The work is the study of Bianchi type-I models with holographic dark energy in the framework of $$ f(R) $$ theory of gravitation. The exact solutions of the field equations are deduced by considering the exponential and power-law volumetric expansion. Various physical and kinematical properties of the models are discussed. In addition to make our interpretation more clear for that we have taken the statefinder diagnostic pair $$ \{ r,s\} $$ and cosmic jerk parameter $$ j(t) $$ to characterize different phases of the universe. The holographic scalar fields of dark energy are reconstructed and quintessence potential for both the models describing accelerated expansion of the universe is also obtained.

中文翻译：

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ΛCDM 宇宙学模型与 f(R) 引力理论的精华

工作是在$$f(R)$$万有引力理论的框架内研究具有全息暗能量的Bianchi I型模型。通过考虑指数和幂律体积膨胀推导出场方程的精确解。讨论了模型的各种物理和运动学特性。除了使我们的解释更加清晰之外，我们还采用了状态查找器诊断对 $$ \{ r,s\} $$ 和 cosmic jerk 参数 $$ j(t) $$ 来表征宇宙的不同阶段。重建了暗能量的全息标量场，并获得了描述宇宙加速膨胀的两种模型的精髓潜力。