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.