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arXiv 1901.01031gr-qcastro-ph.CO
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作为统一的暗能量模型的扩展的各向同性流体

Extended logotropic fluids as unified dark energy models

Kuantay Boshkayev, Rocco D'Agostino, Orlando Luongo

摘要:

我们在这里研究扩展类的logotropic流体\textit{unified dark energy models}。在Anton-Schmidt方案的假设下,我们认为宇宙服从单一流体,其压力通过对数状态方程演化。这个结果与各向同性应力下的晶体类似。因此,我们调查的热力学和动力学的后果整合的声速,以获得压力的密度,导致扩展版本的Anton-Schmidt宇宙流体。在这幅图中,我们得到了在红外区域扩展Anton-Schmidt压力的重要结果。低能情况与宇宙在没有任何宇宙学常数的情况下加速有关。因此,我们推导出我们的流体的拉格朗日$\mathcal{L}=\mathcal{L}(X)$的有效表示,仅取决于动力学项$X$。我们分析了相对论和非相对论的限制。在非相对论极限下,我们用密度$ρ$和标量场$\vartheta$构造了哈密顿量和拉格朗日量,而在相对论极限下,我们找不到拉格朗日量的解析表达式,因此,在无旋理想流体的假设下,我们得到了作为$ρ$的函数的势.我们证明了该模型是\emph{logotropic dark energy models}的自然推广。最后,我们分析了一类带有一个额外参数$β$的广义Chaubergin气体模型。有趣的是,我们发现,这种情况下的拉格朗日和纯logotropic一个重合的非相对论制度。

英文摘要:

We here study extended classes of logotropic fluids as \textit{unified dark energy models}. Under the hypothesis of the Anton-Schmidt scenario, we consider the universe obeying a single fluid whose pressure evolves through a logarithmic equation of state. This result is in analogy with crystals under isotropic stresses. Thus, we investigate thermodynamic and dynamical consequences by integrating the speed of sound to obtain the pressure in terms of the density, leading to an extended version of the Anton-Schmidt cosmic fluids. Within this picture, we get significant outcomes expanding the Anton-Schmidt pressure in the infrared regime. The low-energy case becomes relevant for the universe to accelerate without any cosmological constant. We therefore derive the effective representation of our fluid in terms of a Lagrangian $\mathcal{L}=\mathcal{L}(X)$, depending on the kinetic term $X$ only. We analyze both the relativistic and non-relativistic limits. In the non-relativistic limit we construct both the Hamiltonian and Lagrangian in terms of density $ρ$ and scalar field $\vartheta$, whereas in the relativistic case no analytical expression for the Lagrangian can be found. Thus, we obtain the potential as a function of $ρ$, under the hypothesis of irrotational perfect fluid. We demonstrate that the model represents a natural generalization of \emph{logotropic dark energy models}. Finally, we analyze an extended class of generalized Chaplygin gas models with one extra parameter $β$. Interestingly, we find that the Lagrangians of this scenario and the pure logotropic one coincide in the non-relativistic regime.

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