Einstein's field equations with variable gravitational and cosmological constants are considered in the presence of bulk viscous fluid for the totally anisotropic Bianchi type II space-time in such a way as to preserve the energy momentum tensor. We have presented solutions of field equations which represent expanding, shearing and non-rotating cosmological models of the universe. The physical behaviours of the models are discussed .We observe that the results obtained match with recent observations of SNIa.
KeywordsBianchi IICosmologyHubble ParameterBulk ViscosityVariable G and Λ
E. Guzman, “General Vacuum Solution for Brans-Dicke Bianchi Type II,” Astrophysics and Space Science, Vol. 179, No. 2, 1996, pp. 331-334. doi:10.1007/BF00646953
J. K. Singh and S. Ram, “A Study on Totally Anisotropic bianchi Type II Space-Time,” IL Nuova Cimento B, Vol. 111, 1996, pp. 1487-1494.
D. Saez and V. J. Ballester, “A Simple Coupling with Cosmological Implications,” Physics Letter A, Vol. 113, No. 9, 1985, pp. 467-470. doi:10.1016/0375-9601(86)90121-0
Y. K. Lau and S. J. Prokhovnik, “The Large Numbers Hypothesis and a Realistic Theory of Gravitation,” Australian Journal Physics, Vol. 39, No. 3, 1986, pp. 339- 346. doi:10.1071/PH860339
J. K. Singh, C. P. Singh and S. Ram, “Totally Anisotropic Bianchi Type II Cosmological Models in Lyra’s Geometry,” Proceeding of Mathematical Society B.H.U, Vol. 11, 1996, pp. 83-88.
A. K. Yadav and A. Haque, “Lyra’s Cosmology of Massive String in Anisotropic Bianchi-II Space-Time,” International Journal of Theoretical Physics, Vol. 50, 2011, pp. 2850-2863. doi:10.1007/s100773-011-0784-0
C. W. Misner, “Transport Processes in the Primordial Fireball,” Nature, Vol. 214, 1967, pp. 40-41. doi:10.1038/214040a0
C. W. Misner, “The Isotropy of the Universe,” Astrophysics Journal, Vol. 151, 1968, pp. 431-457. doi:10.1086/149448
G. L. Murphy, “Bing-Bang without Singularities,” Physical Review D, Vol. 8, No. 12, 1973, pp. 4231-4233. doi:10.1103/PhysRevD.8.4231
I. Grin, “Viscous Inflationary Universe Models,” Astrophysics and Space Science, Vol. 173, No. 2, 1990, pp. 191-225. doi:10.1007/BF00643930
K. A. Dunn and B. O. J. Tupper, “Tilting and Viscous Models in a Class of Type-VI0 Cosmologies,” Astrophysical Journal, Vol. 222, No. 2, 1978, pp. 405-411. doi:10.1086/156154
A. A. Coley and B. O. J. Tupper, “Viscous-Fluid Collapse,” Physical Review D, Vol. 29, No. 12, 1984, pp. 2701-2704. doi:10.1103/PhysRevD.29.2701
A. Banerjee and N. O. Santos, “Solutions of Einstein- Yang-Mills Equations with Plane Symmetry,” Journal of Mathematical Physics, Vol. 24, No. 11, 1983, pp. 2635- 2636. doi:10.1063/1.525637
A. Banerjee and N. O. Santos, “Spatially Homogeneous Cosmological Models,” General Relativity and Gravitation, Vol. 16, No. 3, 1984, pp. 217-224. doi:10.1007/BF00762537
T. Padmanabhan and S. M. Chitre, “Viscous Universe,” Physics Letter A, Vol. 120, No. 9, 1987, pp. 433-436. doi:10.1016/0375-9601(87)90104-6
P. G. Bergmann, “Comments on the Scalar-Tensor Theory,” International Journal of Theoretical Physics, Vol. 1, No. 1, 1968, pp. 25-36. doi:10.1007/BF00668828
J. Drietlein, “Broken Symmetry and Cosmological Constant,” Physical Review Letter, Vol. 33, No. 20, 1974, pp. 1243-1244. doi:10.1103/PhysRevLett.33.1243
P. A. M. Dirac, “The Cosmological Constant,” Nature, Vol. 139, 1937, pp. 323-323. doi:10.1038/139323a0
A. Beesham, “Comment on the Paper ‘The Cosmological Constant L as a Possible Link to Einstein’ Theory of Gravity, the Problem of Hadronic and Creation,” IL Nuovo Cimento, Vol. B96, No. 4, 1986, pp. 17-20.
A. Beesham, “Variable-G Cosmology and Creation,” International Journal of Theoretical Physics, Vol. 25, No. 12, 1986, pp. 1295-1298. doi:10.1007/BF00670415
M. S. Berman, “Cosmological Models with Variable Gravitation and Cosmological Constant,” General Relativity and Gravitation, Vol. 23, No. 4, 1991, pp. 465-469. doi:10.1007/BF00756609
D. Kalligas, P. Wesson and C. W. F. Everitt, “Flat FRW Models with Variable-G and L,” General Relativity and Gravitation, Vol. 24, 1992, pp. 351-357. doi:10.1007/BF00760411
Abdussattar and R. G. Vishwakarma, “Some FRW Models with Variable G and L,” Classical Quantum Gravity, Vol. 14, No. 4, 1997, pp. 945-953. doi:10.1088/0264-9381/14/4/011
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
A. I. Arbab, “Bianchi Type I Viscous Universe with Variable G and L,” General Relativity and Gravitation, Vol. 30, No. 9, 1998, pp. 1401-1405. doi:10.1023/A:1018856625508
T. Singh, A. Beesam and W. S. Mbokazi, “Bulk Viscous Cosmological Models with Variable G and L,” General Relativity and Gravitation, Vol. 30, No. 4, 1991, pp. 573- 581. doi:10.1023/A:1018866107585
C. P. Singh, S. Kumar and A. Pradhan, “Early Viscous Universe with Variable Gravitational and Cosmological Constants,” Classical Quantum Gravity, Vol. 24, No. 2, 2007, pp. 455-474. doi:10.1088/0264-9381/24/2/011
A. Pradhan and S. S. Kumhar, “LRS Bianchi Type II Bulk Viscous Fluid Universe with Decaying Vacuum Energy Density L,” International Journal of Theoretical Physics, Vol. 48, No. 5, 2009, pp. 1466-1477. doi:10.1007/s10773-008-9918-4
M. K. Verma and S. Ram, “Bulk Viscous Bianchi Type- III Cosmological Model with Time-Dependent G and L,” International Journal of Theoretical Physics Vol. 49, No. 4, 2010, pp. 693-700. doi:10.1007/s10773-010-0248-y
M. K. Verma and S. Ram, “Spatially Homogeneous Bulk Viscous Fluid Models with Time-Dependent Gravitational Constant and Cosmological Term,” Advanced Studies in Theoretical Physics, Vol. 5, No. 8, 2011, pp. 387-398.
R. Bali and S. Tinker, “Bianchi Type III Bulk Viscous Barotropic Fluid Cosmological Models with Variable G and L,” Chinese Physics Letter, Vol. 26, No. 2, 2009, pp. 029802-029806. doi:10.1088/0256-307X/26/2/029802
S. Weinberg, “Nonlinear Realizations of Chiral Symmetry,” Physical Review, Vol. 166, No. 5, 1968, pp. 1568- 1577. doi:10.1103/PhysRev.166.1568