Lorentz invariance violation (LIV) is often described by dispersion relations of the form Ei2 = mi2+pi2+δi,n E2+n with delta different based on particle type i, with energy E, momentum p and rest mass m. Kinematics and energy thresholds of interactions are modified once the LIV terms become comparable to the squared masses of the particles involved. Thus, the strongest constraints on the LIV coefficients δi,n tend to come from the highest energies. At sufficiently high energies, photons produced by cosmic ray interactions as they propagate through the Universe could be subluminal and unattenuated over cosmological distances. Cosmic ray interactions can also be modified and lead to detectable fingerprints in the energy spectrum and mass composition observed on Earth. The data collected at the Pierre Auger Observatory are therefore possibly sensitive to both the electromagnetic and hadronic sectors of LIV. In this article, we explore these two sectors by comparing the energy spectrum and the composition of cosmic rays and the upper limits on the photon flux from the Pierre Auger Observatory with simulations including LIV. Constraints on LIV parameters depend strongly on the mass composition of cosmic rays at the highest energies. For the electromagnetic sector, while no constraints can be obtained in the absence of protons beyond 1019 eV, we obtain δγ,0 > -10-21, δγ,1 > -10-40 eV-1 and δγ,2 > -10-58 eV-2 in the case of a subdominant proton component up to 1020 eV. For the hadronic sector, we study the best description of the data as a function of LIV coefficients and we derive constraints in the hadronic sector such as δhad,0 < 10-19, δhad,1 < 10-38 eV-1 and δhad,2 < 10-57 eV-2 at 5σ CL.The successful installation, commissioning, and operation of the Pierre Auger Observatory
would not have been possible without the strong commitment and effort from the technical
and administrative staff in Malargüe. We are very grateful to the following agencies and
organizations for financial support: Argentina — Comisión Nacional de Energía Atómica;
Agencia Nacional de Promoción Científica y Tecnológica (ANPCyT); Consejo Nacional de
Investigaciones Científicas y Técnicas (CONICET); Gobierno de la Provincia de Mendoza;
Municipalidad de Malargüe; NDM Holdings and Valle Las Leñas; in gratitude for their continuing cooperation over land access; Australia — the Australian Research Council; Belgium
— Fonds de la Recherche Scientifique (FNRS); Research Foundation Flanders (FWO); Brazil
— Conselho Nacional de Desenvolvimento Científico e Tecnológico (CNPq); Financiadora
de Estudos e Projetos (FINEP); Fundação de Amparo à Pesquisa do Estado de Rio de
Janeiro (FAPERJ); São Paulo Research Foundation (FAPESP) Grants No. 2019/10151-2,
No. 2010/07359-6 and No. 1999/05404-3; Ministério da Ciência, Tecnologia, Inovações e
Comunicações (MCTIC); Czech Republic — Grant No. MSMT CR LTT18004, LM2015038,
LM2018102, CZ.02.1.01/0.0/0.0/16_013/0001402, CZ.02.1.01/0.0/0.0/18_046/0016010 and
CZ.02.1.01/0.0/0.0/17_049/0008422; France — Centre de Calcul IN2P3/CNRS; Centre National de la Recherche Scientifique (CNRS); Conseil Régional Ile-de-France; Département
Physique Nucléaire et Corpusculaire (PNC-IN2P3/CNRS); Département Sciences de l’Univers
(SDU-INSU/CNRS); Institut Lagrange de Paris (ILP) Grant No. LABEX ANR-10-LABX-63
within the Investissements d’Avenir Programme Grant No. ANR-11-IDEX-0004-02; Germany
— Bundesministerium für Bildung und Forschung (BMBF); Deutsche Forschungsgemeinschaft
(DFG); Finanzministerium Baden-Württemberg; Helmholtz Alliance for Astroparticle Physics
(HAP); Helmholtz-Gemeinschaft Deutscher Forschungszentren (HGF); Ministerium für Innovation, Wissenschaft und Forschung des Landes Nordrhein-Westfalen; Ministerium für Wissenschaft, Forschung und Kunst des Landes Baden-Württemberg; Italy — Istituto Nazionale
di Fisica Nucleare (INFN); Istituto Nazionale di Astrofisica (INAF); Ministero dell’Istruzione,
dell’Università e della Ricerca (MIUR); CETEMPS Center of Excellence; Ministero degli
Affari Esteri (MAE); México — Consejo Nacional de Ciencia y Tecnología (CONACYT)
No. 167733; Universidad Nacional Autónoma de México (UNAM); PAPIIT DGAPA-UNAM;
The Netherlands — Ministry of Education, Culture and Science; Netherlands Organisation
for Scientific Research (NWO); Dutch national e-infrastructure with the support of SURF
Cooperative; Poland — Ministry of Education and Science, grant No. DIR/WK/2018/11;
National Science Centre, Grants No. 2016/22/M/ST9/00198, 2016/23/B/ST9/01635, and
2020/39/B/ST9/01398; Portugal — Portuguese national funds and FEDER funds within
Programa Operacional Factores de Competitividade through Fundação para a Ciência e
a Tecnologia (COMPETE); Romania — Ministry of Research, Innovation and Digitization, CNCS/CCCDI — UEFISCDI, projects PN19150201/16N/2019, PN1906010, TE128
and PED289, within PNCDI III; Slovenia — Slovenian Research Agency, grants P1-0031,
P1-0385, I0-0033, N1-0111; Spain — Ministerio de Economía, Industria y Competitividad
(FPA2017-85114-P and PID2019-104676GB-C32), Xunta de Galicia (ED431C 2017/07), Junta
de Andalucía (SOMM17/6104/UGR, P18-FR-4314) Feder Funds, RENATA Red Nacional
Temática de Astropartículas (FPA2015-68783-REDT) and María de Maeztu Unit of Excellence
(MDM-2016-0692); U.S.A. — Department of Energy, Contracts No. DE-AC02-07CH11359,
No. DE-FR02-04ER41300, No. DE-FG02-99ER41107 and No. DE-SC0011689; National Science
Foundation, Grant No. 0450696; The Grainger Foundation; Marie Curie-IRSES/EPLANET;
European Particle Physics Latin American Network; and UNESCO.S
