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=(γ−1)ρ, where 0≤γ≤2 and viscous term as a
bulk viscosity due to isotropic model, of the form ζ=ζ0+ζ1H, where ζ0 and ζ1 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)=αT ( α is a constant). A big-rip
singularity is also observed for γ<0 at a finite value of cosmic time
under certain constraints. We study all possible scenarios with the possible
positive and negative ranges of α 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 ζ0 and ζ1. 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