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arXiv 1406.4258gr-qc
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修正$f(R,T)$引力理论中的粘性宇宙学Friedmann模型

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

C. P. Singh, Pankaj Kumar

备注：
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
发表信息：
The European Physical Journal C, Vol. 74, page 3070 (2014)
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摘要：

本文在平坦的Friedmann-Robertson-Walker模型框架下，将体粘滞引入修正引力理论的形式体系中，其中引力作用量包含一个一般函数$f(R,T)$，其中$R$和$T$分别表示曲率标量和能量动量张量的迹.作为理想流体的状态方程，我们取$p=(γ-1)ρ$，其中$0 \leq γ\leq 2$和粘性项作为各向同性模型的体粘度，形式为$ζ=ζ_{0}+ζ_{1}H$，其中$ζ_{0}$和$ζ_{1}$是常数，$H$是哈勃参数。通过假设$f(R,T) = R+2f(T)$形式的最简单的特定模型，分别用非粘性和粘性流体获得相应场方程的精确非奇异解，其中$f(T)=αT$（$α$是常数）。在一定的约束条件下，在宇宙时间的有限值上，也观察到了$γ<0$的大裂缝奇点。我们研究了所有可能的情况下，可能的积极和消极的$α$的范围来分析宇宙的膨胀历史。我们观察到宇宙在$ζ_0$和$ζ_1$的某些约束下加速或表现出从减速相到加速相的转变。我们通过标度因子与宇宙时间的关系图比较了粘性模型和非粘性模型，发现体粘滞系数在宇宙膨胀中起主要作用。对于非粘性和粘性流体的减速参数绘制了类似的图，并发现从减速到加速阶段的过渡具有某种形式的体积粘度。

英文摘要：

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 $0 \leq γ\leq 2$ and viscous term as a bulk viscosity due to 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 $f(R,T) = R+2f(T)$, 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 $ζ_0$ and $ζ_1$. 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.

机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。

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