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