Bianchi-Type VI_{0} Bulk Viscous Fluid Models with Variable Gravitational and Cosmological Constants

ABSTRACT

This paper deals with Bianchi type VI0 anisotropic cosmological models filled with a bulk viscous cosmic fluid in the presence of time-varying gravitational and cosmological constant. Physically realistic solutions of Einstein's field equations are obtained by assuming the conditions 1) the expansion scalar is proportional to shear scalar 2) the coefficient of the bulk viscosity is a power function of the energy density and 3) the cosmic fluid obeys the barotropic equation of state. We observe that the corresponding models retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Physical behaviours of the cosmological models are also discussed.

This paper deals with Bianchi type VI0 anisotropic cosmological models filled with a bulk viscous cosmic fluid in the presence of time-varying gravitational and cosmological constant. Physically realistic solutions of Einstein's field equations are obtained by assuming the conditions 1) the expansion scalar is proportional to shear scalar 2) the coefficient of the bulk viscosity is a power function of the energy density and 3) the cosmic fluid obeys the barotropic equation of state. We observe that the corresponding models retain the well established features of the standard cosmology and in addition, are in accordance with recent type Ia supernovae observations. Physical behaviours of the cosmological models are also discussed.

Cite this paper

nullM. Verma and S. Ram, "Bianchi-Type VI_{0} Bulk Viscous Fluid Models with Variable Gravitational and Cosmological Constants," *Applied Mathematics*, Vol. 2 No. 3, 2011, pp. 348-354. doi: 10.4236/am.2011.23041.

nullM. Verma and S. Ram, "Bianchi-Type VI

References

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[2] J. D. Barrow, “Heliam Formation in Cosmologies with Anisotropic Curvature,” Royal Astronomical Society, Vol. 211, No. 1, 1984, pp. 221-227.

[3] G. F. R. Ellis and M. A. H. MacCallum, “A Class of Homogeneous Cosmological models,” Communications in Mathematical Physics, Vol. 12, No. 2, 1969, pp. 108-141. doi:10.1007/BF01645908

[4] C. B. Collins, “More Qualitative Cosmology,” Communications in Mathematical Physic, Vol. 23, No. 2, 1971, pp. 137-158. doi:10.1007/BF01877756

[5] V. A. Ruban, “Preprint No. 412, Leningrade Institute of Nuclear Physics, B. P. Konstrantinova,” Preprint, 1978.

[6] K. A. Dunn and B. O. J. Tupper, “A Class of Bianchi Type VI0 Cosmological Models with Electromagenitic Field,” The Astrophysical Journal, Vol. 204, No. 1, 1976, pp. 322-329. doi:10.1086/154175

[7] D. Lorentz, “Tilted Electromagnetic Bianchi Type-III Cosmological Solution,” Astrophysics and Space Science, Vol. 85, No. 1-2, 1982, pp. 59-61. doi:10.1007/BF00653432

[8] S. R. Roy and J. P. Singh, “Some Bianchi VI0 Cosmological Models with Free Gravitational Field of the Magnetic Type,” Acta Physics Austriaca, Vol. 55, No. 2, 1983, pp. 57-66.

[9] Shri Ram, “LRS Bianchi Type I Perfect Fluid Solutions Generated From Know Solutions,” Journal of Mathematical Physics, Vol. 28, No. 8, 1989, pp. 917-921.

[10] B. M. Ribeiro and A. K. Sanyal, “Bianchi-VI0 Viscous Fluid Cosmology with Magnetic Field,” Journal of Mathematical Physics, Vol. 28, No. 3, 1987, pp. 657-660. doi:10.1063/1.527599

[11] L. K. Patel and S. S. Koppar, “Some Bianchi Type VI0 Viscous Fluid Cosmological Models,” Journal of the Australian Mathematical Society, Series B, Vol. 33, 1991.

[12] R. Bali, A. Pradhan and A. Hassan, “Bianchi Type VI0 Magnetized Barotropic Bulk Viscous Fluid Massive String Universe in General Relativity,” International Journal of Theoretical Physics, Vol. 47, No. 10, 2008, pp. 2594-2604. doi:10.1007/s10773-008-9694-1

[13] R. Bali, R. Banerjee and S. K. Banerjee, “Bianchi Type VI0 Bulk Viscous Massive String Cosmological Models in General Relativity,” Astrophysics and Space Science, Vol. 317, No. 1-2, 2008, pp. 21-26. doi:10.1007/s10509-008-9848-x

[14] R. Bali, R. Banerjee and S. K. Banerjee, “Some LRS Bianchi Type VI0 Cosmological Models with Special Free Gravitational Fields,” Electronic Journal of Theoretical Physics, Vol. 6, No. 21, 2009, pp. 165-174.

[15] Ya. B. Zeldovich, “The Equation of State at Ultra High Densities and Its Relativistic limitations,” Soviet Physics - JETP, Vol. 14, 1968, pp. 1143-1147.

[16] R. V. Wagoner, “Scalar-Tensor Theory and Gravitational Waves,” Physical Review D, Vol. 1, No. 12, 1970, pp. 3209-3216. doi:10.1103/PhysRevD.1.3209

[17] A. D. Linde, “Is the Cosmological Constant a Constant,” JETP Letters, Vol. 19, No. 5, 1974, p. 183.

[18] R. G. Vishwakarma, “Machian Model of Dark Energy,” Quantum Gravity, Vol. 19, No. 18, 2002, pp. 4747-4752. doi:10.1088/0264-9381/19/18/309

[19] D. Kalligas, P. Wesson and C. W. F. Everitt, “Flat FRW Models with Variable-G and Variable-?,” General Relativity and Gravitation, Vol. 24, 1992, pp. 351-357. doi:10.1007/BF00760411

[20] A. I. Arbab, “Cosmological Models with Variable Cosmological and Gravitational Constants and Bulk Viscous Fluid,” General Relativity and Gravitation, Vol. 29, No. 1, 1997, pp. 61-74. doi:10.1023/A:1010252130608

[21] Abdussattar and R. G. Vishwakarma “Some FRW Models with Variable G and ?,” Quantum Gravity, Vol. 14, No. 4, 1997, pp. 945-953. doi:10.1088/0264-9381/14/4/011

[22] A. Pradhan and V. K. Yadav, “Bulk Viscous Anisotropic Comological Models with variable G and ?,” International Journal of Modern Physics D, Vol. 11, No. 6, 2002, pp. 857-868. doi:10.1142/S0218271802002153

[23] A. Pradhan, A. K. Singh and S. Otarod, “FRW Universe with Variable G and Lambda Terms,” Romanian Journal of Physics, Vol. 52, No. 3-4, 2007, pp. 445-458

[24] J. P. Singh, A. Pradhan and A. K. Singh, “Bianchi Type-I Cosmological Models with Variable G and Lambda-Term in General Relativity,” Astrophysics and Space Science, Vol. 314, No. 1-3, 2008, pp. 83-88. doi:10.1007/s10509-008-9742-6

[25] C. P. Singh, S. Kumar and A. Pradhan, “Early Viscous Universe with Variable Gravitational and Cosmological Constants,” Quantum Gravity, Vol. 14, No. 2, 2007, pp. 445-474.

[26] J. P. Singh and S. K. Tiwari, “Perfect Fluid Bianchi Type I Cosmological Models with Variable G and ?,” Pramana–Journal of Physics, Vol. 70, No. 4, 2008, pp. 565-574.

[27] G. P. Singh and S. Kotambkar, “Higher-Dimensional Dissipative Cosmology with Varying G and ?,” General Relativity and Gravitation, Vol. 33, No. 4, 2001, pp. 621-630.

[28] G. P. Singh and A. Y. Kale, “Anisotropic Bulk Viscous Cosmological Models with Variable G and ?,” International Journal of Theoretical Physics, Vol. 48, No. 4, 2009, pp. 1175-1185.

[29] R. Bali and S. Tinker, “Bianchi Type-III Bulk Viscous Barotropic Fluid Cosmological Models with Variable G and ?,” Chinese Physics Letters, Vol. 26, No. 2, 2009, pp. 029802. doi:10.1088/0256-307X/26/2/029802

[30] M. K. Verma and Shri Ram, “Bulk Viscous Bianchi Type-III Model with Time-Dependent G and ?,” International Journal of Theoretical Physics, Vol. 49, No. 4, 2009, pp. 693-700. doi:10.1007/s10773-010-0248-y

[31] A. Pradhan and R. Bali, “Magnetized Bianchi Type VI0 Barotropic Massive String Universe with Decaying Vacuum Energy Density ?,” Electronic Journal of Theoretical Physics, Vol. 5, No. 19, 2008, pp. 91-104.

[32] A. Pradhan, P. Yadav and K. Jotania, “A New Class of LRS Bianchi Type VI0 Universe with Free Gravitational Field and Decaying Vacuum Energy Density,” arXiv:0907.485 [gr-qc], 2009.

[33] R. Maartens, “Dissipative Cosmology,” Quantum Gravity, Vol. 12, No. 6, 1995, pp. 1455-1465. doi:10.1088/0264-9381/12/6/011

[34] S. Weinberg, “In Gravitation and Cosmology,” Wiley, New York, 1972.

[35] G. L. Murphy, “Big-Bang without Singularities,” Physical Review D, Vol. 8, No. 12, 1973, pp. 4231-4233. doi:10.1103/PhysRevD.8.4231

[36] V. A. Belinskii and I. M. Khalatnikov, “Effect of Viscosity on Nature of Cosmological Evolution,” Soviet Physics-JETP, Vol. 42, No. 2, 1976, pp. 205.

[1] M. P. Ryan and L. C. Shpley, “Homogeneous Relativistic Cosmologies,” Princeton University Press, Princeton 1975.

[2] J. D. Barrow, “Heliam Formation in Cosmologies with Anisotropic Curvature,” Royal Astronomical Society, Vol. 211, No. 1, 1984, pp. 221-227.

[3] G. F. R. Ellis and M. A. H. MacCallum, “A Class of Homogeneous Cosmological models,” Communications in Mathematical Physics, Vol. 12, No. 2, 1969, pp. 108-141. doi:10.1007/BF01645908

[4] C. B. Collins, “More Qualitative Cosmology,” Communications in Mathematical Physic, Vol. 23, No. 2, 1971, pp. 137-158. doi:10.1007/BF01877756

[5] V. A. Ruban, “Preprint No. 412, Leningrade Institute of Nuclear Physics, B. P. Konstrantinova,” Preprint, 1978.

[6] K. A. Dunn and B. O. J. Tupper, “A Class of Bianchi Type VI0 Cosmological Models with Electromagenitic Field,” The Astrophysical Journal, Vol. 204, No. 1, 1976, pp. 322-329. doi:10.1086/154175

[7] D. Lorentz, “Tilted Electromagnetic Bianchi Type-III Cosmological Solution,” Astrophysics and Space Science, Vol. 85, No. 1-2, 1982, pp. 59-61. doi:10.1007/BF00653432

[8] S. R. Roy and J. P. Singh, “Some Bianchi VI0 Cosmological Models with Free Gravitational Field of the Magnetic Type,” Acta Physics Austriaca, Vol. 55, No. 2, 1983, pp. 57-66.

[9] Shri Ram, “LRS Bianchi Type I Perfect Fluid Solutions Generated From Know Solutions,” Journal of Mathematical Physics, Vol. 28, No. 8, 1989, pp. 917-921.

[10] B. M. Ribeiro and A. K. Sanyal, “Bianchi-VI0 Viscous Fluid Cosmology with Magnetic Field,” Journal of Mathematical Physics, Vol. 28, No. 3, 1987, pp. 657-660. doi:10.1063/1.527599

[11] L. K. Patel and S. S. Koppar, “Some Bianchi Type VI0 Viscous Fluid Cosmological Models,” Journal of the Australian Mathematical Society, Series B, Vol. 33, 1991.

[12] R. Bali, A. Pradhan and A. Hassan, “Bianchi Type VI0 Magnetized Barotropic Bulk Viscous Fluid Massive String Universe in General Relativity,” International Journal of Theoretical Physics, Vol. 47, No. 10, 2008, pp. 2594-2604. doi:10.1007/s10773-008-9694-1

[13] R. Bali, R. Banerjee and S. K. Banerjee, “Bianchi Type VI0 Bulk Viscous Massive String Cosmological Models in General Relativity,” Astrophysics and Space Science, Vol. 317, No. 1-2, 2008, pp. 21-26. doi:10.1007/s10509-008-9848-x

[14] R. Bali, R. Banerjee and S. K. Banerjee, “Some LRS Bianchi Type VI0 Cosmological Models with Special Free Gravitational Fields,” Electronic Journal of Theoretical Physics, Vol. 6, No. 21, 2009, pp. 165-174.

[15] Ya. B. Zeldovich, “The Equation of State at Ultra High Densities and Its Relativistic limitations,” Soviet Physics - JETP, Vol. 14, 1968, pp. 1143-1147.

[16] R. V. Wagoner, “Scalar-Tensor Theory and Gravitational Waves,” Physical Review D, Vol. 1, No. 12, 1970, pp. 3209-3216. doi:10.1103/PhysRevD.1.3209

[17] A. D. Linde, “Is the Cosmological Constant a Constant,” JETP Letters, Vol. 19, No. 5, 1974, p. 183.

[18] R. G. Vishwakarma, “Machian Model of Dark Energy,” Quantum Gravity, Vol. 19, No. 18, 2002, pp. 4747-4752. doi:10.1088/0264-9381/19/18/309

[19] D. Kalligas, P. Wesson and C. W. F. Everitt, “Flat FRW Models with Variable-G and Variable-?,” General Relativity and Gravitation, Vol. 24, 1992, pp. 351-357. doi:10.1007/BF00760411

[20] A. I. Arbab, “Cosmological Models with Variable Cosmological and Gravitational Constants and Bulk Viscous Fluid,” General Relativity and Gravitation, Vol. 29, No. 1, 1997, pp. 61-74. doi:10.1023/A:1010252130608

[21] Abdussattar and R. G. Vishwakarma “Some FRW Models with Variable G and ?,” Quantum Gravity, Vol. 14, No. 4, 1997, pp. 945-953. doi:10.1088/0264-9381/14/4/011

[22] A. Pradhan and V. K. Yadav, “Bulk Viscous Anisotropic Comological Models with variable G and ?,” International Journal of Modern Physics D, Vol. 11, No. 6, 2002, pp. 857-868. doi:10.1142/S0218271802002153

[23] A. Pradhan, A. K. Singh and S. Otarod, “FRW Universe with Variable G and Lambda Terms,” Romanian Journal of Physics, Vol. 52, No. 3-4, 2007, pp. 445-458

[24] J. P. Singh, A. Pradhan and A. K. Singh, “Bianchi Type-I Cosmological Models with Variable G and Lambda-Term in General Relativity,” Astrophysics and Space Science, Vol. 314, No. 1-3, 2008, pp. 83-88. doi:10.1007/s10509-008-9742-6

[25] C. P. Singh, S. Kumar and A. Pradhan, “Early Viscous Universe with Variable Gravitational and Cosmological Constants,” Quantum Gravity, Vol. 14, No. 2, 2007, pp. 445-474.

[26] J. P. Singh and S. K. Tiwari, “Perfect Fluid Bianchi Type I Cosmological Models with Variable G and ?,” Pramana–Journal of Physics, Vol. 70, No. 4, 2008, pp. 565-574.

[27] G. P. Singh and S. Kotambkar, “Higher-Dimensional Dissipative Cosmology with Varying G and ?,” General Relativity and Gravitation, Vol. 33, No. 4, 2001, pp. 621-630.

[28] G. P. Singh and A. Y. Kale, “Anisotropic Bulk Viscous Cosmological Models with Variable G and ?,” International Journal of Theoretical Physics, Vol. 48, No. 4, 2009, pp. 1175-1185.

[29] R. Bali and S. Tinker, “Bianchi Type-III Bulk Viscous Barotropic Fluid Cosmological Models with Variable G and ?,” Chinese Physics Letters, Vol. 26, No. 2, 2009, pp. 029802. doi:10.1088/0256-307X/26/2/029802

[30] M. K. Verma and Shri Ram, “Bulk Viscous Bianchi Type-III Model with Time-Dependent G and ?,” International Journal of Theoretical Physics, Vol. 49, No. 4, 2009, pp. 693-700. doi:10.1007/s10773-010-0248-y

[31] A. Pradhan and R. Bali, “Magnetized Bianchi Type VI0 Barotropic Massive String Universe with Decaying Vacuum Energy Density ?,” Electronic Journal of Theoretical Physics, Vol. 5, No. 19, 2008, pp. 91-104.

[32] A. Pradhan, P. Yadav and K. Jotania, “A New Class of LRS Bianchi Type VI0 Universe with Free Gravitational Field and Decaying Vacuum Energy Density,” arXiv:0907.485 [gr-qc], 2009.

[33] R. Maartens, “Dissipative Cosmology,” Quantum Gravity, Vol. 12, No. 6, 1995, pp. 1455-1465. doi:10.1088/0264-9381/12/6/011

[34] S. Weinberg, “In Gravitation and Cosmology,” Wiley, New York, 1972.

[35] G. L. Murphy, “Big-Bang without Singularities,” Physical Review D, Vol. 8, No. 12, 1973, pp. 4231-4233. doi:10.1103/PhysRevD.8.4231

[36] V. A. Belinskii and I. M. Khalatnikov, “Effect of Viscosity on Nature of Cosmological Evolution,” Soviet Physics-JETP, Vol. 42, No. 2, 1976, pp. 205.