Abstract This paper is devoted to investigate the modified f(R) theory of gravity, where R represents the Ricci scalar respectively. For our current work, we consider the Friedmann-Robertson-Walker (FRW) space-time for finding solutions of field equations. Furthermore, some numerical solutions are examined by taking the Klein-Gordon Equation and using distinct values of the equation of state (EoS) parameter. In this way, we have discussed the solutions for acceleration expansion of the Universe, sub-relativistic Universe, radiation Universe, ultra-relativistic Universe, dust Universe, and stiff fluid Universe respectively. Moreover, their behaviours are examined by using power-law and exponential law techniques. The bouncing scenario is also discussed by choosing some particular values of the model parameters and observed the energy conditions, which are satisfied for a successful bouncing model. It is also concluded that some solution in f(R) theory of gravity supports the concept of exotic matter and accelerated expansion of the Universe due to a large amount of negative pressure.

中文翻译：

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修正 f(R) 引力下某些宇宙学解的动力学

摘要 本文致力于研究修正的f(R)引力理论，其中R分别代表Ricci标量。对于我们当前的工作，我们考虑使用 Friedmann-Robertson-Walker (FRW) 时空来寻找场方程的解。此外，通过采用 Klein-Gordon 方程并使用状态方程 (EoS) 参数的不同值来检查一些数值解。这样，我们分别讨论了宇宙加速膨胀、亚相对论宇宙、辐射宇宙、超相对论宇宙、尘埃宇宙和刚性流体宇宙的解。此外，他们的行为是通过使用幂律和指数律技术来检查的。还通过选择模型参数的一些特定值并观察能量条件来讨论弹跳场景，这对于成功的弹跳模型是满意的。还得出结论，f(R) 引力理论中的一些解支持奇异物质的概念和宇宙由于大量负压而加速膨胀的概念。