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De Sitter Relativity: a New Road to Quantum Gravity?

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Abstract

The Poincaré group generalizes the Galilei group for high-velocity kinematics. The de Sitter group is assumed to go one step further, generalizing Poincaré as the group governing high-energy kinematics. In other words, ordinary special relativity is here replaced by de Sitter relativity. In this theory, the cosmological constant Λ is no longer a free parameter, and can be determined in terms of other quantities. When applied to the whole universe, it is able to predict the value of Λ and to explain the cosmic coincidence. When applied to the propagation of ultra-high energy photons, it gives a good estimate of the time delay observed in extragalactic gamma-ray flares. It can, for this reason, be considered a new paradigm to approach the quantum gravity problem.

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References

  1. Padmanabhan, T.: Class. Quantum Gravity 4, L107 (1987)

    Article  ADS  Google Scholar 

  2. Amelino-Camelia, G.: Lect. Not. Phys. 541, 1 (2000). gr-qc/9910089

    Article  ADS  MathSciNet  Google Scholar 

  3. Protheroe, R.J., Meyer, H.: Phys. Lett. B 493, 1 (2000)

    Article  ADS  Google Scholar 

  4. Ahluwalia, D.V.: Mod. Phys. Lett. A 17, 1135 (2002). gr-qc/0205121

    Article  ADS  MathSciNet  Google Scholar 

  5. Jacobson, T., Liberati, S., Mattingly, D.: Phys. Rev. D 66, 081302 (2002). hep-ph/0112207

    Article  ADS  Google Scholar 

  6. Brandenberger, R.H., Martin, J.: Int. J. Mod. Phys. A 17, 3663 (2002). hep-th/0202142

    Article  MATH  ADS  Google Scholar 

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

    Article  ADS  MathSciNet  Google Scholar 

  8. Albert, J., et al. (for the MAGIC Collaboration), Ellis, J., Mavromatos, N.E., Nanopoulos, D.V., Sakharov, A.S., Sarkisyan, E.K.G.: Probing quantum gravity using photons from a Mkn 501 flare observed by MAGIC. astro-ph/0708.2889

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

    Article  ADS  Google Scholar 

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

    Article  MATH  ADS  MathSciNet  Google Scholar 

  11. Kowalski-Glikman, J.: Lect. Notes Phys. 669, 131 (2005). hep-th/0405273

    Article  ADS  Google Scholar 

  12. Kowalski-Glikman, J.: In: Oriti, D. (ed.) Approaches to Quantum Gravity—Toward a New Understanding of Space, Time, and Matter. Cambridge University Press, Cambridge (2006). gr-qc/0603022

    Google Scholar 

  13. Das, A., Kong, O.W.C.: Phys. Rev. D 73, 124029 (2006). gr-qc/0603114

    Article  ADS  Google Scholar 

  14. Aldrovandi, R., Beltrán Almeida, J.P., Pereira, J.G.: Class. Quantum Gravity 24, 1385 (2007). gr-qc/0606122

    Article  MATH  ADS  Google Scholar 

  15. Guo, H.Y., Huang, C.G., Xu, Z., Zhuo, B.: Phys. Lett. A 331, 1 (2004). hep-th/0403171

    Article  MATH  ADS  MathSciNet  Google Scholar 

  16. Inönü, E., Wigner, E.P.: Proc. Natl. Acad. Sci. 39, 510 (1953)

    Article  MATH  ADS  Google Scholar 

  17. Inönü, E.: In: Gürsey, F. (ed.) Group theoretical concepts and methods in elementary particle physics, Istanbul Summer School of Theoretical Physics. Gordon and Breach, New York (1962)

    Google Scholar 

  18. Gilmore, R.: Lie Groups, Lie Algebras, and Some of Their Applications. Wiley, New York (1974)

    MATH  Google Scholar 

  19. Gürsey, F.: In: Gürsey, F. (ed.) Group theoretical concepts and methods in elementary particle physics, Istanbul Summer School of Theoretical Physics. Gordon and Breach, New York (1962)

    Google Scholar 

  20. Bacry, H., Lévy-Leblond, J.M.: J. Math. Phys. 9, 1605 (1968)

    Article  MATH  ADS  Google Scholar 

  21. Duval, C., Burdet, G., Künsle, H.P.K., Perrin, M.: Phys. Rev. D 31, 1841 (1985)

    Article  ADS  MathSciNet  Google Scholar 

  22. Aldrovandi, R., Barbosa, A.L., Crispino, L.C.B., Pereira, J.G.: Class. Quantum Gravity 16, 495 (1999)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  23. Aldrovandi, R., Beltrán Almeida, J.P., Mayor, C.S.O., Pereira, J.G.: Lorentz transformations in de Sitter relativity. gr-qc/0709.3947

  24. Girelli, F., Livine, E.R.: J. Phys. Conf. Ser. 67, 012030 (2007). gr-qc/0612111

    Article  ADS  Google Scholar 

  25. Mansouri, F.: Phys. Lett. B 538, 239 (2002). hep-th/0203150

    Article  MATH  ADS  Google Scholar 

  26. Aldrovandi, R., Beltrán Almeida, J.P., Pereira, J.G.: J. Geom. Phys. 56, 1042 (2006). gr-qc/0403099

    Article  MATH  ADS  MathSciNet  Google Scholar 

  27. Narlikar, J.V.: An Introduction to Cosmology, 3rd edn. Cambridge University Press, Cambridge (2002)

    Google Scholar 

  28. Aldrovandi, R., Beltrán Almeida, J.P., Mayor, C.S.O., Pereira, J.G.: In: Adenier, G., Khrennikov, A., Lahti, P., Man’ko, V.I., Nieuwenhuizen, T. (eds.) Quantum Theory: Reconsideration of Foundations 4. AIP Conference Proceedings, vol. 962, p. 175 (2007). gr-qc/0710.0610

  29. Weinberg, S.: Gravitation and Cosmology. Wiley, New York (1972), p. 371

    Google Scholar 

  30. Coleman, S.: Aspects of Symmetry. Cambridge University Press, Cambridge (1985)

    MATH  Google Scholar 

  31. Ciufolini, I., Wheeler, J.A.: Gravitation and Inertia. Princeton University Press, Princeton (1995), p. 28

    MATH  Google Scholar 

  32. Riess, A.G., et al.: Astrophys. J. 116, 1009 (1998)

    Google Scholar 

  33. Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)

    Article  ADS  Google Scholar 

  34. de Bernardis, P., et al.: Nature 404, 955 (2000)

    Article  ADS  Google Scholar 

  35. Hanany, S., et al.: Astrophys. J. Lett. 545, 5 (2000)

    Article  ADS  Google Scholar 

  36. Carroll, S.M.: Living Rev. Relativ. 4, 1 (2001). astro-ph/0004075

    ADS  Google Scholar 

  37. Pathria, R.K.: Statistical Mechanics, 2nd edn. Butterworth-Heinemann, Oxford (1996)

    MATH  Google Scholar 

  38. Møller, C.: The Theory of Relativity, 2nd edn. Clarendon, Oxford (1966)

    Google Scholar 

  39. Guillemin, V., Sternberg, S.: Geometric Asymptotics. AMS, Providence (1977)

    MATH  Google Scholar 

  40. Hawking, S.W., Ellis, G.F.R.: The Large Scale Structure of Space-Time. Cambridge University Press, Cambridge (1973)

    MATH  Google Scholar 

  41. Aldrovandi, R., Pereira, J.G.: An Introduction to Geometrical Physics. World Scientific, Singapore (1995)

    MATH  Google Scholar 

  42. Faraoni, V., Cooperstock, F.I.: Eur. J. Phys. 19, 419 (1998). physics/9807056

    Article  MATH  Google Scholar 

  43. McLenaghan, R.G.: Ann. Inst. H. Poincaré 20, 153 (1974)

    MATH  MathSciNet  Google Scholar 

  44. Sonego, S., Faraoni, V.: J. Math. Phys. 33, 625 (1991)

    Article  ADS  MathSciNet  Google Scholar 

  45. Noonan, T.W.: Class. Quantum Gravity 12, 1087 (1995)

    Article  MATH  ADS  MathSciNet  Google Scholar 

  46. Espósito Miguel, W.R., Pereira, J.G.: Int. J. Mod. Phys. D 10, 41 (2001). gr-qc/0006098

    Article  MATH  Google Scholar 

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  1. Instituto de Física Teórica, Universidade Estadual Paulista, Rua Pamplona 145, 01405-900, São Paulo, Brazil

    R. Aldrovandi & J. G. Pereira

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  1. R. Aldrovandi
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  2. J. G. Pereira
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Correspondence to J. G. Pereira.

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Aldrovandi, R., Pereira, J.G. De Sitter Relativity: a New Road to Quantum Gravity?. Found Phys 39, 1–19 (2009). https://doi.org/10.1007/s10701-008-9258-5

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