Astrophysics and Space Science

, Volume 355, Issue 1, pp 179–185 | Cite as

Brane viscous cosmology in the plasma era

  • Iver Brevik
Original Article


We consider how the five-dimensional Randall-Sundrum (one-brane) theory becomes modified when account is taken of the bulk viscosity of the cosmic fluid on the brane. We focus on the plasma era between 1012 K (muon pair annihilation) to about 5×109 K (electron-positron annihilation), which includes the first order quark-hadron transition beginning at an energy density of about 5×109 MeV4. Various possibilities are examined for modeling the bulk viscosity, preference being at the end given to the results calculated from relativistic kinetic theory. According to this, the viscosity is negligible at the highest temperatures, but may amount to a few per cent corrections in the later stages of the plasma era. We also briefly consider anisotropic universes where the shear viscosity comes into play, and show that in the case of the Kasner model the influences from bulk viscosity and shear viscosity become comparable when the anisotropy parameter of the universe is of order A∼10−11 in the beginning of the plasma era, and A∼10−2 in its later region.


Viscous cosmology Bulk viscosity Plasma era 



I thank Kazuo Ghoroku for valuable discussions and correspondence on this topic. Also, I thank Lars Husdal for making me aware of the paper by Hogeveen et al. (1986).


  1. Alishahiha, M., Karch, A., Silverstein, E.: J. High Energy Phys. 0506, 028 (2005a) ADSCrossRefGoogle Scholar
  2. Alishahiha, M., Karch, A., Silverstein, E., Tong, D.: AIP Conf. Proc. 743, 393 (2005b) ADSCrossRefGoogle Scholar
  3. Babington, J., Erdmenger, J., Evans, N., Guralnik, Z., Kirsch, I.: (2003). arXiv:hep-th/0306018
  4. Brevik, I.: Eur. Phys. J. C 56, 579 (2008) ADSCrossRefGoogle Scholar
  5. Brevik, I., Ghoroku, K.: Phys. Rev. D 16, 1249 (2007) Google Scholar
  6. Brevik, I., Grøn, Ø.: Relativistic universe models. In: Recent Advances in Cosmology, p. 97. Nova Scientific Publishers, New York (2013) Google Scholar
  7. Brevik, I., Hallanger, A.: Phys. Rev. D 69, 624009 (2004) ADSGoogle Scholar
  8. Brevik, I., Ghoroku, K., Odintsov, S.D., Yahiro, M.: Phys. Rev. D 66, 064016 (2002) ADSMathSciNetCrossRefGoogle Scholar
  9. Brevik, I., Nojiri, S., Odintsov, S.D., Vanzo, L.: Phys. Rev. D 70, 043520 (2004) ADSMathSciNetCrossRefGoogle Scholar
  10. Brevik, I., Børven, J.-M., Ng, S.: Gen. Relativ. Gravit. 38, 907 (2006) ADSCrossRefGoogle Scholar
  11. Casero, R., Nunez, C., Paredes, A.: Phys. Rev. D 73, 086005 (2006) ADSMathSciNetCrossRefGoogle Scholar
  12. De Risi, G., Harko, T., Lobo, F.S.N., Pun, C.S.J.: Nucl. Phys. B 805, 190 (2008) ADSCrossRefGoogle Scholar
  13. Erdmenger, J., Ghoroku, K., Meyer, R.: Phys. Rev. D 84, 026004 (2011) ADSCrossRefGoogle Scholar
  14. Erdmenger, J., Ghoroku, K., Meyer, R., Papadimitriou, I.: Fortschr. Phys. 60, 991 (2014) (special issue). arXiv:1205.0677 CrossRefGoogle Scholar
  15. Evans, N., Shock, J.P.: (2004). arXiv:hep-th/0403279
  16. Ghoroku, K., Yahiro, M.: Phys. Lett. B 604, 235 (2004) ADSMathSciNetCrossRefGoogle Scholar
  17. Ghoroku, K., Ishihara, M., Nakamura, A.: Phys. Rev. D 74, 124020 (2006) ADSMathSciNetCrossRefGoogle Scholar
  18. Ghoroku, K., Ishihara, M., Nakamura, A.: Phys. Rev. D 75, 046005 (2007) ADSCrossRefGoogle Scholar
  19. Grøn, Ø.: Astrophys. Space Sci. 173, 191 (1990) ADSMathSciNetCrossRefGoogle Scholar
  20. Gubser, S.S., Klebanov, I.R., Polyakov, A.M.: Phys. Lett. B 428, 105 (1998) ADSMathSciNetCrossRefGoogle Scholar
  21. Hawking, S.W., Maldacena, J.M., Strominger, A.: J. High Energy Phys. 0105, 001 (2001) ADSCrossRefGoogle Scholar
  22. Hirayama, T.: J. High Energy Phys. 0606, 013 (2006) ADSCrossRefGoogle Scholar
  23. Hogeveen, F., van Leeuwen, W.A., Salvati, G.A.Q., Schelling, E.E.: Physica (Amsterdam) 134A, 458 (1986) ADSCrossRefGoogle Scholar
  24. Hosoya, A., Sakagami, M., Takao, M.: Ann. Phys. (N.Y.) 154, 229 (1984) ADSCrossRefGoogle Scholar
  25. Karch, A., Katz, E.: J. High Energy Phys. 0206, 043 (2003) ADSGoogle Scholar
  26. Kovtun, P.: J. Phys. A, Math. Theor. 45, 473001 (2012) ADSMathSciNetCrossRefGoogle Scholar
  27. Kovtun, P., Son, D.T., Starinets, A.O.: J. High Energy Phys. 10, 064 (2003) ADSCrossRefGoogle Scholar
  28. Kruczenski, M., Mateos, D., Myers, R.C., Winters, D.J.: J. High Energy Phys. 0307, 049 (2003a) ADSCrossRefGoogle Scholar
  29. Kruczenski, M., Mateos, D., Myers, R.C., Winters, D.J.: (2003b). arXiv:hep-th/0311270
  30. Maldacena, J.M.: Adv. Theor. Math. Phys. 2, 231 (1998) ADSMathSciNetCrossRefGoogle Scholar
  31. Murphy, G.L.: Phys. Rev. D 8, 4231 (1973) ADSCrossRefGoogle Scholar
  32. Nunez, C., Paredes, A., Ramallo, A.V.: J. High Energy Phys. 0312, 024 (2003) ADSCrossRefGoogle Scholar
  33. Plumari, S., Puglisi, A., Scardina, F., Greco, V.: Phys. Rev. C 86, 054902 (2012) ADSCrossRefGoogle Scholar
  34. Polyakov, A.M.: Int. J. Mod. Phys. A 14, 645 (1999) ADSCrossRefGoogle Scholar
  35. Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 4690 (1999) ADSMathSciNetCrossRefGoogle Scholar
  36. Sakai, S., Sonnenshein, J.: (2003). arXiv:hep-th/0305049
  37. Thomas, L.H.: Q. J. Math. (Oxford) 1, 239 (1930) ADSCrossRefGoogle Scholar
  38. Tripathy, S.K.: Astrophys. Space Sci. 350, 367 (2014). arXiv:1407.7791 ADSCrossRefGoogle Scholar
  39. Weinberg, S.: Astrophys. J. 168, 175 (1971) ADSCrossRefGoogle Scholar
  40. Witten, E.: Adv. Theor. Math. Phys. 2, 253 (1998) ADSMathSciNetCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media Dordrecht 2014

Authors and Affiliations

  1. 1.Department of Energy and Process EngineeringNorwegian University of Science and TechnologyTrondheimNorway

Personalised recommendations