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Lorentz Breaking Effective Field Theory and Observational Tests

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Analogue Gravity Phenomenology

Part of the book series: Lecture Notes in Physics ((LNP,volume 870))

Abstract

Analogue models of gravity have provided an experimentally realizable test field for our ideas on quantum field theory in curved spacetimes but they have also inspired the investigation of possible departures from exact Lorentz invariance at microscopic scales. In this role they have joined, and sometime anticipated, several quantum gravity models characterized by Lorentz breaking phenomenology. A crucial difference between these speculations and other ones associated to quantum gravity scenarios, is the possibility to carry out observational and experimental tests which have nowadays led to a broad range of constraints on departures from Lorentz invariance. We shall review here the effective field theory approach to Lorentz breaking in the matter sector, present the constraints provided by the available observations and finally discuss the implications of the persisting uncertainty on the composition of the ultra high energy cosmic rays for the constraints on the higher order, analogue gravity inspired, Lorentz violations.

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Notes

  1. 1.

    Anisotropic scaling [34–36] techniques were recently recognized to be the most appropriate way of handling higher order operators in Lorentz breaking theories and in this case the highest order operators are indeed crucial in making the theory power counting renormalizable. This is why we shall adopt sometime the expression “naively non renormalizable”.

  2. 2.

    I disregard here the possible appearance of dissipative terms [82] in the dispersion relation, as this would correspond to a theory with unitarity loss and to a more radical departure from standard physics than that envisaged in the framework discussed herein (albeit a priori such dissipative scenarios are logically consistent and even plausible within some quantum/emergent gravity frameworks).

  3. 3.

    We consider here only κ=3,4, for which these relationships have been demonstrated.

  4. 4.

    Actually these criteria allow the addition of other (CPT even) terms, but these would not lead to modified dispersion relations (they can be thought of as extra, Planck suppressed, interaction terms) [92].

  5. 5.

    Note however, that some knowledge of DSR phenomenology can be obtained by considering that, as in Special Relativity, any phenomenon that implies the existence of a preferred reference frame is forbidden. Thus, the detection of such a phenomenon would imply the falsification of both special and doubly-special relativity. An example of such a process is the decay of a massless particle.

  6. 6.

    Note that for an object located at cosmological distance (let z be its redshift), the distance d becomes

    $$ d(z) = \frac{1}{H_{0}}\int^{z}_0 \frac{1+z'}{\sqrt{\varOmega_{\varLambda } + \varOmega_{m}(1+z')^{3}}} dz' , $$
    (13.71)

    where d(z) is not exactly the distance of the object as it includes a (1+z)2 factor in the integrand to take into account the redshift acting on the photon energies.

  7. 7.

    Faraday rotation is negligible at high energies.

  8. 8.

    The same paper claims also a strong constraint on the parameter ξ (4). Unfortunately, such a claim is based on the erroneous assumption that the EFT order six operators responsible for this term imply opposite signs for opposite helicities of the photon. We have instead seen that the CPT evenness of the relevant dimension six operators imply a helicity independent dispersion relation for the photon (see Eq. (13.54)).

  9. 9.

    This is a somewhat harsh statement given that it was shown in [183] that a substantial (albeit reduced) high energy gamma ray flux is still expected also in the case of mixed composition, so that in principle the previously discussed line of reasoning based on the absence of upper threshold for UHE gamma rays might still work.

  10. 10.

    UHE nuclei suffer mainly from photo-disintegration losses as they propagate in the intergalactic medium. Because photo-disintegration is indeed a threshold process, it can be strongly affected by LV. According to [185], and in the same way as for the proton case, the mean free paths of UHE nuclei are modified by LV in such a way that the final UHECR spectra after propagation can show distinctive LV features. However, a quantitative evaluation of the propagated spectra has not been performed yet.

References

  1. Mavromatos, N.E.: Lect. Notes Phys. 669, 245 (2005). ar**v:gr-qc/0407005

    Article  ADS  Google Scholar 

  2. Weinberg, S.: Phys. Rev. D 72, 043514 (2005). ar**v:hep-th/0506236

    Article  MathSciNet  ADS  Google Scholar 

  3. Damour, T., Polyakov, A.M.: Nucl. Phys. B 423, 532 (1994). ar**v:hep-th/9401069

    Article  MathSciNet  ADS  MATH  Google Scholar 

  4. Barrow, J.D.: ar**v:gr-qc/9711084 (1997)

  5. Bleicher, M., Hofmann, S., Hossenfelder, S., Stoecker, H.: Phys. Lett. B 548, 73 (2002). ar**v:hep-ph/0112186

    Article  ADS  Google Scholar 

  6. Kostelecky, V.A.: Phys. Rev. D 69, 105009 (2004). ar**v:hep-th/0312310

    Article  ADS  Google Scholar 

  7. Mattingly, D.: Living Rev. Relativ. 8, 5 (2005). ar**v:gr-qc/0502097

    ADS  Google Scholar 

  8. Dirac, P.A.M.: Nature 168, 906 (1951)

    Article  MathSciNet  ADS  Google Scholar 

  9. Bjorken, J.D.: Ann. Phys. 24, 174 (1963)

    Article  MathSciNet  ADS  Google Scholar 

  10. Phillips, P.R.: Phys. Rev. 146, 966 (1966)

    Article  ADS  Google Scholar 

  11. Blokhintsev, D.I.: Sov. Phys. Usp. 9, 405 (1966)

    Article  ADS  Google Scholar 

  12. Pavlopoulos, T.G.: Phys. Rev. 159, 1106 (1967)

    Article  ADS  Google Scholar 

  13. Rédei, L.B.: Phys. Rev. 162, 1299 (1967)

    Article  ADS  Google Scholar 

  14. Nielsen, H.B., Ninomiya, M.: Nucl. Phys. B 141, 153 (1978)

    Article  MathSciNet  ADS  Google Scholar 

  15. Ellis, J., Gaillard, M.K., Nanopoulos, D.V., Rudaz, S.: Nucl. Phys. B 176, 61 (1980)

    Article  ADS  Google Scholar 

  16. Zee, A.: Phys. Rev. D 25, 1864 (1982)

    Article  ADS  Google Scholar 

  17. Nielsen, H.B., Picek, I.: Phys. Lett. B 114, 141 (1982)

    Article  ADS  Google Scholar 

  18. Chadha, S., Nielsen, H.B.: Nucl. Phys. B 217, 125 (1983)

    Article  ADS  Google Scholar 

  19. Nielsen, H.B., Picek, I.: Nucl. Phys. B 211, 269 (1983)

    Article  ADS  Google Scholar 

  20. Auger, P., Roth, M.: ar**v:0706.2096 [astro-ph] (2007)

  21. HiRes, Abbasi, R., et al.: ar**v:astro-ph/0703099 (2007)

  22. Kostelecky, V.A., Samuel, S.: Phys. Rev. D 39, 683 (1989)

    Article  ADS  Google Scholar 

  23. Colladay, D., Kostelecky, V.: Phys. Rev. D 58, 116002 (1998). ar**v:hep-ph/9809521

    Article  ADS  Google Scholar 

  24. Kostelecky, E., Alan, V.: Prepared for 3rd Meeting on CPT and Lorentz Symmetry (CPT 04), Bloomington, Indiana, 8–11 Aug 2007

    Google Scholar 

  25. Amelino-Camelia, G., Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., Sarkar, S.: Nature 393, 763 (1998). ar**v:astro-ph/9712103

    Article  ADS  Google Scholar 

  26. Coleman, S.R., Glashow, S.L.: Phys. Lett. B 405, 249 (1997). ar**v:hep-ph/9703240

    Article  ADS  Google Scholar 

  27. Coleman, S.R., Glashow, S.L.: ar**v:hep-ph/9808446 (1998)

  28. Coleman, S.R., Glashow, S.L.: Phys. Rev. D 59, 116008 (1999). ar**v:hep-ph/9812418

    Article  ADS  Google Scholar 

  29. Gonzalez-Mestres, L.: ar**v:hep-ph/9610474 (1996)

  30. Gonzalez-Mestres, L.: physics/9712005 (1997)

  31. Jacobson, T., Liberati, S., Mattingly, D.: Phys. Rev. D 67, 124011 (2003). ar**v:hep-ph/0209264

    Article  ADS  Google Scholar 

  32. Mattingly, D., Jacobson, T., Liberati, S.: Phys. Rev. D 67, 124012 (2003). ar**v:hep-ph/0211466

    Article  ADS  Google Scholar 

  33. Jacobson, T., Liberati, S., Mattingly, D.: Ann. Phys. 321, 150 (2006). ar**v:astro-ph/0505267

    Article  ADS  MATH  Google Scholar 

  34. Anselmi, D.: J. High Energy Phys. 0802, 051 (2008). ar**v:0801.1216 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  35. Horava, P.: Phys. Rev. D 79, 084008 (2009). ar**v:0901.3775 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  36. Visser, M.: ar**v:0912.4757 [hep-th] (2009)

  37. Myers, R.C., Pospelov, M.: Phys. Rev. Lett. 90, 211601 (2003). ar**v:hep-ph/0301124

    Article  MathSciNet  ADS  Google Scholar 

  38. Mattingly, D.: ar**v:0802.1561 [gr-qc] (2008)

  39. Riess, A.G., et al. (Supernova Search Team): Astron. J. 116, 1009 (1998). ar**v:astro-ph/9805201

    Article  ADS  Google Scholar 

  40. Perlmutter, S., et al. (Supernova Cosmology Project): Astrophys. J. 517, 565 (1999). ar**v:astro-ph/9812133

    Article  ADS  Google Scholar 

  41. Greisen, K.: Phys. Rev. Lett. 16, 748 (1966)

    Article  ADS  Google Scholar 

  42. Zatsepin, G.T., Kuz’min, V.A.: On the interaction of cosmic rays with photons. In: Cosmic rays, Moscow, vol. 11, pp. 45–47 (1969)

    Google Scholar 

  43. Takeda, M., et al.: Phys. Rev. Lett. 81, 1163 (1998). ar**v:astro-ph/9807193

    Article  ADS  Google Scholar 

  44. Protheroe, R., Meyer, H.: Phys. Lett. B 493, 1 (2000). ar**v:astro-ph/0005349

    Article  ADS  Google Scholar 

  45. Adam, T., et al. (OPERA Collaboration): ar**v:1109.4897 (2011). http://press.web.cern.ch/press/pressreleases/Releases2011/PR19.11E.html

  46. Amelino-Camelia, G., et al.: Int. J. Mod. Phys. D 20, 2623 (2011). ar**v:1109.5172 [hep-ph]

    Article  MathSciNet  ADS  MATH  Google Scholar 

  47. Cohen, A.G., Glashow, S.L.: Phys. Rev. Lett. 107, 181803 (2011). ar**v:1109.6562 [hep-ph]

    Article  ADS  Google Scholar 

  48. Maccione, L., Liberati, S., Mattingly, D.M.: ar**v:1110.0783 [hep-ph] (2011)

  49. Carmona, J., Cortes, J.: ar**v:1110.0430 [hep-ph] (2011)

  50. Antonello, M., et al. (ICARUS Collaboration): ar**v:1203.3433 [hep-ex] (2012)

  51. Amelino-Camelia, G., Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V.: Int. J. Mod. Phys. A 12, 607 (1997). ar**v:hep-th/9605211

    Article  MathSciNet  ADS  MATH  Google Scholar 

  52. Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V.: Phys. Rev. D 61, 027503 (2000). ar**v:gr-qc/9906029

    Article  MathSciNet  ADS  Google Scholar 

  53. Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V.: Phys. Rev. D 62, 084019 (2000). ar**v:gr-qc/0006004

    Article  MathSciNet  ADS  Google Scholar 

  54. Ellis, J.R., Mavromatos, N.E., Sakharov, A.S.: Astropart. Phys. 20, 669 (2004). ar**v:astro-ph/0308403

    Article  ADS  Google Scholar 

  55. Gambini, R., Pullin, J.: Phys. Rev. D 59, 124021 (1999). ar**v:gr-qc/9809038

    Article  MathSciNet  ADS  Google Scholar 

  56. Carroll, S.M., Harvey, J.A., Kostelecky, V.A., Lane, C.D., Okamoto, T.: Phys. Rev. Lett. 87, 141601 (2001). ar**v:hep-th/0105082

    Article  MathSciNet  ADS  Google Scholar 

  57. Lukierski, J., Ruegg, H., Zakrzewski, W.J.: Ann. Phys. 243, 90 (1995). ar**v:hep-th/9312153

    Article  MathSciNet  ADS  MATH  Google Scholar 

  58. Amelino-Camelia, G., Majid, S.: Int. J. Mod. Phys. A 15, 4301 (2000). ar**v:hep-th/9907110

    MathSciNet  ADS  MATH  Google Scholar 

  59. Burgess, C.P., Cline, J., Filotas, E., Matias, J., Moore, G.D.: J. High Energy Phys. 03, 043 (2002). ar**v:hep-ph/0201082

    Article  ADS  Google Scholar 

  60. Gasperini, M.: Phys. Lett. B 163, 84 (1985)

    Article  ADS  Google Scholar 

  61. Gasperini, M.: Phys. Lett. B 180, 221 (1986)

    Article  ADS  Google Scholar 

  62. Gasperini, M.: Class. Quantum Gravity 4, 485 (1987)

    Article  MathSciNet  ADS  MATH  Google Scholar 

  63. Gasperini, M., D’Azeglio, C.M.: Lorentz noninvariance and the universality of free fall in quasi-riemannian gravity. In: Gravitational Measurements, Fundamental Metrology and Constants, vol. 1, pp. 181–190. Springer, Berlin (1988)

    Chapter  Google Scholar 

  64. Gasperini, M.: Gen. Relativ. Gravit. 30, 1703 (1998). ar**v:gr-qc/9805060

    Article  MathSciNet  ADS  MATH  Google Scholar 

  65. Mattingly, D., Jacobson, T.: ar**v:gr-qc/0112012 (2001)

  66. Eling, C., Jacobson, T., Mattingly, D.: ar**v:gr-qc/0410001 (2004)

  67. Jacobson, T.: ar**v:0801.1547 [gr-qc] (2008)

  68. Sotiriou, T.P., Visser, M., Weinfurtner, S.: J. High Energy Phys. 0910, 033 (2009). ar**v:0905.2798 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  69. Blas, D., Pujolas, O., Sibiryakov, S.: Phys. Rev. Lett. 104, 181302 (2010). ar**v:0909.3525 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  70. Jacobson, T.: Phys. Rev. D 81, 101502 (2010). ar**v:1001.4823 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  71. Barcelo, C., Liberati, S., Visser, M.: Living Rev. Relativ. 8, 12 (2005). ar**v:gr-qc/0505065

    ADS  Google Scholar 

  72. Unruh, W.: Phys. Rev. Lett. 46, 1351 (1981)

    Article  ADS  Google Scholar 

  73. Visser, M.: ar**v:gr-qc/9311028 (1993)

  74. Garay, L., Anglin, J., Cirac, J., Zoller, P.: Phys. Rev. Lett. 85, 4643 (2000). ar**v:gr-qc/0002015

    Article  ADS  Google Scholar 

  75. Barcelo, C., Liberati, S., Visser, M.: Class. Quantum Gravity 18, 1137 (2001). ar**v:gr-qc/0011026

    Article  MathSciNet  ADS  MATH  Google Scholar 

  76. Balbinot, R., Fagnocchi, S., Fabbri, A., Procopio, G.P.: Phys. Rev. Lett. 94, 161302 (2005). ar**v:gr-qc/0405096

    Article  MathSciNet  ADS  Google Scholar 

  77. Barcelo, C., Liberati, S., Sonego, S., Visser, M.: Phys. Rev. D 77, 044032 (2008). ar**v:0712.1130

    Article  ADS  Google Scholar 

  78. Barcelo, C., Liberati, S., Visser, M.: Phys. Rev. A 68, 053613 (2003). ar**v:cond-mat/0307491

    Article  ADS  Google Scholar 

  79. Weinfurtner, S., Visser, M., Jain, P., Gardiner, C.: PoS QG-PH, 044 (2007). ar**v:0804.1346 [gr-qc]

    Google Scholar 

  80. Weinfurtner, S., Jain, P., Visser, M., Gardiner, C.: Class. Quantum Gravity 26, 065012 (2009). ar**v:0801.2673 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  81. Jain, P., Weinfurtner, S., Visser, M., Gardiner, C.: ar**v:0705.2077 [cond-mat.other] (2007)

  82. Parentani, R.: PoS QG-PH, 031 (2007). ar**v:0709.3943 [hep-th]

    Google Scholar 

  83. Collins, J., Perez, A., Sudarsky, D., Urrutia, L., Vucetich, H.: Phys. Rev. Lett. 93, 191301 (2004). ar**v:gr-qc/0403053

    Article  MathSciNet  ADS  Google Scholar 

  84. Groot Nibbelink, S., Pospelov, M.: Phys. Rev. Lett. 94, 081601 (2005). ar**v:hep-ph/0404271

    Article  MathSciNet  ADS  Google Scholar 

  85. Bolokhov, P.A., Nibbelink, S.G., Pospelov, M.: Phys. Rev. D 72, 015013 (2005). ar**v:hep-ph/0505029

    Article  ADS  Google Scholar 

  86. ATLAS-Collaboration, https://twiki.cern.ch/twiki/bin/view/AtlasPublic/CombinedSummaryPlots

  87. Liberati, S., Visser, M., Weinfurtner, S.: Phys. Rev. Lett. 96, 151301 (2006). ar**v:gr-qc/0512139

    Article  ADS  Google Scholar 

  88. Liberati, S., Visser, M., Weinfurtner, S.: Class. Quantum Gravity 23, 3129 (2006). ar**v:gr-qc/0510125

    Article  MathSciNet  ADS  MATH  Google Scholar 

  89. Pospelov, M., Shang, Y.: Phys. Rev. D 85, 105001 (2012). ar**v:1010.5249 [hep-th]

    Article  ADS  Google Scholar 

  90. Kostelecky, V.A., Mewes, M.: Phys. Rev. D 66, 056005 (2002). ar**v:hep-ph/0205211

    Article  ADS  Google Scholar 

  91. Yao, W.M., et al. (Particle Data Group): J. Phys. G 33, 1 (2006)

    Article  ADS  Google Scholar 

  92. Bolokhov, P.A., Pospelov, M.: Phys. Rev. D 77, 025022 (2008). ar**v:hep-ph/0703291

    Article  ADS  Google Scholar 

  93. Jacobson, T.A., Liberati, S., Mattingly, D., Stecker, F.W.: Phys. Rev. Lett. 93, 021101 (2004). ar**v:astro-ph/0309681

    Article  ADS  Google Scholar 

  94. Stecker, F., Glashow, S.L.: Astropart. Phys. 16, 97 (2001). ar**v:astro-ph/0102226

    Article  ADS  Google Scholar 

  95. Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V.: Phys. Lett. B 293, 37 (1992). ar**v:hep-th/9207103

    Article  MathSciNet  ADS  Google Scholar 

  96. Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., Sakharov, A.S.: Int. J. Mod. Phys. A 19, 4413 (2004). ar**v:gr-qc/0312044

    Article  MathSciNet  ADS  MATH  Google Scholar 

  97. Polchinski, J.: ar**v:hep-th/9611050 (1996)

  98. von Ignatowsky, W.: Verh. Dtsch. Phys. Ges. 12, 788 (1910)

    Google Scholar 

  99. von Ignatowsky, W.: Phys. Z. 11, 972 (1910)

    Google Scholar 

  100. von Ignatowsky, W.: Arch. Math. Phys. 3(17), 1 (1911)

    Google Scholar 

  101. von Ignatowsky, W.: Arch. Math. Phys. 3(18), 17 (1911)

    Google Scholar 

  102. von Ignatowsky, W.: Phys. Z. 12, 779 (1911)

    MATH  Google Scholar 

  103. Liberati, S., Sonego, S., Visser, M.: Ann. Phys. 298, 167 (2002). ar**v:gr-qc/0107091

    Article  MathSciNet  ADS  MATH  Google Scholar 

  104. Sonego, S., Pin, M.: J. Math. Phys. 50, 042902 (2009). ar**v:0812.1294 [gr-qc]

    Article  MathSciNet  ADS  Google Scholar 

  105. Baccetti, V., Tate, K., Visser, M.: J. High Energy Phys. 1205, 119 (2012). ar**v:1112.1466 [gr-qc]

    Article  ADS  Google Scholar 

  106. Cohen, A.G., Glashow, S.L.: Phys. Rev. Lett. 97, 021601 (2006). ar**v:hep-ph/0601236

    Article  MathSciNet  ADS  Google Scholar 

  107. Bogoslovsky, G.Y.: ar**v:math-ph/0511077 (2005)

  108. Bogoslovsky, G.Y.: Phys. Lett. A 350, 5 (2006). ar**v:hep-th/0511151

    Article  ADS  MATH  Google Scholar 

  109. Gibbons, G.W., Gomis, J., Pope, C.N.: Phys. Rev. D, Part. Fields 76, 081701 (2007)

    Article  MathSciNet  ADS  Google Scholar 

  110. Amelino-Camelia, G.: Int. J. Mod. Phys. D 11, 35 (2002). ar**v:gr-qc/0012051

    Article  MathSciNet  ADS  MATH  Google Scholar 

  111. Magueijo, J., Smolin, L.: Phys. Rev. Lett. 88, 190403 (2002). ar**v:hep-th/0112090

    Article  ADS  Google Scholar 

  112. Magueijo, J., Smolin, L.: Phys. Rev. D 67, 044017 (2003). ar**v:gr-qc/0207085

    Article  MathSciNet  ADS  Google Scholar 

  113. Amelino-Camelia, G.: Int. J. Mod. Phys. D 12, 1211 (2003). ar**v:astro-ph/0209232

    Article  ADS  Google Scholar 

  114. Lukierski, J.: ar**v:hep-th/0402117 (2004)

  115. Amelino-Camelia, G.: ar**v:0806.0339 [gr-qc] (2008)

  116. Carmona, J., Cortes, J., Indurain, J., Mazon, D.: Phys. Rev. D 80, 105014 (2009). ar**v:0905.1901 [hep-th]

    Article  ADS  Google Scholar 

  117. Judes, S., Visser, M.: Phys. Rev. D 68, 045001 (2003). ar**v:gr-qc/0205067

    Article  MathSciNet  ADS  Google Scholar 

  118. Ahluwalia, D.V.: ar**v:gr-qc/0212128 (2002)

  119. Rembielinski, J., Smolinski, K.A.: Bull. Soc. Sci. Lett. Lodz 53, 57 (2003). ar**v:hep-th/0207031

    MathSciNet  Google Scholar 

  120. Schutzhold, R., Unruh, W.G.: JETP Lett. 78, 431 (2003). ar**v:gr-qc/0308049

    Article  ADS  Google Scholar 

  121. Hossenfelder, S.: Phys. Rev. Lett. 104, 140402 (2010). ar**v:1004.0418 [hep-ph]

    Article  ADS  Google Scholar 

  122. Amelino-Camelia, G., et al.: Phys. Rev. D 78, 025005 (2008). ar**v:0709.4600 [hep-th]

    Article  MathSciNet  ADS  Google Scholar 

  123. Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J., Smolin, L.: Phys. Rev. D 84, 084010 (2011). ar**v:1101.0931 [hep-th]

    Article  ADS  Google Scholar 

  124. Smolin, L.: ar**v:0808.3765 [hep-th] (2008)

  125. Rovelli, C.: ar**v:0808.3505 [gr-qc] (2008)

  126. Amelino-Camelia, G., Freidel, L., Kowalski-Glikman, J., Smolin, L.: Phys. Rev. D 84, 087702 (2011). ar**v:1104.2019 [hep-th]

    Article  ADS  Google Scholar 

  127. Hossenfelder, S.: ar**v:1202.4066 [hep-th] (2012)

  128. Kostelecky, V.A., Russell, N.: ar**v:0801.0287 (2008)

  129. Ellis, J.R., Mavromatos, N.E., Nanopoulos, D.V., Sakharov, A.S., Sarkisyan, E.K.G.: Astropart. Phys. 25, 402 (2006). ar**v:astro-ph/0510172

    Article  ADS  Google Scholar 

  130. Magic, J.A., et al.: ar**v:0708.2889 [astro-ph] (2007)

  131. Maccione, L., Liberati, S., Celotti, A., Kirk, J.G., Ubertini, P.: ar**v:0809.0220 [astro-ph] (2008)

  132. Gleiser, R.J., Kozameh, C.N.: Phys. Rev. D 64, 083007 (2001). ar**v:gr-qc/0102093

    Article  ADS  Google Scholar 

  133. McMaster, W.H.: Rev. Mod. Phys. 33, 8 (1961)

    Article  MathSciNet  ADS  Google Scholar 

  134. Baccetti, V., Tate, K., Visser, M.: J. High Energy Phys. 1203, 087 (2012). ar**v:1111.6340 [hep-ph]

    Article  ADS  Google Scholar 

  135. Gelmini, G., Nussinov, S., Yaguna, C.E.: J. Cosmol. Astropart. Phys. 0506, 012 (2005). ar**v:hep-ph/0503130

    Article  ADS  Google Scholar 

  136. Kluzniak, W.: Astropart. Phys. 11, 117 (1999)

    Article  ADS  Google Scholar 

  137. Altschul, B.: Phys. Rev. D 74, 083003 (2006). ar**v:hep-ph/0608332

    Article  MathSciNet  ADS  Google Scholar 

  138. Liberati, S., Maccione, L.: Annu. Rev. Nucl. Part. Sci. 59, 245 (2009). ar**v:0906.0681

    Article  ADS  Google Scholar 

  139. Maccione, L., Liberati, S., Celotti, A., Kirk, J.: J. Cosmol. Astropart. Phys. 2007, 013 (2007). ar**v:0707.2673 [astro-ph]

    Article  Google Scholar 

  140. Kennel, C.F., Coroniti, F.V.: Astrophys. J. 283, 694 (1984)

    Article  ADS  Google Scholar 

  141. Fan, Y.-Z., Wei, D.-M., Xu, D.: Mon. Not. R. Astron. Soc. 376, 1857 (2006). ar**v:astro-ph/0702006

    Article  ADS  Google Scholar 

  142. Dean, A.J., et al.: Science 321, 1183 (2008)

    Article  ADS  Google Scholar 

  143. Forot, M., Laurent, P., Grenier, I.A., Gouiffes, C., Lebrun, F.: ar**v:0809.1292 [astro-ph] (2008)

  144. Jacobson, T., Liberati, S., Mattingly, D.: Nature 424, 1019 (2003). ar**v:astro-ph/0212190

    Article  ADS  Google Scholar 

  145. Kirk, J.G., Lyubarsky, Y., Petri, J.: ar**v:astro-ph/0703116 (2007)

  146. Parmar, A.N., et al.: INTEGRAL mission. In: Truemper, J.E., Tananbaum, H.D. (eds.) X-Ray and Gamma-Ray Telescopes and Instruments for Astronomy. Proceedings of the SPIE, vol. 4851, pp. 1104–1112 (2003)

    Chapter  Google Scholar 

  147. McGlynn, S., et al.: ar**v:astro-ph/0702738 (2007)

  148. Petri, J., Kirk, J.G.: Astrophys. J. 627, L37 (2005). ar**v:astro-ph/0505427

    Article  ADS  Google Scholar 

  149. Weisskopf, M.C., Silver, E.H., Kestenbaum, H.L., Long, K.S., Novick, R.: Astrophys. J. Lett. 220, L117 (1978)

    Article  ADS  Google Scholar 

  150. Ng, C.Y., Romani, R.W.: Astrophys. J. 601, 479 (2004). ar**v:astro-ph/0310155

    Article  ADS  Google Scholar 

  151. Kanbach, G., Slowikowska, A., Kellner, S., Steinle, H.: AIP Conf. Proc. 801, 306 (2005). ar**v:astro-ph/0511636

    Article  ADS  Google Scholar 

  152. Mitrofanov, I.G.: Nature 426, 139 (2003)

    Article  ADS  Google Scholar 

  153. Coburn, W., Boggs, S.E.: Nature 423, 415 (2003). ar**v:astro-ph/0305377

    Article  ADS  Google Scholar 

  154. Stecker, F.W.: Astropart. Phys. 35, 95 (2011). ar**v:1102.2784 [astro-ph]

    Article  ADS  Google Scholar 

  155. Laurent, P., Gotz, D., Binetruy, P., Covino, S., Fernandez-Soto, A.: ar**v:1106.1068 [astro-ph.HE] (2011)

  156. Aharonian, F., et al. (The HEGRA): Astrophys. J. 614, 897 (2004). ar**v:astro-ph/0407118

    Article  ADS  Google Scholar 

  157. Auger, P., Abraham, J., et al.: Science 318, 938 (2007). ar**v:0711.2256 [astro-ph]

    Article  ADS  Google Scholar 

  158. Galaverni, M., Sigl, G.: Phys. Rev. Lett. 100, 021102 (2008). ar**v:0708.1737 [astro-ph]

    Article  ADS  Google Scholar 

  159. Maccione, L., Liberati, S.: J. Cosmol. Astropart. Phys. 0808, 027 (2008). ar**v:0805.2548 [astro-ph]

    Article  ADS  Google Scholar 

  160. Gelmini, G., Kalashev, O., Semikoz, D.V.: ar**v:astro-ph/0506128 (2005)

  161. Auger, P., Abraham, J., et al.: Astropart. Phys. 29, 243 (2008). ar**v:0712.1147 [astro-ph]

    Article  ADS  Google Scholar 

  162. Rubtsov, G.I., et al.: Phys. Rev. D 73, 063009 (2006). ar**v:astro-ph/0601449

    Article  ADS  Google Scholar 

  163. Galaverni, M., Sigl, G.: Phys. Rev. D 78, 063003 (2008). ar**v:0807.1210 [astro-ph]

    Article  ADS  Google Scholar 

  164. Aloisio, R., Blasi, P., Ghia, P.L., Grillo, A.F.: Phys. Rev. D 62, 053010 (2000). ar**v:astro-ph/0001258

    Article  ADS  Google Scholar 

  165. Alfaro, J., Palma, G.: Phys. Rev. D 67, 083003 (2003). ar**v:hep-th/0208193

    Article  ADS  Google Scholar 

  166. Scully, S., Stecker, F.: Astropart. Phys. 31, 220 (2009). ar**v:0811.2230 [astro-ph]

    Article  ADS  Google Scholar 

  167. Stecker, F.W., Scully, S.T.: New J. Phys. 11, 085003 (2009). ar**v:0906.1735 [astro-ph.HE]

    Article  ADS  Google Scholar 

  168. Maccione, L., Taylor, A.M., Mattingly, D.M., Liberati, S.: J. Cosmol. Astropart. Phys. 0904, 022 (2009). ar**v:0902.1756 [astro-ph.HE]

    Article  ADS  Google Scholar 

  169. Kelley, J. (IceCube Collaboration): Nucl. Phys. A 827, 507C (2009)

    Article  ADS  Google Scholar 

  170. Gonzalez-Garcia, M., Maltoni, M.: Phys. Rev. D 70, 033010 (2004). ar**v:hep-ph/0404085

    Article  ADS  Google Scholar 

  171. Huelsnitz, W., Kelley, J. (IceCube Collaboration): Search for quantum gravity with IceCube and high energy atmospheric neutrinos. In: International Cosmic Ray Conference (ICRC 2009) (2009)

    Google Scholar 

  172. Abbasi, R., et al. (IceCube Collaboration): Phys. Rev. D 82, 112003 (2010). ar**v:1010.4096 [astro-ph.HE]

    Article  ADS  Google Scholar 

  173. Stodolsky, L.: Phys. Lett. B 201, 353 (1988)

    Article  ADS  Google Scholar 

  174. Longo, M.J.: Phys. Rev. Lett. 60, 173 (1988)

    Article  ADS  Google Scholar 

  175. Ellis, J.R., Harries, N., Meregaglia, A., Rubbia, A., Sakharov, A.: Phys. Rev. D 78, 033013 (2008). ar**v:0805.0253 [hep-ph]

    Article  ADS  Google Scholar 

  176. Sakharov, A., Ellis, J., Harries, N., Meregaglia, A., Rubbia, A.: J. Phys. Conf. Ser. 171, 012039 (2009). ar**v:0903.5048 [hep-ph]

    Article  ADS  Google Scholar 

  177. Carmona, J., Cortes, J., Mazon, D.: Phys. Rev. D 85, 113001 (2012). ar**v:1203.2585

    Article  ADS  Google Scholar 

  178. Mattingly, D.M., Maccione, L., Galaverni, M., Liberati, S., Sigl, G.: J. Cosmol. Astropart. Phys. 1002, 007 (2010). ar**v:0911.0521 [hep-ph]

    Article  ADS  Google Scholar 

  179. Barwick, S.W.: J. Phys. Conf. Ser. 60, 276 (2007). ar**v:astro-ph/0610631

    Article  ADS  Google Scholar 

  180. Ward, B.: Phys. Rev. D 85, 073007 (2012). ar**v:1201.1322 [hep-ph]

    Article  ADS  Google Scholar 

  181. Abraham, J., et al. (Pierre Auger Observatory Collaboration): Phys. Rev. Lett. 104, 091101 (2010). ar**v:1002.0699 [astro-ph.HE]

    Article  ADS  Google Scholar 

  182. Glushkov, A., et al.: JETP Lett. 87, 190 (2008). ar**v:0710.5508 [astro-ph]

    Article  ADS  Google Scholar 

  183. Hooper, D., Taylor, A.M., Sarkar, S.: Astropart. Phys. 34, 340 (2011). ar**v:1007.1306 [astro-ph.HE]

    Article  ADS  Google Scholar 

  184. Abraham, J., et al. (The Pierre Auger Collaboration): Phys. Lett. B 685, 239 (2010). ar**v:1002.1975 [astro-ph.HE]

    Article  ADS  Google Scholar 

  185. Saveliev, A., Maccione, L., Sigl, G.: J. Cosmol. Astropart. Phys. 1103, 046 (2011). ar**v:1101.2903 [astro-ph.HE]

    Article  ADS  Google Scholar 

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Acknowledgements

I wish to that Luca Maccione and David Mattingly for useful insights, discussions and feedback on the manuscript preparation.

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  1. SISSA, Via Bonomea 265, 34136, Trieste, Italy

    Stefano Liberati

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Editors and Affiliations

  1. School of Engineering and Physical Science, Heriot-Watt University, Edinburgh, United Kingdom

    Daniele Faccio

  2. Dipartimento di Matematica, Politecnico di Milano, Milano, Italy

    Francesco Belgiorno

  3. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Sergio Cacciatori

  4. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Vittorio Gorini

  5. Int. School for Adv. Studies (SISSA), Trieste, Italy

    Stefano Liberati

  6. Dipartimento di Fisica e Matematica, Universita’ dell’Insubria, Como, Italy

    Ugo Moschella

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Liberati, S. (2013). Lorentz Breaking Effective Field Theory and Observational Tests. In: Faccio, D., Belgiorno, F., Cacciatori, S., Gorini, V., Liberati, S., Moschella, U. (eds) Analogue Gravity Phenomenology. Lecture Notes in Physics, vol 870. Springer, Cham. https://doi.org/10.1007/978-3-319-00266-8_13

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