Imperfect fluid cosmological model in modified gravity

Abstract

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 + ξ1 a˙ a + ξ2 a¨ a˙ , where ξ 0, ξ 1 and ξ 2 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 + 2 f(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 = 2 3 , γ = 1 and γ = 4 3 , with positive and negative ranges of λ to observe the accelerated expansion history of the universe. Finally, a big-rip singularity is observed.