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 $p=(\gamma-1)\rho$, 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.
Highlights
Bertolami et al [18] generalized f (R) gravity by introducing an explicit coupling between an arbitrary function of the Ricci scalar R and the matter Lagrangian density Lm
The negative pressure generated by the bulk viscosity cannot avoid the dark energy of the universe to be phantom
In order to compare (8) with Einstein’s case, we find that the gravitational field equations (8) can be recast in such a form that the higher order corrections coming both from the geometry, and from matter–geometry coupling, provide an energy–momentum tensor of geometrical and matter origin, describing an effective source term on the right hand side of (8)
Summary
Bertolami et al [18] generalized f (R) gravity by introducing an explicit coupling between an arbitrary function of the Ricci scalar R and the matter Lagrangian density Lm. A well-known result of the FRW cosmological solutions, corresponding to the universe filled with perfect fluid and bulk viscous stresses, is the possibility of violating dominant energy condition (DEC). We study the FRW model with bulk viscosity in modified f (R, T ) gravity theory and investigate the effects of the bulk viscosity in explaining the early and late time acceleration of the universe. In order to compare (8) with Einstein’s case, we find that the gravitational field equations (8) can be recast in such a form that the higher order corrections coming both from the geometry , and from matter–geometry coupling, provide an energy–momentum tensor of geometrical and matter origin, describing an effective source term on the right hand side of (8). The main issue arises of the content of the universe through the energy–momentum tensor and of the matter Lagrangian Lm and the trace of the energy– momentum tensor
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