In this contribution, we investigate hierarchical nature of large-scale structure clustering through the oscillatory nature of the solutions of the Schrödinger-like Friedmann equation in a modified gravitational background described by the f (R) gravity theory. We find the cosmological solutions to the Schrödinger equation for different ranges of n of the $R^n$ toy model for both radiation and matter-dominated epochs of the expansion history for open, flat and closed spacetimes. Our results show that for certain choices of the model parameters and initial conditions, the formation and distribution of cosmic structures might indeed be hierarchical, leading to a natural explanation for the breakdown of the cosmological principle on small scales.

在这篇文章中，我们通过f  ( R ) 引力理论描述的修正引力背景中薛定谔式弗里德曼方程解的振荡性质来研究大规模结构聚类的层次性质。我们找到了薛定谔方程的宇宙学解，对于不同的n范围$R^n$开放、平坦和封闭时空膨胀历史的辐射和物质主导时代的玩具模型。我们的研究结果表明，对于模型参数和初始条件的某些选择，宇宙结构的形成和分布可能确实是分层的，从而自然地解释了宇宙学原理在小尺度上的崩溃。