Effect of the Modified Gravity on the Large-scale Structure Formation

Abstract

We investigate the formation of the large-scale structures in the present accelerated era in the 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 behavior 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 → 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 the 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.