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.

15 pages, 7 figures