Imperfect fluid cosmological model in modified gravity

Abstract

In this article, we considered the bulk viscous fluid in the formalism of modified gravity in which the general form of a gravitational action is $f(R, T)$ function, where $R$ is the curvature scalar and $T$ is the trace of the energy momentum tensor within the frame of flat FRW space time. The cosmological model dominated by bulk viscous matter with 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 $ξ=ξ_0+ξ_1\frac{\dot{a}}{a}+ξ_2\frac{\ddot{a}}{\dot{a}}$, where $ξ_0$, $ξ_1$ and $ξ_2$ are constants. We take $p=(γ-1)ρ$, where $0\leγ\le2$ as an equation of state for 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 the four possible scenarios for different values of $γ$, such as $γ=0$, $γ=\frac{2}{3}$, $γ=1$ and $γ=\frac{4}{3}$ with the possible positive and negative ranges of $λ$ to observe the accelerated expansion history of the universe. Finally, a big-rip singularity is observed.