标题： 延展对数流体作为统一暗能量模型 显示英文标题

标题： Extended logotropic fluids as unified dark energy models

摘要： 我们这里研究了扩展的对数型流体类，即\textit{统一暗能量模型}。 在 Anton-Schmidt 场景假设下，我们考虑了一个单一流体支配的宇宙，其压力通过对数状态方程演化。 这一结果与处于各向同性应力下的晶体相类似。 因此，我们通过积分声速以密度表示压力，从而研究热力学和动力学结果，得到 Anton-Schmidt 宇宙流体的扩展版本。 在此框架内，我们在红外区域扩展了 Anton-Schmidt 压力，得到了显著的结果。 低能情况对于无宇宙常数的宇宙加速变得相关。 因此，我们以仅依赖于动能项$X$的拉格朗日量$\mathcal{L}=\mathcal{L}(X)$表示我们的流体的有效形式。 我们分析了相对论和非相对论极限。 在非相对论极限中，我们用密度$\rho$和标量场$\vartheta$构造哈密顿量和拉格朗日量，而在相对论情况下无法找到拉格朗日量的解析表达式。 因此，在无旋完美流体假设下，我们将势能表示为$\rho$的函数。 我们证明该模型代表了\emph{logotropic暗能量模型}的自然推广。 最后，我们分析了一类具有一个额外参数$\beta$的广义Chaplygin气体模型。有趣的是，我们发现这种情景的拉格朗日量与纯对数型模型在非相对论极限下是一致的。 显示英文摘要

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 $\rho$ 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 $\rho$, 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 $\beta$. Interestingly, we find that the Lagrangians of this scenario and the pure logotropic one coincide in the non-relativistic regime.