We consider the fractal universe model with timelike fractal profile in flat Friedmann–Robertson–Walker (FRW) universe model and check the thermodynamic stability of various dark energy models. These dark energy models include family of Chaplygin gas models (such as generalized Chaplygin gas, modified Chaplygin gas, generalized cosmic Chaplygin gas, variable modified Chaplygin gas) and parametrized equation-of-state (Chevallier–Polarski–Linder) model. To check the stability of these models in fractal framework thermodynamically, we construct total equation-of-state parameter for each case. The conditions to check the stability of models depending on some thermodynamic quantities yield three conditions on this parameter. We graphically check the behavior of the equation-of-state parameter along with stability of each model. It is concluded that the dark energy models are thermodynamically stable under appropriate choices of model parameters.

中文翻译：

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Chaplygin 气体模型的热稳定性和 Chevallier-Polarski-Linder 参数化

我们在平面弗里德曼-罗伯逊-沃克（FRW）宇宙模型中考虑具有类时分形轮廓的分形宇宙模型，并检查各种暗能量模型的热力学稳定性。这些暗能量模型包括 Chaplygin 气体模型家族（如广义 Chaplygin 气体、修改的 Chaplygin 气体、广义宇宙 Chaplygin 气体、可变修改的 Chaplygin 气体）和参数化状态方程（Chevallier-Polarski-Linder）模型。为了从热力学上检查这些模型在分形框架中的稳定性，我们为每种情况构建了总状态方程参数。根据某些热力学量检查模型稳定性的条件在该参数上产生了三个条件。我们以图形方式检查状态方程参数的行为以及每个模型的稳定性。