Imperfect fluid cosmological model in modified gravity

In this article, we considered a bulk viscous fluid in the formalism of modified gravity in which the general form of the gravitational action is f(R, T), where R is the curvature scalar and T is the trace of the energy momentum tensor, within the framework of a flat FRW space time. The cosmological model is dominated by bulk viscous matter with its total bulk viscous coefficient expressed as a linear combination of the velocity and acceleration of the expansion of the universe in such a way that ξ=ξ0+ξ1a˙a+ξ2a¨a˙, where ξ0, ξ1 and ξ2 are constants. We take p=(γ−1)ρ, where 0 ≤ γ ≤ 2, as the equation of state for a perfect fluid. The exact solutions to the corresponding field equations are obtained by assuming a particular model of the form of f(R,T)=R+2f(T), where f(T)=λT,λ is constant. We studied four possible scenarios of the universe for different values of γ, namely γ=0,γ=23,γ=1 and γ=43, with positive and negative ranges of λ to observe the accelerated expansion history of the universe. Finally, a big-rip singularity is observed.