An Accurate Fitting Function For Scale-dependent Growth Rate in Hu-Sawicki \(f(R)\) Gravity

Abstract

We present a simple fitting formula for the scale-dependent growth rate of Hu-Sawicki model in \(f(R)\) modified gravity. We compare the accuracy of the fitting function against numerical results and report achieving a sub-percent maximum error for all different studied cases. The validity of the fitting function is tested against a wide range of scales, \(10^{-4} \le k \le 5 \ [\mathrm{Mpc}^{-1}]\) , for various redshift values in the range of \(z \in [0.0,\ 3.0]\) and different \(|f_R^0|\) values. This formula is useful in producing predictions for cosmological probes that are sensitive to growth rate such as redshift space distortions, galaxy-galaxy correlation function, peculiar velocity statistics and pairwise velocities of galaxy clusters.