Brane world solutions of perfect fluid in the background of a bulk containing dust or a cosmological constant

Tanwi Bandyopadhyay1, Subenoy Chakraborty2 and Asit Banerjee3


The paper presents some solutions to the five-dimensional Einstein equations with a perfect fluid on the brane, with pure dust filling the entire bulk in one case and a cosmological constant (or vacuum) in the bulk for another case. In the first case, there is a linear relationship between isotropic pressure, energy density and the brane tension, while in the second case the perfect fluid is assumed to be in the form of a Chaplygin gas. Cosmological solutions are found both for the brane and the bulk scenarios, and some interesting features are obtained for the Chaplygin gas on the brane which are distinctly different from standard cosmology in four dimensions.


  1. L. Randall and R. Sundrum, Phys. Rev. Lett. 83 3370 (1999); Phys. Rev. Lett. 83 4690 (1999).
  2. T. Shiromizu, K. Maeda, and M. Sasaki, Phys. Rev. D 62 024012 (2000).
  3. P. Binetruy, C. Deffayet, U. Ellwanger, and D. Langlois, Phys. Lett. B 477 285 (2000); Nucl. Phys. B 565 269 (2000).
  4. J. Ponce de Leon, Mod. Phys. Lett. A 17, 2425 (2002); Mod. Phys. Lett.A 16, 2291 (2001).
  5. R. Maartens (private communication); A. Mazumdar, R. N. Mohapatra, and A. Perez-Lorenzana, JCAP 0406, 004 (2004); C. Bogdanos C and K. Tamvakis, hep-th/0609100.
  6. V. Gorini, A. Kamenshchik, and U. Moschella U, Phys. Rev. D 67 063509 (2003); V. Gorini, A. Kamenshchik, U. Moschella, and V. Pasquier V, in: Recent Developments in Theoretical and Experimental General Relativity, Gravitation, and Relativistic Field Theories (Rio de Janeiro, 2003), p. 840-859; gr-qc/0403062.
  7. S.J. Perlmutter et al., Astroph. J. 517 565 (1999).
  8. P. J. E. Peebles and B. Ratra, Rev. Mod. Phys. 75, 559 (2003); T. Padmanabhan, Phys. Rep. 380, 235 (2003); A. Krause and Siew-Phang Ng, Int. J. Mod. Phys. A 21, 1091 (2006) and references therein.
  9. J. Ponce de Leon, gr-qc/0511150.
  10. J. Ponce de Leon, Gen. Rel. Grav. 37 53 (2005).
  11. J. Ponce de Leon, Class. Quant. Grav. 20 5321 (2003).
  12. M. K. Mak and T. Harko, Phys. Rev. D 71 104022 (2005).
  13. E. Papantonopoulos, hep-th/0202044.
  14. P. Brax and C. Van de Bruck, Class. Quant. Grav. 20 R201 (2003).
  15. Mukherjee et al., Class. Quant. Grav. 23 6927 (2006).
  16. U. Debnath, A. Banerjee, and S. Chakraborty, Class. Quant. Grav. 21 5609 (2004).
  17. M. C. Bento, O. Bertolami, and A. A. Sen, Phys. Rev. D 66 043507 (2002).
For more information about this paper please visit Springer's Home Page of this paper.

Back to The Contents Page