The modified field equations are written in logarithmic and power law versions of entropy corrected models in Einstein’s gravity in the background of FRW universe. In one section, a brief review of the Hořava–Lifshitz gravity is discussed and the modified field equations in logarithmic and power law versions of entropy corrected models in Hořava–Lifshitz gravity are formulated. The stability analysis for these models is performed by describing the dynamical system. In another section, a brief review of the fractal universe is presented and the modified field equations in logarithmic and power law versions of entropy corrected models in fractal universe are formulated. The stability analysis of the dynamical system for these models in the framework of fractal universe is described. Furthermore, the bouncing scenarios of the universe in Hořava–Lifshitz gravity and fractal model for both logarithmic and power law entropy corrected versions in \(k=0, +\,1, -\,1\) separately are analyzed. For different cases, the validity of null energy condition at the time of bounce is examined and the behaviors of the physical quantities are depicted through diagrams. Finally, the modifications in Newton’s law of gravitation are discussed for the chosen models.

中文翻译：

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Hořava–Lifshitz重力和分形宇宙中熵校正模型的弹跳宇宙学

修改后的场方程在FRW宇宙背景下以爱因斯坦引力的熵校正模型的对数和幂定律形式编写。在一个部分中，将对Hořava–Lifshitz引力进行简要回顾，并在Hořava–Lifshitz引力的熵校正模型的对数和幂定律版本中拟定修正场方程。这些模型的稳定性分析是通过描述动力学系统来进行的。在另一部分中，对分形宇宙进行了简要回顾，并提出了分形宇宙中熵校正模型的对数和幂定律版本中的修正场方程。描述了在分形宇宙框架内这些模型的动力学系统的稳定性分析。此外，\（k = 0，+ \，1，-\，1 \）分别进行分析。对于不同的情况，检查了反弹时零能量条件的有效性，并通过图表描述了物理量的行为。最后，针对所选模型讨论了牛顿引力定律的修改。