Reconstruction of cosmological matter perturbations in modified gravity

Abstract

The analysis of perturbative quantities is a powerful tool to distinguish between different dark energy models and gravity theories degenerated at the background level. In this work, we generalize the integral solution of the matter density contrast for general relativity gravity [V. Sahni and A. Starobinsky, Int. J. Mod. Phys. D 15, 2105 (2006)., U. Alam, V. Sahni, and A. A. Starobinsky, Astrophys. J. 704, 1086 (2009).] to a wide class of modified gravity (MG) theories. To calculate this solution, it is necessary to have prior knowledge of the Hubble rate, the density parameter at the present epoch (${\mathrm{\ensuremath{\Omega}}}_{m0}$), and the functional form of the effective Newton's constant that characterizes the gravity theory. We estimate in a model-independent way the Hubble expansion rate by applying a nonparametric reconstruction method to model-independent cosmic chronometer data and high-$z$ quasar data. In order to compare our generalized solution of the matter density contrast, using the nonparametric reconstruction of $H(z)$ from observational data, with a purely theoretical one, we choose a parametrization of the screened modified gravity and the ${\mathrm{\ensuremath{\Omega}}}_{m0}$ from WMAP-9 Collaborations. Finally, we calculate the growth index for the analyzed cases, finding very good agreement between theoretical values and the obtained ones using the approach presented in this work.