粘性暗能量模型的奇异性和熵
Singularity and entropy of the viscosity dark energy model
摘要：
本文引入体粘滞系数来描述宇宙非理想流体对宇宙演化的影响，建立统一的暗能量和暗物质模型。此外，我们还推导出了体粘滞率形式与哈勃参数之间的一般关系，为粘滞率DE模型的建立提供了一个步骤。特别地，本文对孟晓晖和窦晓在2009年\cite{md}中提出的一个依赖于红移的粘度参数$ζ\proptoλ_{0}+λ_{1}(1+z)^{n}$进行了深入的研究.此外，我们使用最近发布的超新星数据集（宪法数据集）来约束模型参数。为了区分所提出的具体的暗能量模型和著名的$Λ$ CDM模型，本文对该体粘滞模型应用了状态发现诊断方法，作为对我们之前进行的$Om$参数诊断和减速参数分析的补充。DE模型的演化行为和趋势显示在statefinder诊断参数对\{ $r,s$ \}的平面上，其中固定点代表$Λ$ CDM模型。讨论了这种体粘性宇宙学中可能存在的奇异性，得出结论：在适当选择的不同参数区域内，这种具体的粘性DE模型可以具有不同的晚期演化行为，并且可以避免晚期奇异性。我们还计算了体粘滞暗能量框架下的宇宙熵，发现粘滞DE模型中的总熵随标度因子的演化单调增加，这种单调增加的性质可以指示宇宙演化中的时间箭头，尽管时间箭头的量子化版本仍然令人困惑。
英文摘要：
In this paper bulk viscosity is introduced to describe the effects of cosmic non-perfect fluid on the cosmos evolution and to build the unified dark energy (DE) with (dark) matter models. Also we derive a general relation between the bulk viscosity form and Hubble parameter that can provide a procedure for the viscosity DE model building. Especially, a redshift dependent viscosity parameter $ζ\proptoλ_{0}+λ_{1}(1+z)^{n}$ proposed in the previous work by X.H.Meng and X.Dou in 2009\cite{md} is investigated extensively in this present work. Further more we use the recently released supernova dataset (the Constitution dataset) to constrain the model parameters. In order to differentiate the proposed concrete dark energy models from the well known $Λ$CDM model, statefinder diagnostic method is applied to this bulk viscosity model, as a complementary to the $Om$ parameter diagnostic and the deceleration parameter analysis performed by us before. The DE model evolution behavior and tendency are shown in the plane of the statefinder diagnostic parameter pair \{$r,s$\} where the fixed point represents the $Λ$CDM model. The possible singularity property in this bulk viscosity cosmology is also discussed to which we can conclude that in the different parameter regions chosen properly, this concrete viscosity DE model can have various late evolution behaviors and the late time singularity could be avoided. We also calculate the cosmic entropy in the bulk viscosity dark energy frame, and find that the total entropy in the viscosity DE model increases monotonously with respect to the scale factor evolution, thus this monotonous increasing property can indicate an arrow of time in the universe evolution, though the quantum version of the arrow of time is still puzzling.
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