Effect of the modified gravity on the large scale structure formation

TL;DR

This paper studies how modified gravity theories, specifically $f(R)$ gravity, influence the growth of large-scale structures in the universe's late accelerated expansion era, revealing complex effects on matter perturbation growth.

Contribution

It provides an analysis of linear matter perturbation growth in $f(R)$ gravity, highlighting how modifications to gravity affect structure formation at low redshift.

Findings

Modified gravity alters the effective gravitational constant $G_{eff}$.

$f(R)$ gravity can both enhance and suppress structure growth.

Accelerated expansion generally slows down large-scale structure formation.

Abstract

We investigate the formation of the large scale structures in the present accelerated era in $f(R)$ gravity background. This is done by considering the linear growth of matter perturbations at low redshift $z<1$. The effect of $f(R)$ alters the behaviour of the matter density perturbations from the matter dominated universe to the late-time accelerated universe which is encoded in the Newtonian gravitational constant as $G\rightarrow G_{eff}$. The modified gravitational constant ($G_{eff}$) depends on the form of $f(R)$. The late-time accelerated expansion affects the formation of large scale structures by slowing down the growth of matter density. On the other hand, $f(R)$ increases the growth rate of the matter density perturbations. We have found that the source term in $f(R)$ background, $G_{eff}\Omega_m$ overcomes the accelerated expansion and the effect of accelerated expansion suppresses the formation of the large scale structures in the asymptotic future.