Observational constraints on growth index with cosmography

In the literature, it was proposed that the growth index γ is useful to distinguish the scenarios of dark energy and modified gravity. In the present work, we consider the constraints on the growth index γ by using the latest observational data. To be model-independent, we use cosmography to describe the cosmic expansion history, and also expand the general γ(z) as a Taylor series with respect to redshift z or y-shift, y= z/ (1 + z). We find that the present value γ= γ(z= 0) ≃ 0.42 (for most of viable f(R) theories) is inconsistent with the latest observational data at high confidence level (C.L.). On the other hand, γ≃ 0.55 (for dark energy models in GR) can be consistent with the latest observational data at 1 σ C.L. in five of the nine cases under consideration, but is inconsistent beyond 2 σ C.L. in the other four cases (while it is still consistent within the 3 σ region). Thus, we can say nothing firmly about γ≃ 0.55. We also find that a varying γ(z) is favored.