On the evolution of inhomogeneous perturbations in the ΛCDM model and f(R) modified gravity theories

We focus on weak inhomogeneous models of the Universe at low redshifts, described by the Lemaitre-Tolman-Bondi (LTB) metric. The principal aim of this work is to compare the evolution of inhomogeneous perturbations in the ΛCDM cosmological model and f(R) modified gravity theories, considering a flat Friedmann-Lemaitre-Robertson-Walker (FLRW) metric for the background. More specifically, we adopt the equivalent scalar-tensor formalism in the Jordan frame, in which the extra degree of freedom of the f(R) function is converted into a non-minimally coupled scalar field. We investigate the evolution of local inhomogeneities in time and space separately, following a linear perturbation approach. Then, we obtain spherically symmetric solutions in both cosmological models. Our results allow us to distinguish between the presence of a cosmological constant and modified gravity scenarios, since a peculiar Yukawa-like solution for radial perturbations occurs in the Jordan frame. Furthermore, the radial profile of perturbations does not depend on a particular choice of the f(R) function, hence our results are valid for any f(R) model.