  Two different realistic $F(R)$ modified gravity models are considered in the
framework of the Friedmann-Lemetre-Robertson-Walker universe. The parameters of
these two models are adjusted to reach coherence with the most recent and
accurate observations of the current universe. A study of the growth of matter
density perturbations is done, and several parametrizations of the growth index
are developed for both models. The ansatz for the growth index given by $\gamma
= \gamma_0 + \gamma_1 z/(1+z)$ seems to be the best parametrization for the two
models considered. Finally, the values obtained for $\gamma_0$ and $\gamma_1$
can be used in order to characterize these two models and to differentiate them
from others such as the Hu-Sawicki model.
