110 B.Satyannarayana, R. Santhi Kumar, T.Ramprasad International Journal of Computer & Mathematical Sciences IJCMS ISSN 2347 – 8527 Volume 5, Issue 2 February 2016 Anisotropic Bianchi Type-I Cosmological Model in Modified Theory of Gravitation B.Satyannarayana, Assistant Professor, GMR Institute of Technology, Rajam, Srikakulam Dist, Andhra Pradesh State-532127, India. R. Santhi Kumar, Associate Professor, Aditya Institute of Technology and management, K.Kotturu, Srikakulam Dist, Andhra Pradesh -532203, India. T.Ramprasad , Assistant Professor, GMR Institute of Technology, Rajam, Srikakulam Dist, Andhra Pradesh State- 532127, India. ABSTRACT A spatially homogeneous and anisotropic Bianchi type-I model is obtained in the presence of perfect fluid source in the frame work of f( R,T ) gravity ( Harko et al. in Phys.Rev. D 84:024020, 2011) with the help of a special law of variation for Hubble’s parameter proposed by Bermann ( Nuovo Cimento B 74:182, 1983) . A cosmological model with an appropriate choice of the function f( T ) has been constructed . The physical behavior of the model is studied. Keywords LRS Bianchi-I , Cosmic strings ,Bulkviscosity , f (R,T ) gravity 1 Introduction It is well known that the discovery of the accelerated expansionof the universe has revolutionized modern cosmology (Riess et al. 1998; Perlmutter et al. 1999; Bennet et al.2003). Astrophysical observations indicate that this cosmic acceleration is driven by exotic energy with a large negative pressure which is known as dark energy (for a general complete review see Nojiri and Odintsov 2007). In recent yearsmodified theories of gravity are attracting much attention to explore the dark energy and late time acceleration of the universe. Among the various modifications of general relativity, f (R) theory of gravity has gained importance during the last decade since it provides a natural gravitational alternative to dark energy. It has been suggested that cosmic acceleration can be achieved by replacing the Einstein-Hilbert action of general relativity with a general function f (R) of Ricci scalar R. The explanation of cosmic acceleration is obtained just by introducing the term 1/R which is essential at small curvatures. The useful aspects of f (R) gravity are that it gives an easy unification of early time inflation and late time acceleration. It also describes the transition phase of the universe from deceleration to acceleration (Nojiri and Odintsov2007). Capozziello et al.(2007,2008), Multamaki and Vilja(2006, 2007), Sharif (2010). Azadi et al. (2004,2008) Caroll (2008) , Nojiri and Odintsov (2003, 2004, 2007) and Chiba et al. (2007) are some of the authors who have investigatedseveral aspects of f (R) gravity. Copeland et al.(2006) have given a comprehensive review of f (R) gravity. Recently, Harko et al. (2011) proposed another modification of Einstein’s theory of gravitation which is known as f (R,T ) theory of gravity wherein the gravitational Lagrangianis given by an arbitrary function of the Ricci scalar R and of the trace T of the stress energy tensor Tij. They have derived the field equations of f (R,T ) gravity from Hilbert-Einstein type variational principle by taking the action = 1 16 , − 4 + − 4 (1) where f (R,T ) is an arbitrary function of the Ricci scalarR, T is the trace of energy tensor of the matter Tij and Lm is the matter Lagrangian density. By varying the action S of the gravitational field with respect to the metric tensor components gij , they have obtained the field equations of (R,T ) gravity, with the special choice of f (R,T ) (Harkoet al. 2011) given by , = +2() (2) for a detailed derivation of the field equations one can refer to Harko et al. (2011) − 1 2 = 8 +2 ′ + [2 ′ + ()] (3) where the overhead prime indicates derivative with respect to the argument and Tij is given by = + − (4)