Abstract The aim of this paper is to study the Godel type universe in modified f(R, ϕ) theory of gravity, where R stands for Ricci scalar and ϕ be the scalar potential. We investigate the modified field equations by using anisotropic and perfect fluid distributions. In particular, we consider two proposed models with some fixed values of parameters and investigate the exact solutions. The behaviour of energy conditions can be seen by a detailed graphical analysis. Furthermore, Tolman-Oppenheimer-Volkoff equation has been studied for both models in this theory. We have also discussed some exact solutions using perfect fluid. It is concluded that f(R, ϕ) theory of gravity support the phenomenon of cosmic expansion of the universe through Godel type universe for both models.

中文翻译：

---

f(R, ϕ)引力中哥德尔型解的研究

摘要 本文的目的是在修正的f(R, ϕ)引力理论中研究哥德尔型宇宙，其中R代表Ricci标量，ϕ为标量势。我们通过使用各向异性和完美的流体分布来研究修改后的场方程。特别是，我们考虑了两个具有一些固定参数值的建议模型并研究了精确解。能量条件的行为可以通过详细的图形分析看到。此外，该理论中的两个模型都研究了 Tolman-Oppenheimer-Volkoff 方程。我们还讨论了一些使用完美流体的精确解。结论是，对于两种模型，f(R, ϕ) 引力理论都支持宇宙通过哥德尔型宇宙膨胀的现象。