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

Abstract

In this paper, we introduce 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 prefect fluid, we take $p=({\hat{I}}^3-1)\ddot{I}$, where $0\le {\hat{I}}^3\le 2$ and viscous term as a bulk viscosity due to isotropic model, of the form $\hat{I}\P =\hat{I}{\P }_0+\hat{I}{\P }_{1}H$, where $\hat{I}{\P }_0$ and $\hat{I}{\P }_1$ 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 $f(R,T)=R+2f(T)$, where $f(T)=\hat{I}\pm T$ ( $\hat{I}\pm$ is a constant). A big-rip singularity is also observed for ${\hat{I}}^3<0$ at a finite value of cosmic time under certain constraints. We study all possible scenarios with the possible positive and negative ranges of $\hat{I}\pm$ to analyze the expansion history of the universe. It is observed that the universe accelerates or exhibits transition from decelerated phase to accelerated phase under certain constraints of $\hat{I}{\P }_0$ and $\hat{I}{\P }_1$. We compare the viscous models with the non-viscous one through the graph plotted between scale factor and cosmic time and find that bulk viscosity plays the major role in the expansion of the universe. A similar graph is plotted for deceleration parameter with non-viscous and viscous fluids and find a transition from decelerated to accelerated phase with some form of bulk viscosity.

19 pages, 3 figures, the whole paper has been revised to improve the quality of paper. Some references added. arXiv admin note: text overlap with arXiv:1307.4262 by other authors