Cosmic hierarchy in $f(R)$ gravity

TL;DR

This paper explores how modified gravity theories, specifically $f(R)$ gravity, can naturally lead to hierarchical large-scale cosmic structures through oscillatory solutions of a Schr"odinger-like equation, potentially explaining small-scale cosmological inhomogeneities.

Contribution

It provides new solutions to the Schr"odinger-like Friedmann equation in $f(R)$ gravity, demonstrating the potential for hierarchical structure formation in different cosmological epochs and geometries.

Findings

Hierarchical structure formation possible in $f(R)$ gravity models.

Solutions vary with model parameters and initial conditions.

Potential explanation for small-scale cosmological inhomogeneities.

Abstract

In this contribution, we investigate hierarchical nature of large-scale structure clustering through the oscillatory nature of the solutions of the Schr\"{o}dinger-like Friedmann equation in a modified gravitational background described by the $f(R)$ gravity theory. We find the cosmological solutions to the Schr\"{o}dinger 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.