Abstract
In this work we explore the background dynamics when dark energy is coupled to dark matter with a suitable interaction in the universe described by brane cosmology. Here DGP and the RSII brane models have been considered separately. Dark energy in the form of Generalized Cosmic Chaplygin gas is considered. A suitable interaction between dark energy and dark matter is considered in order to at least alleviate (if not solve) the cosmic coincidence problem. The dynamical system of equations is solved numerically and a stable scaling solution is obtained. A significant attempt towards the solution of the cosmic coincidence problem is taken. The statefinder parameters are also calculated to classify the dark energy models. Graphs and phase diagrams are drawn to study the variations of these parameters. It is also seen that the background dynamics of Generalized Cosmic Chaplygin gas is consistent with the late cosmic acceleration, but not without satisfying certain conditions. It has been shown that the universe in both the models follows the power law form of expansion around the critical point, which is consistent with the known results. Future singularities were studied and our models were declared totally free from any types of such singularities. Finally, some cosmographic parameters were also briefly studied. Our investigation led to the fact that although Generalized cosmic Chaplygin gas with a far lesser negative pressure compared to other dark energy models, can overcome the relatively weaker gravity of RS II brane, with the help of the negative brane tension, yet for the DGP brane model with much higher gravitation, the incompetency of Generalized cosmic Chaplygin gas is exposed, and it cannot produce the accelerating scenario until it reaches the phantom era.
This is a preview of subscription content, log in via an institution to check access.
Similar content being viewed by others
Notes
In the presence of a scalar field the transition from a universe filled with matter to an exponentially expanding universe is justified.
References
Alam, U., Sahni, V., Saini, T.D., Starobinsky, A.A.: Mon. Not. R. Astron. Soc. 344, 1057 (2003)
Albert, J., et al. (SNAP Collaboration). arXiv:astro-ph/0507458 (2005a)
Albert, J., et al.: SNAP Collaboration. arXiv:astro-ph/0507459 (2005b)
Alcaniz, J.S., Lima, J.A.S.: Phys. Rev. D 72, 063516 (2005)
Arbab, A.I.: arXiv:astro-ph/9810239 (1998)
Astashenok, A.V., et al.: arXiv:1206.2192v1 [gr-qc] (2012)
Bamba, K., Matsumoto, J., Nojiri, S.: arXiv:1109.1308 [hep-th] (2012a)
Barreiro, T., Sen, A.A.: Phys. Rev. D 70, 124013 (2004)
Benaoum, H.B.: arXiv:hep-th/0205140 (2002)
Bento, M.C., Bertolami, O., Sen, A.A.: Phys. Rev. D 66, 043507 (2002)
Berger, M.S., Shojae, H.: Phys. Rev. D, Part. Fields 73, 083528 (2006). arXiv:gr-qc/0601086
Bouhmadi-Lopez, Lazkoz, R.: Phys. Lett. B 654, 51 (2007). arXiv:0706.3896 [astro-ph]
Brax, P., et al.: Rep. Prog. Phys. 67, 2183 (2004). arXiv:hep-th/0404011
Caldwell, R.R., Kamiokowsky, M., Weinberg, N.N.: Phys. Rev. Lett. 91, 071301 (2003)
Carturan, D., Finelli, F.: Phys. Rev. D 68, 103501 (2003)
Chakraborty, W., Debnath, U., Chakraborty, S.: Gravit. Cosmol. 13, 294 (2007). arXiv:0711.0079 [gr-qc]
Chakraborty, W., Debnath, U.: Gravit. Cosmol. 16, 223 (2010)
Chimento, L.P., Lazkoz, R., Maartens, R., Quiros, I.: J. Cosmol. Astropart. Phys. 0609, 004 (2006). arXiv:astro-ph/0605450
Chowdhury, R., Rudra, P.: arXiv:1204.3531 [gr-qc] (2012)
Csaki, C.: arXiv:hep-th/0404096 (2004)
Dalal, N., Abazajian, K., Jenkins, E., Manohar, A.V.: Phys. Rev. Lett. 87, 141302 (2001). arXiv:astro-ph/0105317v1
Debnath, U.: Astrophys. Space Sci. 312, 295299 (2007)
Debnath, U., Banerjee, A., Chakraborty, S.: Class. Quantum Gravity 21, 5609 (2004)
Deffayet, D.: Phys. Lett. B 502, 199 (2001)
Deffayet, D., Dvali, G.R., Gabadadze, G.: Phys. Rev. D, Part. Fields 65, 044023 (2002). arXiv:astro-ph/0105068
del Campo, S., Herrera, R., Pavon, D.: J. Cosmol. Astropart. Phys. 0901, 020 (2009). arXiv:0812.2210 [gr-qc]
Dvali, G.R., Gabadadze, G., Porrati, M.: Phys. Lett. B 485, 208 (2000) arXiv:hep-th/0005016
Feng, C., et al.: Phys. Lett. B 665, 111 (2008)
Gonzalez-Diaz, P.F.: Phys. Rev. D 68, 021303(R) (2003)
Gorini, V., Kamenshchik, A., Moschella, U. Pasquier: arXiv:gr-qc/0403062
Gorini, V., Kamenshchik, A., Moschella, U.: Phys. Rev. D 67, 063509 (2003)
Griest, K.: Phys. Rev. D66, 123501 (2002). arXiv:astro-ph/0202052
Guo, Z.-K., Zhang, Y.-Z.: Phys. Rev. D 71, 023501 (2005)
Hogg, D.W.: (2000). arXiv:astro-ph/9905116v4
Hu, B., Ling, Y.: Phys. Rev. D 73, 123510 (2006)
Jamil, M.: Int. J. Theor. Phys. 49, 62 (2010a)
Jamil, M.: Int. J. Theor. Phys. 49, 2829–2840 (2010b)
Jamil, M., Debnath, U.: Astrophys. Space Sci. 333, 3 (2011a)
Jamil, M., Debnath, U.: Int. J. Theor. Phys. 50, 1602 (2011b)
Jamil, M., Farooq, M.U.: J. Cosmol. Astropart. Phys. 03, 001 (2010)
Jamil, M., Rahaman, F.: Eur. Phys. J. C 64, 97 (2009)
Jamil, M., Saridakis, E.N.: J. Cosmol. Astropart. Phys. 07, 028 (2010)
Jamil, M., Saridakis, E.N., Setare, M.R.: Phys. Rev. D 81, 023007 (2010)
Jamil, M., Sheykhi, A., Farooq, M.U.: Int. J. Mod. Phys. D 19, 1831 (2010d)
Jamil, M., Momeni, D., Rashid, M.A.: Eur. Phys. J. C 71, 1711 (2011). arXiv:1107.1558v1 [physics.gen-ph]
Jamil, M., Raza, M., Debnath, U.: Astrophys. Space Sci. 337, 799–803 (2012)
Jimenez, J.B., Maroto, A.L.: AIP Conf. Proc. 1122, 107 (2009). arXiv:0812.1970 [astro-ph]
Kamenshchik, A., Moschella, U., Pasquier, V.: Phys. Lett. B 511, 265 (2001)
Kolb, E.W., Turner, M.S.: The Early Universe. Addison-Wesley, Redwood City (1990)
Leon, G., Saridakis, E.N.: Phys. Lett. B 693, 1 (2010). arXiv:0904.1577 [gr-qc]
Lue, A., Starkman, G.D.: Phys. Rev. D 70, 101501 (2004). arXiv:astro-ph/0408246
Maartens, R.: Living Rev. Relativ. 7, 7 (2004). arXiv:gr-qc/0312059
Maartens, R.: Phys. Rev. D 62, 084023 (2000)
Maeda, K., Wands, D.: Phys. Rev. D 62, 124009 (2000)
Nojiri, S., Oditsov, S.D.: Phys. Lett. B 571, 1 (2003)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 70, 103522 (2004)
Nojiri, S., Oditsov, S.D.: Phys. Rep. 505, 59 (2011)
Nojiri, S., Oditsov, S.D., Tsujikawa, S.: Phys. Rev. D 71, 063004 (2005)
Peebles, P.J.E.: Principles of Physical Cosmology. Princeton University Press, Princeton (1993)
Perlmutter, S., et al.: Supernova Cosmology Project Collaboration. Astrophys. J. 517, 565 (1999). arXiv:astro-ph/9812133
Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 3770 (1999a)
Randall, L., Sundrum, R.: Phys. Rev. Lett. 83, 4690 (1999b)
Riess, A.G., et al.: Supernova Search Team Collaboration. Astrophys. J. 607, 665 (2004). arXiv:astro-ph/0402512
Rubakov, V.A.: Phys. Usp. 44, 871 (2001). arXiv:hep-th/0104152
Rudra, P., Debnath, U., Biswas, R.: Astrophys. Space Sci. 339, 53 (2012). arXiv:1109.1481 [gr-qc]
Sahni, V., Saini, T.D., Starobinsky, A.A., Alam, U.: JETP Lett. 77, 201 (2003)
Sasaki, M., Shiromizu, T., Maeda, K.: Phys. Rev. D 62, 024008 (2000)
Setare, M.R.: Phys. Lett. B 642, 1 (2006)
Setare, M.R.: Eur. Phys. J. C 50, 991 (2007)
Setare, M.R., Jamil, M.: Gen. Relativ. Gravit. 43, 293–303 (2011)
Shiromizu, T., Maeda, K., Sasaki, M.: Phys. Rev. D 62, 024012 (2000)
Spergel, D.N., et al.: WMAP Collaboration. Astron. J. Suppl 148, 175 (2003). arXiv:astro-ph/0302209
Weedman, D.W.: Quasar Astronomy. Cambridge University, Cambridge (1986)
Weinberg, S.: Gravitation and Cosmology: Principles and Applications of the General Theory of Relativity. John Wiley and Sons, New York (1972)
Wu, P., Yu, H.: Class. Quantum Gravity 24, 4661 (2007)
Wu, X., Cai, R.G., Zhu, Z.H.: Phys. Rev. D, Part. Fields 77, 043502 (2008)
Zhang, X.: Mod. Phys. Lett. A 20, 2575 (2005)
Zhang, H., Zhu, Z.H.: Phys. Rev. D, Part. Fields 75, 023510 (2007)
Acknowledgement
The author is thankful to the anonymous referee for his invaluable comments on the manuscript.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Rudra, P. Dynamics of interacting generalized cosmic Chaplygin gas in brane-world scenario. Astrophys Space Sci 342, 579–599 (2012). https://doi.org/10.1007/s10509-012-1198-z
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10509-012-1198-z