Some Exact Bianchi Types Cosmological Models in f(R, T) Theory of Gravity

Year 2019, Volume: 2 Issue: 3, 163 - 175, 26.12.2019

Ahmed Al-haysah , Abdulvahid Hasmani

https://doi.org/10.33187/jmsm.435340

Abstract

In this paper, we attempt to study spatially homogeneous Bianchi types-III, V,  VI$_0$ $\&$ VI$_h$  cosmological models in $f(R, T)$  theory of gravity. Here the models are obtained by assuming forms of the function $f(R, T)$ as  $f(R, T)= R + 2f(T)$ and $f(R, T) = f_1(R)+f_2(T)$. The exact solutions of Einstein's field equations (EFEs) have been obtained for two different types of physically viable cosmologies using a special form of Hubble parameter (HP). The physical and geometrical properties of these models have been discussed and expressions for the Ricci scalar $R$ in each case are obtained.

Keywords

Bianchi types-III V VI$_0$ $\&$ VI$_h$, $f(R-T)$ theory of gravity, Cosmic time, Cosmological constant, Exact solutions, Hubble parameter, Variational principle

References

• [1] S. Cotsakis, E. Papantonopoulos, Cosmological Crossroads: An Advanced Course in Mathematical, Physical and String Cosmology, Springer Sci. & Business Media, 2002.
• [2] P. Agrawal, D. Pawar, Plane symmetric cosmological model with quark and strange quark matter in f (R;T) theory of gravity, J. Astrophys. Astr., 38(2) (2017), 1-7, https://doi.org/10.1007/s12036-016-9420-y.
• [3] R. Chaubey, A. Shukla, A new class of Bianchi cosmological models in f (R;T) gravity, Astrophys. Space Sci., 343(1) (2013), 415-422, https://doi.org/10.1007/s10509-012-1204-5.
• [4] T. Harko, F. S. Lobo, S. Nojiri, S. D. Odintsov, f (R;T) gravity, Phys. Rev. D, 84(2) (2011), 024020-1 to 024020-14.
• [5] T. Harko, F. S. Lobo, Generalized dark gravity, Int. J. of Modern Phys. D, 21(11) (2012), 1242019-1 to 1242019-8, https://doi.org/10.1142/S0218-271812420199.
• [6] P. Sahoo, B. Mishra, G. C. Reddy, Axially symmetric cosmological model in f (R;T) gravity, Eur. Phys. J. Plus, 129(3) (2014), 1-8, https://doi.org/10.1140/epjp/i2014-14049-7.
• [7] P. Moraes, P. Sahoo, The simplest non-minimal matter-geometry coupling in the f (R;T) cosmology, The Eur. Phys. J. C, 77(7) (2017), 1-8, https://doi10.1140/epjc/s10052-017-5062-8.
• [8] K. Adhav, LRS Bianchi type-I cosmological model in f (R;T) theory of gravity, Astrophys. Space Sci., 339(2) (2012), 365-369, https://doi.org/10.10-07/s10509-011-09638.
• [9] D. Pawar, P. Arawal, Dark energy cosmological model in f (R;T) theory of gravity, Prespacetime J., 6(3) (2015), 719-732.
• [10] D. Pawar, P. Agrawal. Role of constant deceleration parameter in cosmological model filled with dark energy in f (R;T) theory, Bulg. J. of Phys., 43(2), (2016), 148-155.
• [11] D. Pawar, G. Bhuttampalle, P. Agrawal. Kaluza-klein string cosmological model in f (R;T) theory of gravity, New Astronomy, 65 (2018), 1-6, https://doi.org/10.1016/j.newast.2018.05.002.
• [12] R. S. Kumar, Some exact cosmological models in modified theories of gravitation, Ph.D. Thesis, Acharya Nagarjuna Uni., 2013.
• [13] D. Pawar, P. Arawal, Magnetized domain wall in f (R;T) theory of gravity, New Astronomy, 54 (2017), 56-60, https://doi.org/10.1016/j.newast.2017. 01.006.
• [14] L. D. Landau, The Classical Theory of Fields, Elsevier, 2013.
• [15] A. H. Hasmani, G. Rathva, Algebric computations in general relativity using mathemetica, Prajn. J. of Pure & Appl. Sci., 15 (2007), 77-81.
• [16] A. H. Hasmani, Algebraic computation of newmann-penrose scalars in general relativity using mathematica, J. of Sci. 1 (2010), 82-83.
• [17] V. Johri, K. Desikan, Cosmological models with constant deceleration parameter in Brans-Dicke theory, Gen. Relat. Gravit., 26(12) (1994), 1217-1232, https://doi.org/10.1007/BF0210671.
• [18] M. S. Berman, A special law of variation for hubbles parameter, Nuov. Cim. B, 74(2) (1983), 182-186, https://doi.org/10.1007/BF02721676.
• [19] N. J. Poplawski, The present universe in the Einstein frame, metrica affine R+1=R gravity, Class. Quantum Grav., 23(15) (2006), 4819-4827. https://doi.org/10.1088/0264-9381/23/15/003.
• [20] G. Magnano, Are there metric theories of gravity other than general relativity, Gen. Relat. & Gravi. Phys., (1995), arXiv:gr-qc/9511027v2.