Open Access
Article
Bianchi Type-I Bulk Viscous String Model in f(R) Gravity
*M. Vijaya SanthiCorresponding authorgv.santhi@live.comDepartment of Applied Mathematics, Andhra University-Visakhapatnam, Andhra Pradesh, 530003, IndiaView full profile → , V.U.M. Raoumra057@hotmail.comDepartment of Applied Mathematics, Andhra University-Visakhapatnam, Andhra Pradesh, 530003, IndiaView full profile → , Y. Adityaaditya.y@gmrit.edu.inDepartment of Applied Mathematics, Andhra University-Department of Mathematics GMR Institute of TechnologyRajam, Andhra Pradesh, 532127, IndiaView full profile →
* Corresponding author · click or hover a name for details
- Received:
- 11 Feb 2018
- Accepted:
- 24 Mar 2018
- Published Online:
- 02 Jan 2019
- Article type:
- Article
- Language:
- EN
- Article no.:
- 1726037X.2019.1611729
- Pages:
- 23–38
Abstract
Field equations of undefined theory of gravity are obtained with the aid of locally rotationally symmetric (LRS) Bianchi type-I metric when the matter source is a bulk viscous fluid containing one dimensional cosmic strings. Applying some physically possible conditions, we have obtained a determinate solution of the field equations. The deceleration parameter of our model exhibits a smooth transition from early decelerated phase to late time accelerating phase. We also find that the realistic energy conditions p ≥ 0 and pp ≤ 0 are satisfied in our model. Some other properties of the model are also discussed.
References
M.J.Amir, S.Sattar, Locally Rotationally Symmetric Vacuum Solutions in f(R) Gravity , it Int J Theor Phys , , ( 2014 ), 773 – 787 . R.Bali, A.Pradhan, Bianchi type-III string cosmological model with time dependent bulk viscosity , Chin. Phys. Lett. , ( 2007 ), 585 . K.Bamba, , Dark energy cosmology: the equivalent description via different theoretical models and cosmography tests , Astrophys. Space Sci. , ( 2012 ), 155 - 228 . I.Brevik, O.Gorbunova, Y.A.Shaido, Viscous FRW Cosmology in Modified Gravity , Int. J. Mod. Phys. D, , ( 2005 ), 1899 - 1906 . S.Capozziello, M.Laurentis, Extended Theories of Gravity , Phys. Rep. , ( 2011 ), 167 - 231 . S.Capozziello, , Quintessence without scalar fields , Recent Res. Dev. Astron. Astrophys. , , ( 2003 ), 625 . T.Chiba, , Solar System constraints to general f(R) gravity , Phys. Rev. D, , ( 2007 ) 124014 . C.B.Collins, , Exact spatially homogeneous cosmologies , Gen. Relativ. Gravit. , , ( 1980 ), 805 - 823 . H.K.Eriksen, , Asymmetries in the CMB anisotropy field , Astrophys. J. , , ( 2004 ), 14 - 20 . T.R.Jaffe, , Fast and Efficient Template Fitting of Deterministic Anisotropic Cosmological Models Applied to WMAP Data , Astrophys. J. , , ( 2006 ), 616 - 629 . V.B.Johri, R.Sudharsan, BD-FRW Cosmology with Bulk Viscosity , Aust. J. Phys. , , ( 1989 ), 215 - 222 . S.D.Katore, Bianchi TypeII, VIII and IX String Cosmological Models in f(R) Gravity , Int J Theor Phys54 , ( 2015 ), 2700 - 2711 W.B.Kibble, Topology of cosmic domains and strings, J. Phys. A, , ( 1976 ) 1387 - 1398 . P.S.Letelier, String cosmologies , Phys. Rev. D, , ( 1983 ), 2414 . G.L.Murphy, Big-Bang Model Without Singularities , Phys. Rev. D, , ( 1973 ) 4231 . S.Nojiri, S.D.Odintsov, Unified cosmic history in modified gravity: from F(R) theory to Lorentz non-invariant models , Phys. Rep. , ( 2011 ), 59 - 114 . S.Nojiri, S.D.Odintsov, Modified gravity with negative and positive powers of curvature: Unification of inflation and cosmic acceleration , Phys. Rev. D, , ( 2003 ), 123512 . S.Nojiri, S.D.Odintsov, Introduction to Modified Gravity and Gravitational Alternative for Dark Energy , Int. J. Geom. Meth. Mod. Phys. , , ( 2007 ), 115 - 146 . S.Nojiri, S. D.Odintsov, Modified f ( R, T ) gravity consistent with realistic cosmology: From a matter dominated epoch to a dark energy universe , Phys. Rev. D, , ( 2006 ) 086005 . S.Nojiri, , Modified gravity theories on a nutshell: Inflation, bounce and late-time evolution , Physics Reports, ( 2017 ) 1 – 104 . S.Perlmutter, , Measurements of Omega and Lambda from 42 High-Redshift Supernovae , Astrophys. J. , , ( 1999 ), 565 - 586 . V.U.M.Rao, , Exact Bianchi type II, VIII and IX string cosmological models in Saez-Ballester theory of gravitation , Astrophys Space Sci, , ( 2008 ), 73 - 77 . V.U.M.Rao, , Exact Bianchi type II, VIII and IX string cosmological models in General Relativity and self-creation theory of gravitation , Astrophys Space Sci, , ( 2008 ), 83 - 88 . V.U.M.Rao, , Axially symmetric string cosmological models in Brans-Dicke theory of gravitation Astrophys Space Sci, , ( 2009 ), 401 - 405 . V.U.M.Rao, , FRW Closed Bulk Viscous Cosmological Model in General Scalar Tensor Theory of Gravitation , Prespacetime J. , , ( 2015 ), 531 - 539 . V.U.M.Rao, , Bulk Viscous Cosmological Models with Wet Dark Fluid in a Saez-Ballester Theory of Gravitation , The African Review of Physics, , ( 2015 ), 0060 . V.U.M.Rao, , A New Class of Bulk Viscous Cosmological Models in a Modified Theory of Gravity , Prespacetime J ., , ( 2014 ) 521 - 540 . D.R.K.Reddy, , Kaluza-Klein universe with cosmic strings and bulk viscosity in f ( R, T ) gravity , Astrophys Space Sci, , ( 2013 ) 261 – 265 . D.R.K.Reddy, A string cosmological model in Brans-Dicke theory of gravitation , Astrophys. Space Sci. , , ( 2003 ), 365 - 371 . A.G.Riess, , Observational Evidence from Supernovae for an Accelerating Universe and a Cosmological Constant , Astrophys. J. , , ( 1998 ), 1009 - 1038 . T.V.Sagar, , Bianchi type-III bulk viscous string cosmological model in Brans-Dicke theory of gravitation , Astrophys Space Sci. , , ( 2014 ), 479 - 483 . P.K.Sahoo, B.Mishra, Cylindrically Symmetric Cosmic Strings Coupled with Maxwell Fields in Bimetric Relativity , International Journal of Pure and Applied Mathematics, , ( 2014 ), 275 - 284 . P.K.Sahoo, , Bianchi type string cosmological models in f(R,T) gravity , Eur. Phys. J. Plus, , ( 2016 ) 333 . M.V.Santhi, : Bulk viscous string cosmological models in f ( R) gravity , Canadian Journal of Physics, ( 1 ) , ( 2018 ), 55 - 61 . A.Sheykhi, Magnetic strings in f(R) gravity , Gen. Relativ Gravit, , ( 2012 ), 2271 - 2281 . Shri Ram, M.K.Singh, M.K.Verma, Totally Anisotropic Cosmological Models with Bulk Viscosity for Variable G and Λ , Journal of Modern Physics, , ( 2012 ), 9 - 15 . M.Sharif, M.F.Shamir, Exact solutions of Bianchi-type I and V space-times in the f(R) theory of gravity , Class. Quantum Grav. , , ( 2009 ), 235020 . M.F.Shamir, Some Bianchi type cosmological models in f(R) gravity , Astrophys Space Sci. , , ( 2010 ), 183 - 189 . M.F.Shamir, Plane Symmetric Vacuum Bianchi Type III Cosmology in f (R) Gravity , Int J Theor Phys, , ( 2011 ), 637 - 643 . M.Sharif, M.F.Shamir, Non-vacuum Bianchi types I and V in f(R) gravity , Gen Relativ Gravit, , ( 2010 ), 2643 - 2655 . M.Sharif, H.R.Kausar, Non-vacuum solutions of Bianchi type V I0 universe in f(R) gravity , Astrophys Space Sci. , , ( 2011 ), 463 - 471 . V.Singh, C.P.Singh, Functional form of f(R) with power-law expansion in anisotropic model , Astrophys Space Sci. , , ( 2013 ), 285 - 289 . J.Stachel, Thickening the string. I. The string perfect dust , Phys. Rev. D, , ( 1980 ) 2171 . S.K.Tripathy, , Bulk viscous string cosmological models with electromagnetic field , Astrophys. Space Sci. , , ( 2009 ), 247 - 252 . K.Uddin, , Cosmological perturbations in Palatini-modified gravity , Class. Quantum Grav. , , ( 2007 ) 3951 - 3962 . A.Vilenkin, Cosmic strings and domain walls , Phys. Rep., , ( 1985 ) 263 - 315 . X.X.Wang, Bianchi Type-III String Cosmological Model with Bulk Viscosity in General Relativity , Chin. Phys. Lett. , , ( 2005 ), 29 . I.Yilmaz, , Quark and strange quark matter in f(R) gravity for Bianchi type I and V space-times , Gen Relativ Gravit, , ( 2012 ), 2313 - 2328 .
Views: 11Downloads: 6Citations: 5
