Reconstruction of the null-test for the matter density perturbations
  We systematically study the null-test for the growth rate data first
presented in [S. Nesseris and D. Sapone, arXiv:1409.3697] and we reconstruct it
using various combinations of data sets, such as the $f\sigma_8$ and $H(z)$ or
Type Ia supernovae (SnIa) data. We perform the reconstruction in two different
ways, either by directly binning the data or by fitting various dark energy
models. We also examine how well the null-test can be reconstructed by future
data by creating mock catalogs based on the cosmological constant model, a
model with strong dark energy perturbations, the $f(R)$ and $f(G)$ models, and
the large void LTB model that exhibit different evolution of the matter
perturbations. We find that with future data similar to an LSST-like survey,
the null-test will be able to successfully discriminate between these different
cases at the $5\sigma$ level.
