The purpose of this work is to study the Tsallis, Rényi and Sharma–Mittal holographic dark energy models in order to evaluate the accelerated expansion of the Universe. In this regard, we consider the modified field equations for logarithmic and power law versions of entropy corrected models in FRW Universe filled with interacting dark energy and cold dark matter within the framework of Hořava–Lifshitz gravity. Employing the Nojiri and Odintsov (NO) cut-off as infrared cutoff, we explore the nature of the different cosmological quantities like the equation of state parameter, squared speed of sound and [Formula: see text]–[Formula: see text] cosmological plane during the cosmic evolution. The equation of state parameter shows the different stages of the evolution of the Universe for the considered models. By analyzing the cosmological plane [Formula: see text]–[Formula: see text], we obtain the freezing region for these models. Also, due to the study of squared speed of sound, we show the classically stable behavior of the considered models.

中文翻译：

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研究 Tsallis、Rényi 和 Sharma-Mittal 全息暗能量用于 Hořava-Lifshitz 引力中熵校正的修正场方程

这项工作的目的是研究 Tsallis、Rényi 和 Sharma-Mittal 全息暗能量模型，以评估宇宙的加速膨胀。在这方面，我们考虑了在 Hořava-Lifshitz 引力框架内充满相互作用的暗能量和冷暗物质的 FRW 宇宙中熵校正模型的对数和幂律版本的修正场方程。使用 Nojiri 和 Odintsov (NO) 截止作为红外截止，我们探索不同宇宙学量的性质，如状态参数方程、声速平方和 [公式：见文本]-[公式：见文本] 宇宙学宇宙演化过程中的平面。状态参数方程显示了所考虑模型的宇宙演化的不同阶段。通过分析宇宙平面[公式：见正文]-[公式：见正文]，我们得到了这些模型的冻结区域。此外，由于对声速平方的研究，我们展示了所考虑模型的经典稳定行为。