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We consider general metric $f(R)$ theories of gravity by solving the field equations in the presence of a spherical static mass distribution by analytical perturbative means. Expanding the field equations systematically in $cO(G)$, we solve the resulting set of equations and show that $f(R)$ theories which attempt to solve the dark energy problem very generally lead to $gamma_{PPN}=1/2$ in the solar system. This excludes a large class of theories as possible explanations of dark energy. We also present the first order correction to $gamma_{PPN}$ and show that it cannot have a significant effect.
We study stellar configurations and the space-time around them in metric $f(R)$ theories of gravity. In particular, we focus on the polytropic model of the Sun in the $f(R)=R-mu^4/R$ model. We show how the stellar configuration in the $f(R)$ theory c
A method to set constraints on the parameters of extended theories of gravitation is presented. It is based on the comparison of two series expansions of any observable that depends on H(z). The first expansion is of the cosmographical type, while th
We investigate f(R) theories of gravity within the Palatini approach and show how one can determine the expansion history, H(a), for an arbitrary choice of f(R). As an example, we consider cosmological constraints on such theories arising from the su
It is nowadays accepted that the universe is undergoing a phase of accelerated expansion as tested by the Hubble diagram of Type Ia Supernovae (SNeIa) and several LSS observations. Future SNeIa surveys and other probes will make it possible to better
In this work we investigate the equilibrium configurations of white dwarfs in a modified gravity theory, na-mely, $f(R,T)$ gravity, for which $R$ and $T$ stand for the Ricci scalar and trace of the energy-momentum tensor, respectively. Considering th