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

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 $p=(\gamma-1)\rho$, where $0 \leq \gamma \leq 2$ and viscous term as a
bulk viscosity due to isotropic model, of the form $\zeta
=\zeta_{0}+\zeta_{1}H$, where $\zeta_{0}$ and $\zeta_{1}$ 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 $f(T)=\alpha T$ ( $\alpha$ is a constant). A big-rip
singularity is also observed for $\gamma<0$ at a finite value of cosmic time
under certain constraints. We study all possible scenarios with the possible
positive and negative ranges of $\alpha$ 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 $\zeta_0$ and $\zeta_1$. 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.Comment: 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 author

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