The main motivation of our study is to explore Rényi holographic dark energy, Sharma–Mittal holographic dark energy, Rényi new agegraphic dark energy, and Sharma–Mittal new agegraphic dark energy in the context of generalized Rastall gravity with the two-fluid system, dark energy, and dark matter. In this regard, we have considered the scale factors into two distinct categories, one of which corresponds to the future singularity, whereas the other represents initial singularity. By employing future event horizon as infrared (IR)-cutoff, different cosmological quantities like deceleration parameter, equation of state (EoS) parameter are evaluated, and their ramifications have been described graphically. Analyzing the squared speed of sound, we have seen classically stable and unstable behavior for each of the considered models. Finally, we study ωD–ωD′ plane and find the thawing/freezing regions.

中文翻译：

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Rényi、Sharma-Mittal 全息和新时代暗能量模型在广义 Rastall 引力中的宇宙学后果

我们研究的主要动机是探索 Rényi 全息暗能量、Sharma-Mittal 全息暗能量、Rényi 新时代暗能量和 Sharma-Mittal 新时代暗能量在广义拉斯塔尔引力与二流体系统的背景下，暗能量和暗物质。在这方面，我们将比例因子分为两个不同的类别，其中一个对应于未来的奇点，而另一个代表初始奇点。通过将未来事件视界用作红外 (IR) 截止值，评估了不同的宇宙学量，如减速参数、状态方程 (EoS) 参数，并以图形方式描述了它们的后果。分析声速的平方，我们已经看到每个所考虑模型的经典稳定和不稳定行为。最后，我们研究ωD–ωD'飞机并找到解冻/冻结区域。