Signature of f(R) gravity via Lemaître–Tolman–Bondi inhomogeneous perturbations

We analyze inhomogeneous cosmological models in the local Universe, described by the Lemaître–Tolman–Bondi (LTB) metric and developed using linear perturbation theory on a homogeneous and isotropic Universe background. Focusing on the different evolution of spherical symmetric inhomogeneities, we compare the Λ Λ LTB model, in which the cosmological constant Λ Λ is included in the LTB formalism, with inhomogeneous cosmological models based on f( R) f R modified gravity theories viewed in the Jordan frame. We solve the system of field equations for both inhomogeneous cosmological models adopting the method of separation of variables: we integrate analytically the radial profiles of local perturbations, while their time evolution requires a numerical approach. The main result of the analysis concerns the different radial profiles of local inhomogeneities due to the presence of a non-minimally coupled scalar field in the Jordan frame of f( R) f R gravity. While radial perturbations follow a power-law in the Λ Λ LTB model, Yukawa-like contributions appear in the f( R) f R theory. Interestingly, this latter peculiar behavior of radial profile is not affected by the choice of the f( R) f R functional form. The numerical solution of time-dependent perturbations exhibits a non-diverging profile. This work suggests that investigations about local inhomogeneities in the late Universe may allow us to discriminate if the present cosmic acceleration is caused by a cosmological constant term or a modified gravity effect.