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 = (γ − 1)ρ, where 0 ≤ γ ≤ 2 and a viscous term as a bulk viscosity due to the isotropic model, of the form ζ = ζ 0 + ζ 1 H , where ζ 0 and ζ 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 ) = 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 a transition from a decelerated phase to an accelerated phase under certain constraints of ζ 0 and ζ 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.
Recently, the current authors (arXiv:gr-qc/1609.01477) have proposed and analyzed in detail the logarithmic form of Brans-Dicke scalar field φ as φ ∝ ln(α+βa), where α and β are positive constants, to alleviate the problems of interacting holographic dark energy models in Brans-Dicke theory. In this paper, the cosmological evolution of a new agegraphic dark energy (NADE) model within the framework of Friedmann-Robertson-Walker Universe is analyzed with the same form of scalar field in Brans-Dicke theory. We derive the equation of state parameter w D and deceleration parameter q of NADE model. It is observed that w D → −1 when a → ∞, i.e., the NADE mimics cosmological constant in the late time evolution. Indeed, due to the assumption of logarithmic form of Brans-Dicke scalar field the NADE in Brans-Dicke theory behaves like NADE in general relativity in the late time evolution. The NADE model shows a phase transition from matter dominated phase in early time to accelerated phase in late time. We further extend NADE model by including the interaction between dark matter and NADE. In this case, w D definitely crosses the phantom divide line (w D = −1) in the late time evolution. The phase transition from matter dominated to NADE dominated phase may be achieved at early stage in interacting model. Further, we show that the interacting NADE model resolves the cosmic coincidence problem as the energy density ratio may evolve sufficiently slow at present.
In this paper, an interacting holographic dark energy model with Hubble horizon as an infrared cut-off is considered in the framework of Brans-Dicke theory. We propose a logarithmic form φ ∝ ln(α + βa) of the Brans-Dicke scalar field to alleviate the problems of interacting holographic dark energy models in Brans-Dicke theory. We find that the equation of state parameter w h and deceleration parameter q are negative in the early time which shows the early time inflation. During the evolution the sign of parameter q changes from negative to positive which means that the Universe expands with decelerated rate whereas the sign of w h may change or remain negative throughout the evolution depending on the values of parameters. It is also observed that w h may cross the phantom divide line in the late time evolution. The sign of q changes from positive to negative during late time of evolution which explains the late time accelerated expansion of the Universe. Thus, we present a unified model of holographic dark energy which explains the early time acceleration (inflation), medieval time deceleration and late time acceleration. We also discuss the cosmic coincidence problem. We obtain a time-varying density ratio of holographic dark energy to dark matter which is a constant of order one (r ∼ O(1)) during early and late time evolution. Therefore, our model successfully resolves the cosmic coincidence problem.
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