Open Access Peer-reviewed

Anisotropic Bianchi Type-II Viscous Fluid Models with Time-Dependent Gravitational and Cosmological Constants

M. K. Singh1, M. K. Verma1, Shri Ram1,

1Department of Applied Mathematics, Indian Institute of Technology, Banaras Hindu University, Varanasi, India

International Journal of Physics. 2013, 1(4), 77-83. DOI: 10.12691/ijp-1-4-1
Published online: August 25, 2017

Abstract

This paper deals with totally anisotropic Bianchi type-II cosmological models filled with a bulk viscous fluid in the presence of time-varying gravitational and cosmological constants. Exact solutions of the field equations are obtained by applying a special law of variation for Hubble’s parameter which yields a constant value of the deceleration parameter. Two different physically viable models of the universe are presented in two types of cosmologies, one with power-law expansion and other one with exponential expansion. Cosmological model with power-law expansion has an initial big-bang type singularity at t = 0, whereas the model with exponential expansion has a singularity in infinite past. The physical and dynamical properties of the models are discussed.

Keywords:

Bianchi II, bulk viscosity, gravitational constant, cosmological constant
[1]  M. P. Ryan and L. C. Shepley, Homogeneous Relativistic Cosmologies, Princeton University Press, Priceton, New Jersey, 1975.
 
[2]  E. Asseo and H. Sol, Extragalactic Magnetic Fields. Phys. Rep. 148, 407-435, 1987.View Article
 
[3]  J. Hajj-Boutros, A Method for generating Bianchi type-II cosmological Models. J. Math. Phys. 27, 1592-1594, 1986.View Article
 
[4]  J. Hajj-Boutros, Cosmological Models. Int. J. Theor. Phys. 28, 487-493, 1989.View Article
 
[5]  J. K. Singh and Shri Ram, Cylindrically Symmetric Scalar Waves in General Relativity. IL Nuovo Cimento B 111, 757-762, 1996.
 
[6]  R. Venkateswarlu and D. R. K. Reddy, Exact Bianchi type-II, VIII and IX Cosmological Models with Matter and Electromagnetic Fields in Lyra’s Geometry. Astrophys. Space Sci. 182, 97-103, 1991.View Article
 
[7]  A. A. Coley and J. Wainright, Qualitative Analysis of Two-Fluid Bianchi Cosmologies. Class. Quantum Grav. 9, 651-665, 1991.View Article
 
[8]  C. P. Singh and S. Kumar, Bianchi Type-II Inflationary Models with Constant Deceleration Parameter in General Relativity. Pramana J. Phys. 68, 707-720, 2007.View Article
 
[9]  A. Pradhan, H. Amirhashchi and M. K. Yadav, LRS Bianchi Type-II String Cosmological Models for Perfect Fluid Distribution in General Relativity. Fizika B 18, 35-42, 2009.
 
[10]  A. Pradhan, P. Ram and R. Singh, LRS Bianchi Type-II String Cosmological Model in General Relativity. Astrophys. Space Sci. 331, 275-279, 2011.View Article
 
[11]  H. Amirhashchi and H. Zainuddin, Some LRS Bianchi Type-II String-Dust Cosmological Models in General Relativity. Elect. J. Theor. Phys. 23, 213-220, 2010.
 
[12]  S. Weinberg, Gravitation and cosmology. Wiley New York Chap. 15, 1972.
 
[13]  C. W. Misner, The Isotropy of the Universe. Astrophys J. 151, 431-457, 1968.View Article
 
[14]  V. A. Belinskii and I. M. Khalatnikov, Influence of Viscosity on the Character of Cosmological Evolution. Sov. Phys. JETP 42, 205-210, 1976.
 
[15]  G. L. Murphy, Big-Bang Model without Singularities. Phys. Rev. D 8, 4231-4233, 1973.View Article
 
[16]  P. G. Bergmann, Comments on Scalar Tensor Theory. Int. J. Theor. Phys. 1, 25-36, 1968.View Article
 
[17]  J. Drietlein, Broken Symmetry and the Cosmological Constant. Phys. Rev. Lett. 33, 1243- 1244, 1974.View Article
 
[18]  G. F. F, Ellis, c is the speed of Light, Isn’t? Am. J. Phys. 73, 240-247, 2005.View Article
 
[19]  A. Beesham, Comment on the Paper “The Cosmological Constant as a Possible Primordial Link to Einstein’s Theory of Gravity, the Problem of Hadronic Matter and Problem”. Nuovo Cimento B 96, 17-20, 1986.View Article
 
[20]  M.S. Berman, Cosmological Models with Variable Gravitational and Cosmological Constant “Constant”. Gen. Relativ. Gravit. 23, 465-496, 1991.View Article
 
[21]  D. Kalligas, P. Wesson and C. W. F. Everitt, Flat FRW models with variable G and Λ Gen. Relativ. Gravit. 24, 351-357, 1992.View Article
 
[22]  A. I. Arbab, Cosmological Models with Variable Cosmological and Gravitational “Constants” and Bulk Viscous Models. Gen. Relativ. Gravit. 29, 6174, 1997.View Article
 
[23]  Abdussattar and R. G. Vishwakarma, Some FRW models with variable G and Λ. Class. Quantum Grav. 14, 945-953, 1997.View Article
 
[24]  J. D. Barrow and P. Parsons, Behavior of cosmological models with varying G. Phys. Rev. D 55, 1906-1936, 1997.View Article
 
[25]  A. Pradhan and I. Chakraborty, LRS Bianchi I models with time varying gravitational and cosmological constants. Gravitation and Cosmology 7, 55-57, 2001.
 
[26]  A. Pradhan and V. K. Yadav, Bulk Viscous Anisotropic Cosmological Models with Variable G and Λ. Int. J. Mod. Phys. D 11, 893-912, 2002.View Article
 
[27]  G. P. Singh and S. Kotambkar, Higher-Dimensional Dissipative Cosmology with Varying G and Λ. Gravitation and Cosmology 9, 206-210, 2003.
 
[28]  A. Pradhan, A. K. Singh and S. Otarod, FRW Universe with Variable G and Λ Terms. Roman. J. Phys. 52, 415-429, 2007.
 
[29]  J. P. Singh, A. Pradhan and A. K. Singh, Bianchi Type-I Cosmological Models with Variable G and Λ in General Relativity. Astrophys. Space Sci.314, 83-88, 2008.View Article
 
[30]  T. Padmanabhan and S. M. Chitre, Viscous Universes. Phys. Lett. A 120, 433-436, 1987.View Article
 
[31]  A. Beesham, Bianchi type I Cosmological Models with Variable G and Λ. Gen. Relativ. Gravit. 26, 159-165, 1994.View Article
 
[32]  G. P. Singh and A. Y. Kale, Anisotropic Bulk Viscous Cosmological Models with Variable G and Λ. Int. J. Theor. Phys. 48, 1177-1185, 2009.View Article
 
[33]  C. P. Singh, S. Kumar and A. Pradhan, Early Viscous Universe with Variable Gravitational and Cosmological ‘Constants’.Class. Quantum Gravity 24, 455-474, 2007.View Article
 
[34]  A. Pradhan and S. S. Kumhar, LRS Bianchi Type-II Bulk Viscous Fluid Universe with Decaying vacuum Energy DensityΛ. Int. J. Theor.Phys. 48, 1466-1477, 2009.View Article
 
[35]  J. P. Singh, R. K. Tiwari and P. Shukla, Bianchi Type-III Cosmological Models with Gravitational Constant G and the Cosmological Constant Λ. Chin. Phys. Lett. 12, 3325-3327, 2007.View Article
 
[36]  S. Chakraborty and A. Roy, Anisotropic Cosmological Models with Bulk Viscosity for Variable G and Λ. Astrophys. Space Sci. 313, 389-392, 2008.View Article
 
[37]  R. Bali and S. Tinker, Bianchi Type III Bulk Viscous Barotropic Fluid Cosmological Models with Variable 𝐺 and Λ. Chin. Phys. Lett. 26, 029802-029802-029805, 2009.
 
[38]  M. K.Verma and Shri Ram, Hypersurface-Homogeneous Bulk Viscous Fluid Space-Time with Time-Dependent Cosmological Term. Astrophys. Space Sci. 326, 299-304, 2010.View Article
 
[39]  M. K. Verma and Shri Ram, Bulk Viscous Bianchi Type-II Cosmological Models with Time-Dependent G and Λ. Int. J. Theor.Phys. 49, 693-700, 2010.View Article
 
[40]  M. K. Verma and Shri Ram, Bianchi Type VI0 Bulk Viscous Fluid Models with Variable Gravitational and Cosmological Constant. Appl. Math. 2, 348-354, 2011.View Article
 
[41]  H. Amirshashchi, LRS Bianchi Type-II Stiff Fluid Cosmological Models with Decaying Vacuum Energy Density Λ in General Relativity. Phys. Lett. B 697, 429-433. 2011.View Article
 
[42]  J. K. Singh and N. K. Sharma, Some Bianchi Type-II Cosmological Models in Brans-Dicke Theory. Astrophys. Space Sci. 327, 293-298, 2010.View Article
 
[43]  K. Jotania, P. Yadav and S. A. Faruqi, Magnetized String Cosmology in Anisotropic Bianchi-II Space-time with Variable Cosmological Term-Λ. Int. J. Theor. Phys. 50, 1424-1443, 2011.View Article
 
[44]  P. S. Baghel and J. P. Singh, Bianchi Type V Universe with Bulk Viscous Matter and TimeVarying Gravitational and Cosmological Constants. Research in Astronomy and Astrophysics. 12, 1457-1466, 2012.View Article
 
[45]  Priyanka Kumari, M. K. Singh and Shri Ram, Anisotropic Bianchi Type-III Bulk Viscous Fluid Universe in Lyra Geometry. Adv. Math. Phys.http://dx.doi.org/10.1155/2013/416294, 2013.
 
[46]  M. S. Berman, A Special Law of Variation for Hubble’s Parameter. IL Nuovo. Cim. B 74, 182-186, 1983.View Article
 
[47]  M. S. Berman and F. M. Gomide, Cosmological Models with Constant Deceleration Parameter. Gen. Rel. Grav. 20, 191-198, 1988.View Article
 
[48]  Shri Ram, M. K. Verma and M. Zeyauddin, Spatially Homogeneous Bianchi Type V Cosmological Model in the Scale-Covariant Theory of Gravitation. Chinese Phys. Lett. 26, 089802-089805, 2009.View Article
 
[49]  B. Saha and V. Rikhvitsky, Bianchi Type I Universe with Viscous Fluid and a Λ Term: A Qualitative Analysis. Physica D 219, 168-176, 2006.View Article
 
[50]  B. Saha, Anisotropic Cosmological Models with a Perfect Fluid and a Λ Term. Astrophys. Space Sci. 302, 83-91, 2006.View Article
 
[51]  Shri Ram, M. K.Verma and M. Zeyauddin, Homogeneous Anisotropic Cosmological Models With Viscous Fluid and Heat Flow in Lyra’s Geometry. Mod. Phys. Lett. 24, 1847-1856, 2009.View Article
 
[52]  Shri Ram, M. Zeyauddin and C. P. Singh, Bianchi Type-V Cosmological Models with Perfect Fluid and Heat Conduction in Lyra’s Geometry. Int. J. Mod. Phys. A 23, 4991-5005, 2008.View Article
 
[53]  R. G. Vishwakarma, Is the present expansion of the Universe really accelerating? Mon. Not. R. Astro. Soc. 345, 545-551, 2003.View Article