In this paper, the Lorentz invariance violation (LIV) is introduced in the calculations of photon propagation in the universe. LIV is considered in the photon sector, and the mean-free path of the γγ → e+e- interaction is calculated. The corresponding photon horizon, including LIV effects, is used to predict major changes in the propagation of photons with energy above 1018 eV. The flux of GZK photons on Earth, considering LIV, is calculated for several source models of ultra-high-energy cosmic rays (UHECRs). The predicted flux of GZK gamma-rays is compared to the new upper limits on the photon flux obtained by the Pierre Auger Observatory in order to impose upper limits on the LIV coefficients of order n = 0, 1, and 2. The limits on the LIV coefficients derived here are more realistic than previous works and in some cases more restrictive. The analysis resulted in LIV upper limits in the photon sector of δγ,0limit ∼ -10-20,δγ,1limit ∼ -10-38eV-2, δγ,2limit ∼ -10-56eV-2in the astrophysical scenario, which best describes UHECR data.
Bibliographical noteFunding Information:
R.G.L. is supported by FAPESP (2014/26816-0, 2016/ 24943-0). H.M.H. acknowledges IFSC/USP for their hospitality during the developments of this work, Abdel Pérez Lorenzana for enlightening discussions, and the support from Conacyt Mexico under grant 237004 and the Brazilian agency FAPESP (2017/03680-3). V.d.S. thanks the Brazilian population support via FAPESP (2015/15897-1) and CNPq. This work has partially made use of the computing facilities of the Laboratory of Astroinformatics (IAG/USP, NAT/Unicsul), whose purchase was made possible by the Brazilian agency FAPESP (2009/54006-4) and the INCT-A. The authors acknowledge the National Laboratory for Scientific Computing (LNCC/MCTI, Brazil) for providing HPC resources of the SDumont supercomputer, which have contributed to the research results reported within this paper (http://sdumont. lncc.br).
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All Science Journal Classification (ASJC) codes
- Astronomy and Astrophysics
- Space and Planetary Science