Growth factor parametrization and modified gravity

The growth rate of matter perturbation and the expansion rate of the Universe can be used to distinguish modified gravity and dark energy models in explaining the cosmic acceleration. The growth rate is parametrized by the growth index gamma. We discuss the dependence of gamma on the matter energy density Omega and its current value Omega(0) for a more accurate approximation of the growth factor. The observational data, including the data of the growth rate, are used to fit different models. The data strongly disfavor the Dvali-Gabadadze-Porrati model. For the dark energy model with a constant equation of state, we find that Omega(0)=0.27 +/- 0.02 and w=-0.97 +/- 0.09. For the Lambda CDM model, we find that gamma=0.64(-0.15)(+0.17). For the Dvali-Gabadadze-Porrati model, we find that gamma=0.55(-0.13)(+0.14).