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Effect of the modified gravity on the large scale structure formation

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, $G_{eff}Ω_m$ overcomes the accelerated expansion and the effect of accelerated expansion suppresses the formation of the large scale structures in the asymptotic future.