Non-parametric Reconstruction of Growth Index via Gaussian Processes

The accelerated cosmic expansion could be due to dark energy within general relativity (GR), or modified gravity. It is of interest to differentiate between them, by using both the expansion history and the growth history. In the literature, it was proposed that the growth index $\gamma$ is useful to distinguish these two scenarios. In this work, we consider the non-parametric reconstruction of the growth index $\gamma$ as a function of redshift $z$ from the latest observational data as of July 2018 via Gaussian Processes. We find that $f(R)$ theories and dark energy models within GR (especially $\Lambda$CDM) are inconsistent with the results in the moderate redshift range far beyond $3\sigma$ confidence level. A modified gravity scenario different from $f(R)$ theories is favored. However, these results can also be due to other non-trivial possibilities, in which dark energy models within GR (especially $\Lambda$CDM) and $f(R)$ theories might still survive. In all cases, our results suggest that new physics is required.