LRS Bianchi type-I cosmological model in f (R, T) theory of gravity with Λ(T)

The locally rotationally symmetric (LRS) Bianchi type-I cosmological models have been investigated in f (R, T) theory of gravity, where R is the Ricci scalar and T is the trace of the energy momentum tensor, for some choices of the functional f (R, T) = f(1)(R) + f(2)(T). The exact solutions of the field equations are obtained for the linearly varying deceleration parameter q(t) proposed by Akarsu and Dereli (2012). Keeping an eye on the accelerating nature of the universe in the present epoch, the dynamics and physical behaviour of the models have been discussed. It is interesting to note that in one of the model, the universe ends with a big rip. By taking different functional forms for f(2)(T) we have investigated whether or not the Big Rip can be avoided. We found that, the Big Rip situation can not be avoided and may be inherent in the linearly varying deceleration parameter. We have also applied the State-finder diagnostics to get the geometrical dynamics of the universe at different phases.