Anisotropic solutions in f(R,T) theory of gravity

In this thesis, it has been investigated whether the locally rotationally symmetric Bianchi type-V model, which is one of the homogeneous and anisotropic universe models, has a solution compatible with the current astrophysical observations of the field equations of the f(R,T) theory. The field equations of the locally rotationally symmetric Bianchi type-V universe model have been derived, and their solutions have been investigated under two different assumptions in this theory. The first of these assumptions is that there is a linear proportionality between the deceleration parameter and the Hubble parameter, and the second one is that there is an inverse relationship between the parameters. The solutions of these models have been obtained, some kinematic and dynamic quantities of the models have been calculated and their evolution in time have been discussed through their graphs. Both models have given results that are in good agreement with current values of Hubble and deceleration parameters. However, since the first model obtained has a negative deceleration parameter throughout the evolution of the universe, although it can explain the current accelerated expansion of our universe, it cannot explain the decelerating expansion in the past. In other words, this model is an accelerated universe model and is insufficient to explain the phase transition in the expansion of the universe. On the other hand, the second model is successful in explaining this phase.