Friedmann model with viscous cosmology in modified $$f(R,T)$$ f ( R , T ) gravity theory

In this paper, we introduce the bulk viscosity in the formalism of modified gravity theory in which the gravitational action contains a general function f (R, T ), where R and T denote the curvature scalar and the trace of the energy-momentum tensor, respectively, within the framework of a flat Friedmann-Robertson-Walker model. As an equation of state for a prefect fluid, we take p = ( -1), where 0 2 and a viscous term as a bulk viscosity due to the isotropic model, of the form = 0 + 1 H , where 0 and 1 are constants, and H is the Hubble parameter. The exact non-singular solutions to the corresponding field equations are obtained with non-viscous and viscous fluids, respectively, by assuming a simplest particular model of the form of f (R, T ) = R + 2 f (T ), where f (T ) = T ( is a constant). A big-rip singularity is also observed for < 0 at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits a transition from a decelerated phase to an accelerated phase under certain constraints of 0 and 1 . We compare the viscous models with the non-viscous one through the graph plotted between the scale factor and cosmic time and find that the bulk viscosity plays a major role in the expansion of the universe. A similar graph is plotted for the deceleration parameter with non-viscous and viscous fluids and we find a transition from decelerated to accelerated phase with some form of bulk viscosity.

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