoted to the recent hypothesis by the Pierre Auger Collaboration, which identifies nearby Active Galactic Nuclei - or objects next to them - as probable UHECR sources.
In this work, we compute some phenomenological bounds for the electromagnetic and massive gravitational high-derivative extensions supposing that it is possible to have an astrophysical process that generates simultaneously gravitational and electromagnetic waves. We present Lorentz invariance violating (LIV) higher-order derivative models, following the Myers-Pospelov approach, to electrodynamics and massive gravitational waves. We compute the corrected equation of motion of these models, their dispersion relations and the velocities. The LIV parameters for the gravitational and electromagnetic sectors, $xi_{g}$ and $xi_{gamma}$, respectively, were also obtained for three different approaches: luminal photons, time delay of flight and the difference of graviton and photon velocities. These LIV parameters depend on the mass scales where the LIV-terms become relevant, $M$ for the electromagnetic sector and $M_{1}$ for the gravitational one. We obtain, using the values for $M$ and $M_{1}$ found in the literature, that $xi_{g}sim10^{-2}$, which is expected to be phenomenologically relevant and $xi_{gamma}sim10^{3}$, which cannot be suitable for an effective LIV theory. However, we show that $xi_{gamma}$ can be interesting in a phenomenological point of view if $Mgg M_{1}$. Finally the relation between the variation of the velocities of the photon and the graviton in relation to the speed of light was calculated and resulted in $Delta v_{g}/Delta v_{gamma}lesssim1.82times 10^{-3}$.
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