Abstract
The main purpose of this paper is to explore the solutions of Bianchi type-III cosmological model in Lyra geometry in the background of anisotropic dark energy. The general form of the anisotropy parameter of the expansion for Bianchi type-III space time is obtained in the presence of a single imperfect fluid with a dynamical anisotropic equation of state parameter and a dynamical energy density in Lyra geometry. A special law is assumed for the anisotropy of the fluid with reduces the anisotropy parameter of the expansion to a simple form \(\Delta \propto \frac{1}{H^{2}V^{2}}\). The exact solutions of the field equations, under the assumption on the anisotropy of the fluid, are obtained for exponential and power law volumetric expansion. The isotropy of the fluid, space and expansion are discussed. It is observed that the universe can approach to isotropy monotonically even in the presence of an anisotropic fluid. The anisotropy of the fluid also isotropizes at later times for accelerating models. The expression for the look-back time, proper distance, luminosity distance and angular diameter distance are also derived.
Similar content being viewed by others
References
Riess, A.G., et al.: Astron. J. 116, 1009 (1998)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003)
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 148, 157 (2003)
Campanelli, L., et al.: Phys. Rev. Lett. 97, 131302 (2006)
Campanelli, L., et al.: Phys. Rev. D 76, 063007 (2007)
Koivisto, T., Mota, D.F.: Phys. Rev. D 73, 083502 (2006)
Koivisto, T., Mota, D.F.: (2007). arXiv:0707.0279 astro-ph
Rodrigues, D.C.: Phys. Rev. D 77, 023534 (2008)
Guth, A.H.: Phys. Rev. D 23, 347 (1981)
Sato, K.: Mon. Not. R. Astron. Soc. 195, 467 (1981)
Linde, A.D.: Phys. Lett. B 108, 389 (1982)
Albrecht, A., Steinhardt, P.J.: Phys. Rev. Lett. 48, 1220 (1982)
Feinstein, A., Ibanez, J.: Class. Quantum Gravity 10, 93 (1993)
Aguirregabiria, J.M., et al.: Phys. Rev. D 48, 4662 (1993)
Ellis, G.F.R.: Cosmological models. In: Bonometto, S., et al. (eds.) Modern Cosmology, pp. 108–158. Institute of Physics Publishing, Bristol and Philadelphia (2002)
Ellis, G.F.R.: Gen. Relativ. Gravit. 38, 1003 (2006)
Golovnev, A., et al.: J. Cosmol. Astropart. Phys. 06, 009 (2008)
Sahni, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 9, 373 (2000)
Carroll, S.M., Hoffman, M.: Phys. Rev. D 68, 023509 (2003)
Sahni, V.: Lect. Notes Phys. 653, 141 (2004)
Alam, U., et al.: J. Cosmol. Astropart. Phys. 0406, 008 (2004)
Lopeland, E.J., et al.: Int. J. Mod. Phys. D 15, 1753 (2006)
Sahni, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 15, 2105 (2006)
Turner, M.S., Huterer, D.: J. Phys. Soc. Jpn. 76, 111015 (2007)
Padmanabhan, T.: Gen. Relativ. Gravit. 40, 529 (2008)
Knop, R.K., et al.: Astrophys. J. 598, 102 (2003)
Tegmark, M., et al.: Phys. Rev. D 69, 103501 (2004)
Rahaman, F., Bhui, B., Bhui, B.C.: Astrophys. Space Sci. 301, 47 (2006)
Usmani, A.A., Ghosh, P.P., Mukhopadhyay, U., Ray, P.C., Ray, S.: Mon. Not. R. Astron. Soc. Lett. 386, L92 (2008)
Sharif, M., Zubair, M.: Int. J. Mod. Phys. D 19, 1957 (2010)
Sharif, M., Zubair, M.: Astrophys. Space Sci. 330, 399 (2010)
Akarsu, O., Kilinc, C.B.: Gen. Relativ. Gravit. 42, 763 (2010)
Zimdahl, W., et al.: Phys. Rev. D 64, 063501 (2001)
Armendariz-Picon, C.: J. Cosmol. Astropart. Phys. 07, 007 (2004)
Kiselev, V.V.: Class. Quantum Gravity 21, 3323 (2004)
Novello, M., et al.: Phys. Rev. D 69, 127301 (2004)
Wei, H., Cai, R.G.: Phys. Rev. D 73, 083002 (2006)
Tegmark, M., et al.: Astrophys. J. 606, 702 (2004)
Riess, A.G., et al.: Astrophys. J. 607, 665 (2004)
Astier, P., et al.: Astron. Astrophys. 447, 31 (2006)
Mota, D.F., et al.: Mon. Not. R. Astron. Soc. 382, 793 (2007)
Lyra, G.: Math. Z. 54, 52 (1951)
Sen, D.K.: Z. Phys. 149, 311 (1957)
Dunn, K.A.: J. Math. Phys. 12, 578 (1971)
Halford, W.D.: Aust. J. Phys. 23, 863 (1970)
Soleng, H.H.: Gen. Relativ. Gravit. 19, 1213 (1987)
Bharama, K.S.: Aust. J. Phys. 27, 541 (1974)
Singh, T., Singh, G.P.: J. Math. Phys. 32, 2456 (1991)
Rahaman, F.: Int. J. Mod. Phys. D 9, 775 (2000)
Rahaman, F.: Nuovo Cimento B 118, 17 (2003)
Kotambkar, S., Pradhan, A.: Int. J. Mod. Phys. D 12, 853 (2003)
Pradhan, A., Aotcmshi, I., Singh, G.P.: Astrophys. Space Sci. 288, 315 (2003)
Reddy, D.R.K., Subba Rao, M.V.: Astrophys. Space Sci. 302, 157 (2006)
Mohanty, G., et al.: Astrophys. Space Sci. 310, 273 (2007)
Chaubey, R., Shukla, A.K.: Int. J. Theor. Phys. 52, 735 (2013)
Sahu, S.K., Kumar, T.: Int. J. Theor. Phys. 52, 793 (2013)
Adhav, K.S., Nimkar, A.S., Ugale, M.R., Dawande, M.V.: Int. J. Theor. Phys. 47, 634 (2008)
Bali, R., Tinker, S.: Chin. Phys. Lett. 26, 029802 (2009)
Pradhan, A., Amirhashchi, H.: Astrophys. Space Sci. 332, 441 (2011)
Moussiaux, A., et al.: J. Phys. A, Math. Gen. 14, 277 (1981)
Lorenz-Petzold, D.: Astrophys. Space Sci. 85, 59 (1982)
Xing-Xiang, W.: Chin. Phys. Lett. 22, 29 (2005)
Upadhaya, R.D., Dave, S.: Braz. J. Phys. 38, 4 (2008)
Shamir, M.F., Bhatti, A.A.: arXiv:1206.0391v1 [gr-qc] (2 Jun 2012)
Collins, C.B., Hawking, S.W.: Astrophys. J. 180, 317 (1973)
Kumar, S., Singh, C.P.: Astrophys. Space Sci. 312, 57 (2007)
Singh, C.P., et al.: Astrophys. Space Sci. 315, 181 (2008)
Singh, J.P., Baghel, P.S.: Int. J. Theor. Phys. 48, 449 (2009)
Waga, I.: Astrophys. J. 414, 436 (1993)
Acknowledgements
The author is very much thank full to anonymous referees for their valuable comments which has improved the quality of work.
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Samanta, G.C. Bianchi Type-III Cosmological Models with Anisotropic Dark Energy (DE) in Lyra Geometry. Int J Theor Phys 52, 3442–3456 (2013). https://doi.org/10.1007/s10773-013-1645-9
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10773-013-1645-9