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Bulk Viscous Anisotropic Cosmological Models with Dynamical Cosmological Parameters G and ∧

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^{1}Department of Mathematics, Laxminarayan Institute of Technology, Rashtrasant Tukadoji Maharaj Nagpur University, Nagpur, India.

^{2}Department of Mathematics, Visvesvaraya, National Institute of Technology, Nagpur, India.

^{3}Department of Mathematics, S. B. Jain Institute of Technology Management and Research, Nagpur, India.

This paper deals with the Bianchi type I anisotropic models of the universe, filled with a bulk viscous cosmic fluid, in the presence of variable gravitational and cosmological constants. Some exact solutions of Einstein’s gravitational field equations with bulk viscosity, gravitational and cosmological constants have been obtained. Several well known forms of cosmological terms have been considered to discuss the effect of cosmological variables. The new cosmological models presented in this paper approaches to isotropic model with evolution of universe. The physical and dynamical properties of the models have also been discussed.

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

Kotambkar, S. , Singh, G. and Kelkar, R. (2015) Bulk Viscous Anisotropic Cosmological Models with Dynamical Cosmological Parameters G and ∧.

*Natural Science*,**7**, 179-189. doi: 10.4236/ns.2015.74021.

[1] |
Kantowski, R. and Sachs, R.K. (1966) Some Spatially Homogeneous Anisotropic Relativistic Cosmological Models. Journal of Mathematical Physics, 7, 443.
http://dx.doi.org/10.1063/1.1704952 |

[2] | Kramer, D. and Stephani, H. (1980) Exact Solution of Einstein’s Field Equations. Proceedings General Relativity and Gravitation, Jena, 75-92. |

[3] |
Lorenz, D. (1982) On the Solution for a Vacuum Bianchi Type-III Model with a Cosmological Constant. Journal of Physics A, 15, 2997.
http://dx.doi.org/10.1088/0305-4470/15/9/045 |

[4] | Maartens, R. and Maharaj, S.D. (1988) Anisotropic Spheres with Uniform density in General Relativity CNLS-88-7. |

[5] |
Huang, W.-H. (1990) Anisotropic Cosmological Models with Energy Density Dependent Bulk Viscosity. Journal of Mathematical Physics, 31, 1456.
http://dx.doi.org/10.1063/1.528736 |

[6] | Singh, T. and Singh G.P. (1991) Bianchi Type I Cosmological Models in Lyra’s Geometry: Journal of Mathematical Physics, 32, 2456. |

[7] |
Singh, T. and Singh G.P. (1992) Bianchi Type III and Kantowski-Schas Cosmological Models in Lyra Geometry: International Journal of Theoretical Physics, 31, 1433.
http://dx.doi.org/10.1007/BF00673976 |

[8] |
Singh, T. and Agrawal, A.K. (1993) Homogeneous Anisotropic Cosmological Models with Variable Gravitational and Cosmological “Constants”. International Journal of Theoretical Physics, 32, 1041.
http://dx.doi.org/10.1007/BF01215310 |

[9] |
Chimento, L.P. and Alejandro, S. (1997) Dissipative Cosmological Solutions. Classical and Quantum Gravity, 14, 1811.
http://dx.doi.org/10.1088/0264-9381/14/7/016 |

[10] |
Pradhan, A. and Singh, S.K. (2004) Bianchi Type I Magnetofluid Cosmological Models with Variable Cosmological Cosntant Revisited. International Journal of Modern Physics D, 13, 503-516.
http://dx.doi.org/10.1142/S0218271804004736 |

[11] | Saha, B. (2005) Anisotropic Cosmological Models with Perfect Fluid and dark Energy. Chinese Journal of Physics, 43, 1035-1043. |

[12] |
Reddy, D.R.K. and Naidu, R.L. (2006) On Kantowski—Sachs Cosmological Models in Bimetric Theory of Gravity. Astrophysics and Space Science, 301, 185-187.
http://dx.doi.org/10.1007/s10509-006-1622-3 |

[13] |
Kumar, S. and Singh, C.P. (2007) Anisotropic Bianchi Type I Models with Constant Deceleration Parameter in General Relativity. Astrophysics and Space Science, 312, 57-62.
http://dx.doi.org/10.1007/s10509-007-9623-4 |

[14] | Singh, R.P. and Yadav, L. (2009) Some Bianchi Type I Cosmological Models of the Universe for Viscous Fluid Distribution in Lyra Geometry. Electronic Journal of Theoretical Physics, 6, 61-78. |

[15] |
Pradhan, A., Amirhashchi, H. and Saha, B. (2011) Bianchi Type I Anisotropic Dark Energy Models with Constant Deceleration Parameter. International Journal of Theoretical Physics, 50, 2923-2938.
http://dx.doi.org/10.1007/s10773-011-0793-z |

[16] |
Pradhan, A., Singh, A.K. and Amirhashchi, H. (2012) A New Class of Bianchi Type I Cosmological Models in Scalar Tensor Theory of Gravitation and Late Time Acceleration. International Journal of Theoretical Physics, 51, 3769-3786.
http://dx.doi.org/10.1007/s10773-012-1262-z |

[17] |
Rai, P., Rai, L.N. and Singh, V.K. (2012) Bianchi Type I Cosmological Model Filled with Viscous Fluid in a Modified Brans-Dicke Cosmology. International Journal of Theoretical Physics, 51, 2127-2134.
http://dx.doi.org/10.1007/s10773-012-1092-z |

[18] |
Padmanabhan, T. (2003) Cosmological Constant—The Weight of Vacuum. Physics Reports, 380, 235-320.
http://dx.doi.org/10.1016/S0370-1573(03)00120-0 |

[19] |
Sahni, V. and Starobinsky, A. (2000) The Case of Positive Cosmological Lambda Term. International Journal of Modern Physics D, 9, 373-444.
http://dx.doi.org/10.1142/S0218271800000542 |

[20] | Vishwakarma, R.G. (2000) A Study of Angular Size Redshift Relation for Models in Which Lambda Decays as the Energy Density. Classical and Quantum Gravity, 17, 3833-3842. |

[21] | Vishwakarma, R.G. (2001) Consequences on Variable Lambda Models from Distant Type Ia Supernovae and Compact Radio Sources. Classical and Quantum Gravity, 18, 1159-1172. |

[22] | Vishwakarma, R.G. (2001) Study of the Magnitude Redshift Relation for Type Ia Supernovae in a Model Resulting from a Ricci Symmetry. General Relativity and Gravitation, 33, 1973-1984. |

[23] |
Vishwakarma, R.G. (2002) A Machian Model of Dark Energy. Classical and Quantum Gravity, 19, 4747-4752.
http://dx.doi.org/10.1088/0264-9381/19/18/309 |

[24] |
Peebles, P.J.E. and Ratra, B. (2003) The Cosmological Constant and Dark Energy. Reviews of Modern Physics, 75, 559-606.
http://dx.doi.org/10.1103/RevModPhys.75.559 |

[25] |
Singh, G.P. and Kotambkar, S. (2001) Higher Dimensional Cosmological Model with Gravitational and Cosmological “Constant”. General Relativity and Gravitation, 33, 621-630.
http://dx.doi.org/10.1023/A:1010278213135 |

[26] |
Padmanabhan, T. and Hamsa, P. (2013) CosMIn—The Solution to the Cosmological Constant Problem. International Journal of Modern Physics D, 22, Article ID: 1342001.
http://dx.doi.org/10.1142/S0218271813420017 |

[27] |
Freese, K. and Kinny, W.H. (2003) The Ultimate Fate of Life in an Accelerating Universe. Physics Letters B, 558, 1-8.
http://dx.doi.org/10.1016/S0370-2693(03)00239-9 |

[28] |
Carneiro, S., Pigozzo, C., Borges, H.A. and Alcaniz, J.S. (2006) Supernova Constraints on Decaying Vacuum Cosmology. Physical Review D, 74, Article ID: 023532.
http://dx.doi.org/10.1103/PhysRevD.74.023532 |

[29] | Narimani, A., Scott, D. and Niayesh, A. (2014) How Does Pressure Gravitate? Cosmological Constant Problem Confronts Observational Cosmology. Journal of Cosmology and Astroparticle Physics, 1408, 049. |

[30] | Miao, Y.G. and Zhao, Y.J. (2014) Thermodynamics Approach to Fluid Equation in Lovelock Gravity And f(R) Gravity Revisisted. International Journal of Modern Physics D, 23, Article ID: 1450062. |

[31] |
Beesham, A. (1994) Bianchi Type I Cosmological Models with Variable G and Lambda. General Relativity and Gravitation, 26, 159-165.
http://dx.doi.org/10.1007/BF02105151 |

[32] | Abdel-Rehman, A.-M. M. (1990) A Note on Physical Interpretation of Weyl Gauging. General Relativity and Gravitation, 22, 665. |

[33] | Berman, M.S. (1991) Cosmological Models with Variable Cosmological Term. Physical Review, D 43, 1075-1078. |

[34] |
Kalligas, D., Wesson, P. and Everitt, C.W.F. (1995) Bianchi Type I Cosmological Models with Variable G and Lambda: A Comment. General Relativity and Gravitation, 27, 645-650.
http://dx.doi.org/10.1007/BF02108066 |

[35] |
Abdussattar and Vishwakarma, R.G. (1997) Some FRW Models with Variable G and Lambda. Classical and Quantum Gravity, 14, 945-953.
http://dx.doi.org/10.1088/0264-9381/14/4/011 |

[36] |
Saha, B. (2001) Dirac Spinor in Bianchi Type I Universe with Time Dependent Gravitational and Cosmological Constant. Modern Physics Letters A, 16, 1287-1296.
http://dx.doi.org/10.1142/S0217732301004546 |

[37] | Singh, G.P. and Kotambkar, S. (2003) Higher Dimensional Dissipative Cosmology with Varying G and Lambda. Gravitation and Cosmology, 9, 206-210. |

[38] |
Singh, J.P., Pradhan, A. and Singh, A.K. (2008) Bianchi Type I Cosmological Models with Variable G and Lambda Term in General Relativity. Astrophysics and Space Science, 314, 83-88.
http://dx.doi.org/10.1007/s10509-008-9742-6 |

[39] |
Vishwakarma, R.G. (2005) A Model to Explain Varying Λ, G and σ2 Simulteneously. General Relativity and Gravitation, 37, 1305-1311.
http://dx.doi.org/10.1007/s10714-005-0113-0 |

[40] |
Singh, C.P. and Kumar, S. (2009) Bianchi I Space-Time with Variable Gravitational and Cosmological Constants. International Journal of Theoretical Physics, 48, 2401-2411.
http://dx.doi.org/10.1007/s10773-009-0030-1 |

[41] |
Maartens, R. (1995) Dissipative Cosmology. Classical and Quantum Gravity, 12, 1455-1465.
http://dx.doi.org/10.1088/0264-9381/12/6/011 |

[42] |
Singh, G.P. and Kale, A.Y. (2009) Anisotropic Bulk Viscous Cosmological Models with Variable G and Lambda. International Journal of Theoretical Physics, 48, 1177-1185.
http://dx.doi.org/10.1007/s10773-008-9891-y |

[43] |
Verma, M.K. and Ram, S. (2010) Bulk Viscous Bianchi Type-III Cosmological Model with Time-Dependent G and Λ. International Journal of Theoretical Physics, 49, 693-700.
http://dx.doi.org/10.1007/s10773-010-0248-y |

[44] | Verma, M.K. and Ram, S. (2011) Spatially Homogeneous Bulk Viscous Fluid Models with Time Dependent Gravitational Constant and Cosmological Term. Advanced Studies in Theoretical Physics, 5, 387-398. |

[45] |
Singh, C.P. (2011) Cosmological Models with Time Varying Gravitational and Cosmological Constants. Astrophysics and Space Science, 331, 337-342.
http://dx.doi.org/10.1007/s10509-010-0439-2 |

[46] | Pradhan, A., Saha, B. and Rikhvitsky, V. (2014) Bianchi Type I Transit Cosmological Models with Time Dependent Gravitational and Cosmological Constants-Reexamined. Indian Journal of Physics. |

[47] |
Raychaudhuri, A.K. (1955) Relativistic Cosmology. I. Physical Review, 98, 1123.
http://dx.doi.org/10.1103/PhysRev.98.1123 |

[48] |
Arbab, I.A. (1997) Cosmological Models with Variable Cosmological and Gravitational “Constants” and Bulk Viscous Models. General Relativity and Gravitation, 29, 61-74.
http://dx.doi.org/10.1023/A:1010252130608 |

[49] |
Chen, W. and Wu, Y.S. (1990) Implication of a Cosmological Constant Varying as R-2. Physical Review D, 41, 695-698.
http://dx.doi.org/10.1103/PhysRevD.41.695 |

[50] | Carvalho, J.C., Lima, J.A.S. and Waga, I. (1992) On the Cosmological Consequences of a Time Dependent Lambda Term. Physical Review D, 46, 2404-2407. |

[51] |
Beesham, A. (1993) Cosmological Models with a Variable Cosmological Term and Bulk Viscous Models. Physical Review D, 48, 3539-3543.
http://dx.doi.org/10.1103/PhysRevD.48.3539 |

[52] |
Berman, M.S. (1991) Cosmological Models with Variable Cosmological Term. Physical Review D, 43, 1075-1078.
http://dx.doi.org/10.1103/PhysRevD.43.1075 |

[53] |
Beesham, A. (1994) Bianchi Type I Cosmological Models with Variable G and Lambda. General Relativity and Gravitation, 26, 159-165.
http://dx.doi.org/10.1007/BF02105151 |

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