A systematic study on the Born–Infeld theory within the Palatini approach of f(R) gravity has been performed and the field equations are investigated considering the Hu–Sawicki model. We study the dynamics of the system in the background of isotropic Friedmann–Leimaître–Robertson–Walker (FLRW) model as well as anisotropic Bianchi I and V models. A very useful approach known as dynamical system approach (DSA) has been adopted to find the equilibrium points and to study the physical behaviour of the model under consideration. Moreover, the capability of the model to reproduce the sequence of radiation dominated, matter dominated and late time accelerated expansion is investigated. This analysis provides information about the evolution of anisotropy parameter (shear) and spatial curvature with time and their behaviour in the different eras of the cosmic evolution.

在f ( R的 Palatini 方法中对 Born-Infeld 理论的系统研究) 已经执行了重力，并考虑了 Hu-Sawicki 模型研究了场方程。我们在各向同性 Friedmann-Leimaître-Robertson-Walker (FLRW) 模型以及各向异性 Bianchi I 和 V 模型的背景下研究系统的动力学。一种非常有用的方法称为动态系统方法 (DSA) 已被用于寻找平衡点并研究所考虑模型的物理行为。此外，还研究了模型再现辐射主导、物质主导和后期加速膨胀序列的能力。该分析提供了有关各向异性参数（剪切）和空间曲率随时间的演变及其在宇宙演化不同时代的行为的信息。