Smoothing expansion rate data to reconstruct cosmological matter
  perturbations
  The existing degeneracy between different dark energy and modified gravity
cosmologies at the background level may be broken by analysing quantities at
the perturbative level. In this work, we apply a non-parametric smoothing (NPS)
method to reconstruct the expansion history of the Universe ($H(z)$) from
model-independent cosmic chronometers and high-$z$ quasar data. Assuming a
homogeneous and isotropic flat universe and general relativity (GR) as the
gravity theory, we calculate the non-relativistic matter perturbations in the
linear regime using the $H(z)$ reconstruction and realistic values of
$\Omega_{m0}$ and $\sigma_8$ from Planck and WMAP-9 collaborations. We find a
good agreement between the measurements of the growth rate and $f\sigma_8(z)$
from current large-scale structure observations and the estimates obtained from
the reconstruction of the cosmic expansion history. Considering a recently
proposed null test for GR using matter perturbations, we also apply the NPS
method to reconstruct $f\sigma_8(z)$. For this case, we find a $\sim 2\sigma$
tension (good agreement) with the standard relativistic cosmology when the
Planck (WMAP-9) priors are used.
