Analytic solution for matter density perturbations in a class of viable cosmological f(R) models

TL;DR

This paper derives an analytical solution for matter density perturbations in a specific class of viable f(R) gravity models, providing insights into structure formation during the matter-dominated era.

Contribution

It presents an exact hypergeometric function solution for matter perturbations in a class of f(R) models with inverse power law deviation from Einstein gravity.

Findings

Analytic expression for density perturbations during matter domination.

Derived matter transfer function at sub-Hubble scales.

Enhanced understanding of structure growth in modified gravity models.

Abstract

For a class of viable cosmological models in $f(R)$ gravity which deviation from the Einstein gravity decreases as a inverse power law of the Ricci scalar $R$ for large $R$, an analytic solution for density perturbations in the matter component during the matter dominated stage is obtained in terms of hypergeometric functions. An analytical expression for the matter transfer function at scales much less than the present Hubble scale is also obtained.