Abstract
In this paper, we study an anisotropic Bianchi-I space-time model in f(R) theory of gravity in the presence of perfect fluid as a matter contains. The aim of this paper is to find the functional form of f(R) from the field equations and hence the solution of various cosmological parameters. We assume that the deceleration parameter to be a constant, and the shear scalar proportional to the expansion scalar to obtain the power-law form of the scale factors. We find that the model describes the decelerated phases of the universe under the choice of certain constraints on the parameters. The model does not show the acceleration expansion and also transition from past deceleration to present accelerating epoch. We discuss the stability of the functional form of f(R) and find that it is completely stable for describing the decelerating phase of the universe.
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Abdalla, M.C.B., Nojiri, S., Odintsov, S.D.: Class. Quantum Gravity 22, L35 (2005)
Aktaş, C., Aygün, S., Yilmaz, İ.: Phys. Lett. B 707, 237 (2012)
Amendola, L.: Phys. Rev. D 60, 043501 (1999)
Amendola, L., Tsujikawa, S.: Phys. Lett. B 660, 125 (2008)
Amendola, L., Gannouji, R., Polarski, D., Tsujikawa, S.: Phys. Rev. D 75, 083504 (2007)
Barrow, J.D., Clifton, T.: Class. Quantum Gravity 23, L1 (2006)
Berman, M.S.: Nuovo Cimento B 74, 182 (1983)
Berman, M.S., Gomide, F.M.: Gen. Relativ. Gravit. 20, 191 (1988)
Bertolami, O., Pármos, J.P.: Class. Quantum Gravity 25, 245017 (2008)
Capozziello, S., Francaviglia, M.: Gen. Relativ. Gravit. 40, 357 (2008)
Capozziello, S., Carloni, S., Troisi, A.: Recent Res. Dev. Astron. Astrophys. 1, 625 (2003)
Carroll, S.M.: Living Rev. Relativ. 4, 1 (2001)
Carroll, S.M., Duvvuri, V., Trodden, M., Turner, M.S.: Phys. Rev. D 70, 043528 (2004)
Chiba, T.: Phys. Rev. D 60, 083508 (2003a)
Chiba, T.: Phys. Lett. B 575, 1 (2003b)
Collins, C.B., Glass, e.N., Wilkinson, D.A.: Gen. Relativ. Gravit. 12, 805 (1980)
Copeland, E.J., Sami, M., Tsujikawa, S.: Int. J. Mod. Phys. D 15, 1753 (2006)
Dolgov, A.D., Kawasaki, M.: Phys. Lett. B 573, 1 (2003)
Eisenstein, D.J., et al.: Astrophys. J. 633, 560 (2005)
Elizalde, A., Nojiri, S., Odintsov, S.D., Gomez, D.S.: Eur. Phys. J. C 70, 351 (2010)
Elizalde, A., Nojiri, S., Odintsov, S.D., Sebastiani, L., Zerbini, S.: Phys. Rev. D 83, 086006 (2011)
Frolov, A.V.: Phys. Rev. Lett. 101, 061103 (2008)
Harko, T.: Phys. Lett. B 669, 376 (2008)
Jain, B., Taylor, A.: Phys. Rev. Lett. 91, 141302 (2003)
Kamatsu, E., et al.: Astrophys. J. Suppl. Ser. 180, 330 (2009)
Li, B., Barrow, J.D.: Phys. Rev. D 75, 084010 (2007)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 68, 123512 (2003)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 74, 086005 (2006)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 657, 238 (2007a)
Nojiri, S., Odintsov, S.D.: Phys. Lett. B 646, 105 (2007b)
Nojiri, S., Odintsov, S.D.: Int. J. Geom. Methods Mod. Phys. 4, 115 (2007c)
Nojiri, S., Odintsov, S.D.: Phys. Rev. D 77, 026007 (2008)
Nojiri, S., Odintsov, S.D.: Phys. Rep. 505, 59 (2011)
Nojiri, S., Odintsov, S.D., Saez-Gomez, D.: Phys. Lett. B 681, 74 (2009)
Padmanabhan, T.: Phys. Rep. 380, 235 (2003)
Peebles, P.J.E., Ratra, B.: Rev. Mod. Phys. 75, 559 (2003)
Percival, W.J., et al.: Mon. Not. R. Astron. Soc. 381, 1053 (2007)
Perlmutter, S., et al.: Astrophys. J. 517, 565 (1999)
Riess, A.G., et al.: Astrophys. J. 116, 1009 (1998)
Riess, A.G., et al.: Astrophys. J. 117, 707 (1999)
Sahni, V., Starobinsky, A.A.: Int. J. Mod. Phys. D 9, 373 (2000)
Seljak, U., et al.: Phys. Rev. D 71, 103515 (2005)
Shamir, M.F.: Astrophys. Space Sci. 330, 183 (2010)
Sharif, M., Kausar, H.R.: Astrophys. Space Sci. 332, 463 (2011a)
Sharif, M., Kausar, H.R.: J. Phys. Soc. Jpn. 80, 044004 (2011b)
Sharif, M., Kausar, H.R.: Phys. Lett. B 697, 1 (2011c)
Sharif, M., Shamir, M.F.: Class. Quantum Gravity 26, 235020 (2009)
Sharif, M., Shamir, M.F.: Gen. Relativ. Gravit. 42, 2643 (2010a)
Sharif, M., Shamir, M.F.: Mod. Phys. Lett. A 25, 128 (2010b)
Sharif, M., Zubair, M.: Astrophys. Space Sci. 330, 399 (2010a)
Sharif, M., Zubair, M.: Int. J. Mod. Phys. D 19, 1957 (2010b)
Sharif, M., Zubair, M.: Astrophys. Space Sci. 339, 45 (2012a)
Sharif, M., Zubair, M.: Astrophys. Space Sci. 342, 511 (2012b)
Singh, C.P.: Pramāna 72, 429 (2009a)
Singh, C.P.: Gravit. Cosmol. 15, 381 (2009b)
Singh, C.P., Beesham, A.: Int. J. Mod. Phys. A 25, 3825 (2010)
Singh, C.P., Kumar, S.: Int. J. Mod. Phys. D 15, 419 (2006)
Singh, C.P., Zeyauddin, M., Ram, S.: Int. J. Theor. Phys. 47, 3162 (2008)
Spergel, D.N., et al.: Astrophys. J. Suppl. Ser. 148, 175 (2003)
Steinhardt, P.J., Wang, L.M., Zlatev, I.: Phys. Rev. D 59, 123504 (1999)
Tegmark, M., et al.: Phys. Rev. D 69, 103501 (2004)
Tonry, J.L., et al.: Astrophys. J. 594, 1 (2003)
Yilmaz, İ., Baysal, H., Aktaş, C.: Gen. Relativ. Gravit. 44, 2313 (2012)
Zlatev, I., Wang, L.M., Steinhardt, P.J.: Phys. Rev. Lett. 82, 896 (1999)
Acknowledgements
The authors would like to thanks the anonymous referees for very valuable comments on this work. The authors also express their sincere thanks to Prof. Sami, Center for Theoretical Physics, JMI, India for useful discussion.
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Singh, V., Singh, C.P. Functional form of f(R) with power-law expansion in anisotropic model. Astrophys Space Sci 346, 285–289 (2013). https://doi.org/10.1007/s10509-013-1436-z
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DOI: https://doi.org/10.1007/s10509-013-1436-z