Bianchi Type-II, VIII & IX Perfect Fluid Cosmological Models in Brans Dicke Theory of Gravitation

Velagapudi Uma Maheswara Rao, Mandangi Vijaya Santhi

.

DOI: 10.4236/jmp.2011.210151                

Abstract

Field equations in the presence of perfect fluid distribution are obtained in a scalar tensor theory of gravitation proposed by Brans and Dicke[1] with the aid of Bianchi type-II, VIII & IX metrics. Exact prefect fluid Bianchi type- IX cosmological model is presented since other models doesn’t exist in Brans-Dicke scalar tensor theory of gravitation. Some physical properties of the model are also discussed.

Keywords

Bianchi Type-II, VIII & IX, Brans Dicke Scalar Tensor Theory, Perfect Fluid Distribution

Conflicts of Interest

The authors declare no conflicts of interest.

References

[1]	H. Brans and R. H. Dicke, “Mach’s Principle and a Rela- tivistic Theory of Gravitation,” Physical Review A, Vol. 124, No. 3, 1961, pp.925-935. doi:10.1103/PhysRev.124.925
[2]	C. Mathiazhagan and V. B. Johri, “An Inflationary Uni- verse in Brans-Dicke Theory: A Hopeful Sign of Theo- retical Estimation of the Gravitational Constant,” Classi- cal and Quantum Gravity, Vol. 1, No.2, 1984, pp. L29- L32. doi:10.1088/0264-9381/1/2/005
[3]	L. O. Pimentel, “New Exact Vacuum Solutions in Brans- Dicke Theory,” Modern Physics Letters A, Vol. 12, No. 25, 1997, pp. 1865-1870. doi:10.1142/S0217732397001904
[4]	A. D. Linde, “Extended Chaotic Inflation and Spatial Variations of the Gravitational Constant,” Physics Letters B, Vol. 238, No. 2-4, 1990, pp. 160-165. doi:10.1016/0370-2693(90)91713-L
[5]	T. Singh and L. N. Rai, “Scalar-Tensor Theories of Gra- vitation: Foundations and Prospects,” General Relativity and Gravitation, Vol. 15, No. 9, 1983, pp. 875-902. doi:10.1007/BF00778798
[6]	H. Nariai, “Hamiltonian Approach to the Dynamics of Expanding Homogeneous Universes in the Brans-Dicke Cosmology,” Progress of Theoretical Physics, Vol. 47, No. 6, 1972, pp. 1824-1843. doi:10.1143/PTP.47.1824
[7]	V. A. Belinskii and I. M. Khalatnikov, “Effect of Scalar and Vector Fields on the Nature of the Cosmological Singularity,” Soviet Physics–JETP, Vol. 36, No. 4, 1973, pp. 591-597.
[8]	D. R. K. Reddy and V. U. M. Rao, “Field of a Charged Particle in Brans-Dicke Theory of Gravitation,” Journal of Physics A: Mathematical and General, Vol. 14, No. 8, 1981, pp. 1973-1976. doi:10.1088/0305-4470/14/8/021
[9]	A. Banerjee and N.O. Santos, “Bianchi Type-II Cosmo- logical Models in Brans-Dicke Theory,” Il Nuovo Cimento B, Vol. 67, No. 1, 1982, pp. 31-40. doi:10.1007/BF02721068
[10]	T. Singh, L. N. Rai and T. Singh, “An Anisotropic Cos- mological Model in Brans-Dicke Theory,” Astrophysics and Space Science, Vol. 96, No. 1, 1983, pp. 95-105.
[11]	S. Ram, “Spatially Homogeneous and Anisotropic Cosmological Solution in Brans-Dicke Theory,” General Relativity and Gravitation, Vol. 15, No. 7, 1983, pp. 635- 640. doi:10.1007/BF00759040
[12]	S. Ram and D. K. Singh, “LRS Bianchi Type-V Vacuum Cosmological Solution in Brans-Dicke Theory,” Astrophysics and Space Science, Vol. 98, No. 1, 1984, pp. 193- 196. doi:10.1007/BF00651959
[13]	M. S. Berman, M. M. Som and F. M. Gomide, “Brans- Dicke Static Universes,” General Relativity and Gravita- tion, Vol. 21, No. 3, 1989, pp. 287-292. doi:10.1007/BF00764101
[14]	D. R. K. Reddy, “A String Cosmological Model in a Sca- lar-Tensor Theory of Gravitation,” Astrophysics and Space Science, Vol. 286, No. 3-4, 2003, pp. 359-363. doi:10.1023/A:1026370732619
[15]	D. R. K. Reddy and R. L. Naidu, “Five Dimensional String Cosmological Models in a Scalar-Tensor Theory of Gravitation,” Astrophysics and Space Science, Vol. 307, No. 4, 2007, pp. 395-398. doi:10.1007/s10509-007-9387-x
[16]	K. S. Adhav, A. S. Nimkar and M. V. Dawande, “N- Dimensional String Cosmological Model in Brans-Dicke Theory of Gravitation,” Astrophysics and Space Science, Vol. 310, No. 3-4, 2007, pp. 231-235. doi:10.1007/s10509-007-9506-8
[17]	V. U. M. Rao, T. Vinutha, M. V. Shanthi and K. V. S. Sireesha, “Exact Bianchi Type-V Perfect Fluid Cosmo- logical Models in Brans-Dicke Theory of Gravitation,” Astrophysics and Space Science, Vol. 315, No. 1-4, 2008, pp. 211-214. doi:10.1007/s10509-008-9820-9
[18]	V. U. M. Rao, T. Vinutha and M. V. Santhi, “Bianchi Type-V Cosmological Model with Perfect Fluid Using Negative Constant Deceleration Parameter in a Scalar Tensor Theory Based on Lyra Manifold,” Astrophysics and Space Science, Vol. 314, No. 1-3, 2008, pp. 213-216. doi:10.1007/s10509-008-9757-z
[19]	S. Chakraborty, “A Study on Bianchi-IX Cosmological Model,” Astrophysics and Space Science, Vol. 180, No. 2, 1991, pp. 293-303. doi:10.1007/BF00648184
[20]	R. Bali and S. Dave, “Bianchi Type IX String Cosmo- logical Model in General Relativity,” Pramana Journal of Physics, Vol. 56, No. 4, 2001, pp. 513-518. doi:10.1007/s12043-001-0100-2
[21]	R. Bali and M. K. Yadav, “Bianchi Type-IX Viscous Fluid Cosmological Model in General Relativity,” Pra- mana Journal of Physics, Vol. 64, No. 2, 2005, pp. 187- 196. doi:10.1007/BF02704873
[22]	D. R. K. Reddy, B. M. Patrudu and R. Venkateswarlu, “Exact Bianchi Type-II, VIII and IX Cosmological Mod- els in Scale-Covariant Theory of Gravitation,” Astro- physics and Space Science, Vol. 204, No. 1, 1993, pp. 155-160. doi:10.1007/BF00658101
[23]	K. Shanthi and V. U. M. Rao, “Bianchi Type-II and III Models in Self-Creation Cosmology,” Astrophysics and Space Science, Vol. 179, No.1, 1991, pp. 147-153. doi:10.1007/BF00642359
[24]	V. U. M. Rao and Y. V. S. S. Sanyasiraju, “Exact Bian- chi-Type VIII and IX Models in the Presence of Zero- Mass Scalar Fields,” Astrophysics and Space Science, Vol. 187, No. 1, 1992, pp.113-117. doi:10.1007/BF00642691
[25]	Y. V. S. S. Sanyasiraju and V. U. M. Rao, “Exact Bian- chi-Type VIII and IX Models in the Presence of the Self-Creation Theory of Cosmology,” Astrophysics and Space Science, Vol. 189, No. 1, 1992, pp. 39-43. doi:10.1007/BF00642950
[26]	F. Rahaman, S. Chakraborty, N. Begum, M. Hossain and M. Kalam, “Bianchi-IX String Cosmological Model in Lyra Geometry,” Pramana Journal of Physics, Vol. 60, No. 6, 2003, pp. 1153-1159. doi:10.1007/BF02704282
[27]	D. K. Sen, “A Static Cosmological Model,” Zeitschrift for Physics A, Vol. 149, No. 3, 1957, pp. 311-323.
[28]	G. Lyra, “über eine Modifikation der Riemannschen Geometrie,” Mathematische Zeitschrift, Vol. 54, No. 1, 1951, pp. 52-64. doi:10.1007/BF01175135
[29]	V. U. M. Rao, M. V. Santhi and T. Vinutha, “Exact Bi- anchi Type-II, VIII and IX String Cosmological Models in Saez-Ballester Theory of Gravitation,” Astrophysics and Space Science, Vol. 314, No. 1-3, 2008, pp. 73-77. doi:10.1007/s10509-008-9739-1
[30]	V. U. M. Rao, M. V. Santhi and T. Vinutha, “Exact Bi- anchi Type-II, VIII and IX Perfect Fluid Cosmological Models in Saez-Ballester Theory of Gravitation,” Astro- physics and Space Science, Vol. 317, No. 1-2, 2008, pp. 27-30. doi:10.1007/s10509-008-9849-9
[31]	V. U. M. Rao, M. V. Santhi and T. Vinutha, “Exact Bi- anchi Type-II, VIII and IX String Cosmological Models in General Relativity and Self-Creation Theory of Gravi- tation,” Astrophysics and Space Science, Vol. 317, No. 1-2, 2008, pp. 83-88. doi:10.1007/s10509-008-9859-7