An analytic calculation of the growth index for

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 $$\delta _m$$ 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 $$f_g\equiv d\ln \delta _m/d\ln a$$ to the prediction of $$f_g$$ in general relativity