Volume 53 | Number 6 | Year 2018 | Article Id. IJMTT-V53P558 | DOI : https://doi.org/10.14445/22315373/IJMTT-V53P558

In this paper, we have studied the Bianchi type-I universe with polytropic equation of state in the framework of the second self-creation theory of gravitation proposed by Barber [1]. The field equations have been solved by using (i) the power law relation between the average scale factor 'a' and the scalar field 'a' and (ii) the special law of variation for Hubble’s parameter proposed by Berman [2]. Some physical and kinematical aspects of the models are also discussed.

[1] G. A. Barber, “On two self-creation cosmologies”,Gen.Rel.Grav.,vol.14, pp.117-136, Feb.1982.

[2] M. S. Berman, “A special law of variation for Hubble‟s parameter”, Nuovo Cimento B, vol.74, pp.182-186, Apl. 1983.

[3] C. Brans and R. H. Dicke, “Mach's Principle and a Relativistic Theory of Gravitation‟, Phys. Rev. vol. 124, pp.925, Nov.1961.

[4] G. Mohanty, B. Mishra, R. Das, “Plane symmetric vacuum and Zeldovich fluid models in self creation theory”, Bull.Inst. Math. Aca. Sinca(Roc), vol.28, pp.43-50, March 2000.

[5] G. Mohanty, B.Mishra, “Dissipation of general viscous fluid distribution in Einstein and Barber theories”, Theor. Appl. Mech. vol.26, pp.71-81, 2001.

[6] A. Pradhan, A. K. Vishwakarma, “LRS Bianchi Type-I Cosmological Models in Barber's Second Self Creation Theory”, Int.J.Mod.Phy. D, vol. 11(8), pp.1195-1207, 2002.

[7] C.P. Singh, S. Kumar,“Bianchi type-II space-times with constant deceleration parameter in self creation cosmology”, Astrophys Space Sci, vol.310, pp.31-39, July 2007.

[8] V.U.M. Rao, T. Vinutha, “Plane symmetric string cosmological models in self-creation theory of gravitation” Astrophys Space Sci vol.325, pp.59-62, Jan 2010.

[9] V.U.M. Rao, U.Y. Divya Prasanthi, “Bianchi type-V modified holographic Ricci dark energy model in self-creation theory of gravitation”, Canadian Journal of Physics, vol. 95, pp.554-558, Feb 2017.

[10] D. R. K. Reddy, M. P. V. V. Bhaskara Rao, K. Sbhan Babu, “Bianchi type-II Bulk viscous string cosmological model in self-creation theory of gravitation”, Astrophys. Space Sci. vol. 351(1), pp.385-389, Feb 2014.

[11] S. D. Katore, R. S. Rane, K. S. Wankhade, “FRW cosmological models with bulk-viscosity in Barber's second self-creation theory”, Int.J.Theory.Phys. vol.49, pp.187-193, Jan 2010.

[12] D. D. Pawar, Y. S. Solanke, “Exact Kantowski-Sach Cosmological Models with Constant EoS Parameter in Barber's Second Self- Creation Theory”, Prespacetime journal vol.5, pp.60-68, Feb 2014.

[13] K. D. Naidu, R.L.Naidu, K. Shobanbabu, “Kantowski–Sachs bulk viscous string cosmological model in a self-creation theory of gravitation” Astrophys Space Sci vol. 358, pp.23, July 2015.

[14] M. V. Santhi, V.U.M. Rao,Y. Aditya, “Anisotropic magnetized holographic Ricci dark energy cosmological models”M. Vijaya Santhi, V.U.M. Rao, Y. AdityaCanadian Journal of Physics, vol. 95, pp. 381-392, July 2017.

[15] J. Christensen-Dalsgaard, Lecture Notes on Steller Structure and Evolution, 6th edn. Aarhus University Press, Aarhus 2004.

[16] U. Mukhopadhyay, S. Ray, S.B. Dutta Choudhury, “Dark energy with polytropic equation of state”, Mod.Phys. Lett. A, vol. 23, pp. 3187-3198, Dec 2008.

[17] K. Karami, S. Ghaffari, J. Fehri,“Interacting polytropic gas model of phantom dark energy in non-flat universe”, Eur. Phys. J. C., vol. 64, pp.85-88, Nov.2009.

[18] K. Karami, S. Ghaffari, “The generalized second law of thermodynamics for the interacting polytropic dark energy in non-flat FRW universe enclosed by the apparent horizon”, Phys. Letters B, vol. 688, pp.125-128, May 2010.

[19] M. R. Setare, M. J. S. Houndjo, V. Kamali, “Warm polytropic inflationary universe model”, Int. J. Mod.Phys. D vol.22, pp. 1350041, July 2013.

[20] M. Taji, M. Malekjan, “Interacting Holographic Polytropic Gas Model of Dark Energy”, Int J Theor Phys, vol. 52, pp. 3405-3412, Oct. 2013.

[21] M. A. Rahman, M. Ansari, “Interacting Holographic Polytropic gas model of dark energy with hybrid expansion law in Bianchi type- VI0 space-time”, Astrophys. Space Sci.vol. 354, pp. 617-625, Dec. 2014.

[22] K. S. Adhav, P.R. Agrawal, R.R. Saraogi, “Anisotropic and Homogeneous Cosmological Models with Polytropic Equation of State in General Relativity”, Bulg. J. Phys.vol. 43, pp.171–183, 2016.

[23] D. N. Spergel, et al., “First-Year Wilkinson Microwave Anisotropy Probe (WMAP)*Observations: Determination of Cosmological Parameters”, Ap J S, vol.148, pp.135-159, Sep. 2003.

[24] A.G. Riess, et al.: “Type Ia Supernova Discoveries at z > 1 from the Hubble Space Telescope: Evidence for Past Deceleration and Constraints on Dark Energy Evolution”, Astrophys. J., vol. 607, pp. 665-687, June 2004.

[25] A.G. Riess, et al., “New Hubble space telescope discoveries of type Ia supernovae at z≥ 1: narrowing constraints on the early behavior of dark energy”, Astrophys. J.vol. 659, pp. 98–121, Apr 2007.

[26] K. P. Astier, et al., “The Supernova Legacy Survey: measurement of ΏM, Ώa and w from the first year data set”, Astron. Astrophys, Vol. 447, pp.31-48, Jan. 2006.

[27] Bamba, et al., “Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests”, Astrophys. Space Sci.vol. 342, pp.155-228, Nov. 2012.

S.D. Katore, D.V. Kapse, "Bianchi Type-I Dark Energy Cosmological Model With Polytropic Equation Of State In Barber‟s Second Self-Creation Cosmology," *International Journal of Mathematics Trends and Technology (IJMTT)*, vol. 53, no. 6, pp. 476-487, 2018. *Crossref*, https://doi.org/10.14445/22315373/IJMTT-V53P558