An analytic calculation of the growth index for f(R) dark energy model

Abstract

We derive the analytic formula of the growth index for the $f(R)$ dark energy model where the effect on the growth of matter density perturbation ${\mathit{\delta }}_m$ from modified gravity (MG) is encoded in the effective Newton coupling constant $G_{\mathrm{eff}}$ in MG (or equivalently $g\equiv G_{\mathrm{eff}}/G$). Based on the analytic formula, we propose that the parameter $g$ can be directly found by comparing the observed growth rate $f_g\equiv dln{\mathit{\delta }}_m/dlna$ to the prediction of $f_g$ in general relativity.