International Journal of Theoretical Physics

, Volume 57, Issue 9, pp 2881–2891 | Cite as

Interacting Induced Dark Energy Model

  • Amir F. BahrehbakhshEmail author


Following the idea of the induced matter theory, for a non–vacuum five–dimensional version of general relativity, we propose a model in which the induced terms emerging from the extra dimension in our four–dimensional space–time, supposed to be as dark energy. Then we investigate the FLRW type cosmological equations and illustrate that when the scale factor of the fifth dimension has no dynamics, in early time the universe expands with deceleration and then in late time, expands with acceleration. In this case, the state parameter of the effective dark energy has a range of \(-1<\bar {w}_{X}<0\) and it has the value − 1/2 for present time. The results for current acceleration impose that ΩX > 2ΩM which is in agreement with the measurements. We show that the effective energy density of dark energy have been having the same order of magnitude of the effective energy density of matter from the early time in the decelerating epoch of the universe expansion until now. The model avoids the cosmological coincidence problem.


Extra dimensions Induced–matter theory FLRW cosmology Dark energy Cosmological coincidence problem 



I would like to thank Department of Physics and Astronomy, University of California, Irvine, for the visit opportunity and their accommodations. Also, especial thanks to Tim Tait and Arvind Rajaraman for reading this article and useful comments.


  1. 1.
    Perlmutter, S., et al., [Supernova Cosmology Project Collaboration]: Discovery of a supernova explosion at half the age of the Universe and its cosmological implications. Nature 391, 51 (1998). [astro-ph/9712212]
  2. 2.
    Riess, A.G., et al., [Supernova Search Team]: Observational evidence from supernovae for an accelerating universe and a cosmological constant. Astron. J. 116, 1009 (1998). [astro-ph/9805201]
  3. 3.
    Perlmutter, S., et al., [Supernova Cosmology Project Collaboration]: Measurements of Omega and Lambda from 42 high redshift supernovae. Astrophys. J. 517, 565 (1999). [astro-ph/9812133]
  4. 4.
    de Bernardis, P., et al.: Multiple peaks in the angular power spectrum of the cosmic microwave background: Significance and consequences for cosmology. Astrophys. J. 564, 559 (2002). [astro-ph/0105296]ADSCrossRefGoogle Scholar
  5. 5.
    Carroll, S.M.: Why is the universe accelerating?, eConf C 0307282, TTH09 (2003) [AIP Conf. Proc. 743, 16 (2005)]. [astro-ph/0310342]
  6. 6.
    Sahni, V.: Dark matter and dark energy. Lect. Notes Phys. 653, 141 (2004). [astro-ph/0403324]ADSCrossRefzbMATHGoogle Scholar
  7. 7.
    Kamionkowski, M.: Dark Matter and Dark Energy. arXiv:0706.2986 [astro-ph]
  8. 8.
    Zlatev, I., Wang, L.M., Steinhardt, P.J.: Quintessence, cosmic coincidence, and the cosmological constant. Phys. Rev. Lett. 82, 896 (1999). [astro-ph/9807002]ADSCrossRefGoogle Scholar
  9. 9.
    Albrecht, A., Skordis, C.: Phenomenology of a realistic accelerating universe using only Planck scale physics. Phys. Rev. Lett. 84, 2076 (2000). [astro-ph/9908085]ADSCrossRefGoogle Scholar
  10. 10.
    Bento, M.C., Bertolami, O., Santos, N.M.C.: A Two field quintessence model. Phys. Rev. D 65, 067301 (2002). [astro-ph/0106405]ADSCrossRefGoogle Scholar
  11. 11.
    Blais, D., Polarski, D.: Transient accelerated expansion and double quintessence. Phys. Rev. D 70, 084008 (2004). [astro-ph/0404043]ADSCrossRefGoogle Scholar
  12. 12.
    Armendariz-Picon, C., Mukhanov, V.F., Steinhardt, P.J.: Essentials of k essence. Phys. Rev. D 63, 103510 (2001). [astro-ph/0006373]ADSCrossRefGoogle Scholar
  13. 13.
    Armendariz-Picon, C., Mukhanov, V.F., Steinhardt, P.J.: A Dynamical solution to the problem of a small cosmological constant and late time cosmic acceleration. Phys. Rev. Lett. 85, 4438 (2000). [astro-ph/0004134]ADSCrossRefGoogle Scholar
  14. 14.
    Kamenshchik, A.Y., Moschella, U., Pasquier, V.: An Alternative to quintessence. Phys. Lett. B 511, 265 (2001). [gr-qc/0103004]ADSCrossRefzbMATHGoogle Scholar
  15. 15.
    Scherrer, R.J.: Purely kinetic k-essence as unified dark matter. Phys. Rev. Lett. 93, 011301 (2004). [astro-ph/0402316]ADSCrossRefGoogle Scholar
  16. 16.
    Bento, M.C., Bertolami, O., Sen, A.A.: Generalized Chaplygin gas, accelerated expansion and dark energy matter unification. Phys. Rev. D 66, 043507 (2002). [gr-qc/0202064]ADSCrossRefGoogle Scholar
  17. 17.
    Nojiri, S., Odintsov, S.D.: Introduction to modified gravity and gravitational alternative for dark energy, eConf C 0602061, 06 (2006) [Int. J. Geom. Meth. Mod. Phys. 4, 115 (2007)]. [hep-th/0601213]
  18. 18.
    Schmidt, H.J.: Fourth order gravity: Equations, history, and applications to cosmology, eConf C 0602061, 12 (2006) [Int. J. Geom. Meth. Mod. Phys. 4, 209 (2007)]. [gr-qc/0602017]
  19. 19.
    Li, B., Sotiriou, T.P., Barrow, J.D.: f(T) gravity and local Lorentz invariance. Phys. Rev. D 83, 064035 (2011)., arXiv:1010.1041 [gr-qc]ADSCrossRefGoogle Scholar
  20. 20.
    Myrzakulov, R.: Accelerating universe from F(T) gravity. Eur. Phys. J. C 71, 1752 (2011)., arXiv:1006.1120 [gr-qc]ADSCrossRefGoogle Scholar
  21. 21.
    Harko, T., Lobo, F.S.N., Nojiri, S., Odintsov, S.D.: f(R,T) gravity. Phys. Rev. D 84, 024020 (2011). arXiv:1104.2669 [gr-qc]ADSCrossRefGoogle Scholar
  22. 22.
    Jordan, P.: Projective relativity, friedr. View. Sohn braunschweig (1955)Google Scholar
  23. 23.
    Brans, C., Dicke, R.H.: Mach’s principle and a relativistic theory of gravitation. Phys. Rev. 124, 925 (1961)ADSMathSciNetCrossRefzbMATHGoogle Scholar
  24. 24.
    Dicke, R.H.: Mach’s principle and a relativistic theory of gravitation. ii. Phys Rev. 125, 2194 (1962)MathSciNetCrossRefzbMATHGoogle Scholar
  25. 25.
    Bertotti, B., Iess, L., Tortora, P.: A test of general relativity using radio links with the Cassini spacecraft. Nature 425, 374 (2003). ADSCrossRefGoogle Scholar
  26. 26.
    Fujii, Y., Maeda, K.: The Scalar–Tensor Theory of Gravitation. Cambridge University Press, Cambridge (2004). CrossRefzbMATHGoogle Scholar
  27. 27.
    Kaluza, T.: On the problem of unity in physics. Sitz. Preuss. Akad. Wiss. 33, 966 (1921)Google Scholar
  28. 28.
    Klein, O.: Quantum theory and five-dimensional theory of relativity. Z Phys. 37, 895 (1926). ADSCrossRefGoogle Scholar
  29. 29.
    Overduin, J.M., Wesson, P.S.: Kaluza-Klein gravity. Phys. Rept. 283, 303 (1997). [gr-qc/9805018]ADSMathSciNetCrossRefGoogle Scholar
  30. 30.
    Wesson, P.S.: Space–Time–Matter, Modern Kaluza–Klein Theory. World Scientific, Singapore (1999). zbMATHGoogle Scholar
  31. 31.
    Wesson, P.S.: Five–Dimensional Physics. World Scientific, Singapore (2006). CrossRefzbMATHGoogle Scholar
  32. 32.
    Wesson, P.S.: The status of modern five-dimensional gravity (A short review: Why physics needs the fifth dimension). Int. J. Mod. Phys. D 24(01), 1530001 (2014)., arXiv:1412.6136 [gr-qc]ADSCrossRefzbMATHGoogle Scholar
  33. 33.
    Bahrehbakhsh, A.F.: FLRW cosmology of induced dark energy model and open universe. Can. J. Phys. 95, 1215 (2017)., arXiv:1705.06506 [gr-qc]ADSCrossRefGoogle Scholar
  34. 34.
    Randall, L., Sundrum, R.: A Large mass hierarchy from a small extra dimension. Phys. Rev. Lett. 83, 3370 (1999). [hep-ph/9905221]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  35. 35.
    Ghoroku, K., Tachibana, M., Uekusa, N.: Phys. Rev. D 68, 125002 (2003). [hep-th/0304051]ADSMathSciNetCrossRefGoogle Scholar
  36. 36.
    Brevik, I.H., Hallanger, A.: Randall-Sundrum model in the presence of a brane bulk viscosity. Phys. Rev. D 69, 024009 (2004). [gr-qc/0308058]ADSMathSciNetCrossRefGoogle Scholar
  37. 37.
    Maia, M.D., Monte, E.M., Maia, J.M.F.: The Accelerating universe in brane world cosmology. Phys. Lett. B 585, 11 (2004). [astro-ph/0208223]ADSCrossRefzbMATHGoogle Scholar
  38. 38.
    Maartens, R., Koyama, K.: Brane-World Gravity. Living Rev. Rel. 13, 5 (2010)., arXiv:1004.3962 [hep-th]CrossRefzbMATHGoogle Scholar
  39. 39.
    Khosravi, N.: Über-Gravity and the Cosmological Constant Problem. arXiv:1703.02052 [gr-qc]
  40. 40.
    de Leon, J.P.: Late time cosmic acceleration from vacuum Brans-Dicke theory in 5D. Class. Quant. Grav. 27, 095002 (2010)., arXiv:0912.1026 [gr-qc]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  41. 41.
    Ponce de Leon, J.: Brans-Dicke Cosmology in 4D from scalar-vacuum in 5D JCAP 1003, 030., arXiv:1001.1961 [gr-qc] (2010)
  42. 42.
    Bahrehbakhsh, A.F., Farhoudi, M., Shojaie, H.: FRW cosmology from five dimensional vacuum Brans-Dicke theory. Gen. Rel. Grav. 43, 847 (2011)., arXiv:1005.2501 [gr-qc]ADSMathSciNetCrossRefzbMATHGoogle Scholar
  43. 43.
    Bahrehbakhsh, A.F., Farhoudi, M., Vakili, H.: Dark energy from fifth dimensional Brans-Dicke theory. Int. J. Mod. Phys. D 22, 1350070 (2013)., arXiv:1306.1943 [gr-qc]ADSCrossRefzbMATHGoogle Scholar
  44. 44.
    Clifton, T., Ferreira, P.G., Padilla, A., Skordis, C.: Modified gravity and cosmology. Phys. Rept. 513, 1 (2012)., arXiv:1106.2476 [astro-ph.CO]ADSMathSciNetCrossRefGoogle Scholar
  45. 45.
    Yoo, J., Watanabe, Y.: Theoretical models of dark energy. Int. J. Mod. Phys. D 21, 1230002 (2012). arXiv:1212.4726 [astro-ph.CO]ADSCrossRefzbMATHGoogle Scholar
  46. 46.
    Pavsic, M.: The Landscape of theoretical physics: A Global view. From point particles to the brane world and beyond, in search of a unifying principle, Fundam. Theor. Phys. 119 [gr-qc/0610061] (2001)Google Scholar
  47. 47.
    Bahcall, N.A., Ostriker, J.P., Perlmutter, S., Steinhardt, P.J.: The Cosmic triangle: Assessing the state of the universe. Science 284, 1481 (1999). [astro-ph/9906463]ADSCrossRefGoogle Scholar
  48. 48.
    de Bernardis, P., et al., [Boomerang Collaboration]: A Flat universe from high resolution maps of the cosmic microwave background radiation. Nature 404, 955 (2000). [astro-ph/0004404]
  49. 49.
    Hanany, S., et al.: MAXIMA-1: A Measurement of the cosmic microwave background anisotropy on angular scales of 10 arcminutes to 5 degrees. Astrophys. J. 545, L5 (2000). [astro-ph/0005123]ADSCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2018

Authors and Affiliations

  1. 1.Department of Physics, Faculty of SciencePayam-e-Noor UniversityTehranIran
  2. 2.Department of Physics and AstronomyUniversity of CaliforniaIrvineUSA

Personalised recommendations