An explanation for the tiny value of the cosmological constant and the low vacuum energy density


The paper aims to provide an explanation for the tiny value of the cosmological constant and the low vacuum energy density to represent the dark energy. To accomplish this, we will search for a fundamental principle of symmetry in space-time by means of the elimination of the classical idea of rest, by including an invariant minimum limit of speed in the subatomic world. Such a minimum speed, unattainable by particles, represents a preferred reference frame associated with a background field that breaks down the Lorentz symmetry. The metric of the flat space-time shall include the presence of a uniform vacuum energy density, which leads to a negative pressure at cosmological length scales. Thus, the equation of state for the cosmological constant [p(pressure)\(=-\epsilon \) (energy density)] naturally emerges from such a space-time with an energy barrier of a minimum speed. The tiny values of the cosmological constant and the vacuum energy density will be successfully obtained, being in agreement with the observational results of Perlmutter, Schmidt and Riess.

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  1. 1.

    Bluhm, R.: arXiv:hep-ph/0506054

  2. 2.

    Carroll, S.M., Field, G.B., Jackiw, R.: Phys. Rev. D 41, 1231 (1990)

    Article  ADS  Google Scholar 

  3. 3.

    Sciama, D.W.: On the origin of inertia. Mon. Not. R. Astron. Soc. 113, 34–42 (1953)

    MathSciNet  Article  ADS  MATH  Google Scholar 

  4. 4.

    Schrödinger, E.: Die erfullbarkeit der relativitätsforderung in der klassischem mechanik. Ann. Phys. 77, 325–336 (1925)

    Article  MATH  Google Scholar 

  5. 5.

    Mach, E.: The Science of Mechanics—a Critical and Historical Account of its Development. Open Court, La Salle (1960)

    Google Scholar 

  6. 6.

    Einstein, A.: Äether und Relativitäts-theory. Springer, Berlin (1920)

    Book  Google Scholar 

  7. 7.

    Eling, C., Jacobson, T., Mattingly, D.: arXiv:gr-qc/0410001

  8. 8.

    Licata, I.: Hadronic J. 14, 225–250 (1991)

    MathSciNet  MATH  Google Scholar 

  9. 9.

    Camelia, G.A.: Int. J. Mod. Phys. D 11(1), 35–59 (2002)

    Article  ADS  MATH  Google Scholar 

  10. 10.

    Camelia, G.A., et al.: Nature 393(6687), 763–765 (1998)

    Article  ADS  Google Scholar 

  11. 11.

    Camelia, G.A.: Nature 418(6893), 34–35 (2002)

    Article  ADS  Google Scholar 

  12. 12.

    Camelia, G.A.: Int. J. Mod. Phys. D 11(10), 1643–1669 (2002)

    Article  ADS  MATH  Google Scholar 

  13. 13.

    Magueijo, J., Smolin, L.: Phys. Rev. Lett. 88, 190403 (2002)

    Article  ADS  Google Scholar 

  14. 14.

    Magueijo, J., Albrecht, A.: Phys. Rev. D 59, 043516 (1999)

    Article  ADS  Google Scholar 

  15. 15.

    Magueijo, J., Smolin, L.: Phys. Rev. D 67, 044017 (2003)

    MathSciNet  Article  ADS  Google Scholar 

  16. 16.

    Glikman, J.K., Smolin, L.: Phys. Rev. D 70, 065020 (2004)

    MathSciNet  Article  ADS  Google Scholar 

  17. 17.

    Girelli, F., Livine, E.R.: Phys. Rev. D 69, 104024 (2004)

    Article  ADS  Google Scholar 

  18. 18.

    Gazeau, J. P., Novello, M.: arXiv:gr-qc/0610054

  19. 19.

    Adler, C.J.: Am. J. Phys. 55, 739 (1987)

    Article  ADS  Google Scholar 

  20. 20.

    Feynman, R.P., Leighton, R.B., Sands, M.: Th Feynman Lectures on Physics, 1st edn. Addison-Wesley, Reading (1963). (sections 15-8 and 16-4)

    Google Scholar 

  21. 21.

    Okun, L.V.: Phys. Today 42(6), 31 (1989)

    Article  Google Scholar 

  22. 22.

    Sandin, T.R.: Am. J. Phys. 59, 1032 (1991)

    Article  ADS  Google Scholar 

  23. 23.

    Rindler, W.: Introduction to Special Relativity, pp. 79–80. Clarendon Press, Oxford (1982)

    MATH  Google Scholar 

  24. 24.

    Rindler, W.: Essential Relativity, 2nd edn. Springer, New York (1977). (Section 5.3)

    Book  MATH  Google Scholar 

  25. 25.

    Taylor, E.F., Wheeler, J.A., et al.: Spacetime Physics, 2nd edn, pp. 246–251. W. H. Freeman Co., New York (1992)

    Google Scholar 

  26. 26.

    Binétruy, P., Silk, J.: Phys. Rev. Lett. 87, 031102 (2001)

    Article  ADS  Google Scholar 

  27. 27.

    Carmeli, M., Kuzmenko, T.: arXiv:astro-ph/0102033

  28. 28.

    Schmidt, B.P., et al.: Astrophys. J. 507, 46 (1998)

    Article  ADS  Google Scholar 

  29. 29.

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

    Article  ADS  Google Scholar 

  30. 30.

    Garnavich, P.M., et al.: Astrophys. J. 509, 74 (1998)

    Article  ADS  Google Scholar 

  31. 31.

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

    Article  ADS  Google Scholar 

  32. 32.

    Turner, M.S., Krauss, L.M.: Gen. Relativ. Gravit 27, 1137 (1995). arXiv:astro-ph/9504003

    Article  ADS  MATH  Google Scholar 

  33. 33.

    Wang, Y., Tegmark, M.: Phys. Rev. Lett. 92, 241302 (2004)

    Article  ADS  Google Scholar 

  34. 34.

    Carroll, S. M.: arXiv:astro-ph/0107571

  35. 35.

    Zel’dovich, Ya B.: JETP Lett. 6, 316 (1967)

    ADS  Google Scholar 

  36. 36.

    Weinberg, S.: The cosmological constant problem. Rev. Mod. Phys. 61, 1 (1989)

    MathSciNet  Article  ADS  MATH  Google Scholar 

  37. 37.

    Padmanabhan, T.: Phys. Rept. 380, 235 (2003)

    MathSciNet  Article  ADS  MATH  Google Scholar 

  38. 38.

    Cartan, E.: Les Espaces de Finsler. Actualitès Scientifiques et Industrielles, vol. 79. Hermann, Paris (1934)

    Google Scholar 

  39. 39.

    Goenner, H. F. M.: On the history of geometrization of space-time. arXiv:gr-qc/0811.4529 (2008)

  40. 40.

    Peyghan, E., Tayebi, A., Ahmadi, A.: J. Mathe. Anal. Appl. 391(1), 159–169 (2012)

    MathSciNet  Article  MATH  Google Scholar 

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I am specially grateful to Prof. Jonas Durval Cremasco and Juliano S. Gonschorowski for interesting discussions. I thank Carlos Magno Leiras, Cássio Guilherme Reis, A. C. Amaro de Faria Jr., Alisson Xavier, Emílio C. M. Guerra, G. Vicentini and Paulo R. Souza Coelho for their comprehension of this work’s significance.

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Correspondence to Cláudio Nassif.

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Nassif, C. An explanation for the tiny value of the cosmological constant and the low vacuum energy density. Gen Relativ Gravit 47, 107 (2015).

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  • Cosmological constant
  • Vacuum energy density
  • Background field
  • Minimum speed