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Perturbative quantities, such as the growth rate ($f$) and index ($gamma$), are powerful tools to distinguish different dark energy models or modified gravity theories even if they produce the same cosmic expansion history. In this work, without any assumption about the dynamics of the Universe, we apply a non-parametric method to current measurements of the expansion rate $H(z)$ from cosmic chronometers and high-$z$ quasar data and reconstruct the growth factor and rate of linearised density perturbations in the non-relativistic matter component. Assuming realistic values for the matter density parameter $Omega_{m0}$, as provided by current CMB experiments, we also reconstruct the evolution of the growth index $gamma$ with redshift. We show that the reconstruction of current $H(z)$ data constrains the growth index to $gamma=0.56 pm 0.12$ (2$sigma$) at $z = 0.09$, which is in full agreement with the prediction of the $Lambda$CDM model and some of its extensions.
The cosmological jerk parameter $j$ is reconstructed in a non-parametric way from observational data independent of a fiducial cosmological model. From this kinematical quantity, the equation of state parameter for composite matter distribution is al
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 reconstr
In the context of a Hubble tension problem that is growing in its statistical significance, we reconsider the effectiveness of non-parametric reconstruction techniques which are independent of prescriptive cosmological models. By taking cosmic chrono
Inferring high-fidelity constraints on the spatial curvature parameter, $Omega_{rm K}$, under as few assumptions as possible, is of fundamental importance in cosmology. We propose a method to non-parametrically infer $Omega_{rm K}$ from late-Universe
A non-parametric reconstruction of the deceleration parameter $q$ is carried out. The observational datasets are so chosen that they are model independent as much as possible. The present acceleration and the epoch at which the cosmic acceleration se