The aim of this paper is to investigate the stability of Einstein static cosmos using anisotropic homogeneous perturbations in the background of [Formula: see text] theory in which [Formula: see text] and [Formula: see text] express the Ricci scalar and trace of the stress–energy tensor, respectively. To accomplish this work, we consider perfect fluid distribution and adopt small anisotropic perturbations in the scale factors and matter contents. We develop static and perturbed field equations that are simplified by using equation of state parameter. For the specific models of [Formula: see text] theory with conserved and non-conserved stress–energy tensor, the Einstein solutions are explored and their stability regions are analyzed graphically. We conclude that the static Einstein stable universe with anisotropic perturbations exists in this framework contrary to general relativity.

中文翻译：

---

f(R,T)理论中各向异性扰动爱因斯坦宇宙的稳定性

本文的目的是在[公式：见文]理论的背景下，利用各向异性均匀摄动研究爱因斯坦静态宇宙的稳定性，其中[公式：见文]和[公式：见文]表达了里奇标量和轨迹分别为应力-能量张量。为了完成这项工作，我们考虑了完美的流体分布，并在比例因子和物质含量中采用了小的各向异性扰动。我们开发了通过使用状态参数方程简化的静态和扰动场方程。对于具有守恒和非守恒应力-能量张量的[公式：见正文]理论的具体模型，探索了爱因斯坦解并以图形方式分析了它们的稳定性区域。