Using a novel and self-consistent approach that avoids the scalar-tensor identification in the Einstein frame, we reanalyze the viability of f (R) gravity within the context of solar-system tests. In order to do so, we depart from a simple but fully relativistic system of differential equations that describe a compact object in a static and spherically symmetric spacetime, and then make suitable linearizations that apply to non-relativistic objects such as the Sun. We then show clearly under which conditions the emerging chameleon-like mechanism can lead to a Post-Newtonian Parameter γ compatible with the observational bounds. To illustrate this method, we use several specific f (R) models proposed to explain the current acceleration of the Universe, and we show which of them are able to satisfy those bounds. PACS numbers: 04.50.Kd, 95.36.+x, 04.40.Dg
I. INTRODUCTIONf (R) gravity remains one of the most popular and viable mechanisms to explain the current accelerated expansion of the Universe (see Refs [1-6] for a review) while predicting an equation of state for the "dark energy" that changes in cosmic time and that might accommodate to future observations better than a simple cosmological constant Λ [7-9]. This proposal consists of taking for the action functional a (non linear) function f (R) of the Ricci scalar R different from the General Relativity (GR) f GR (R) = R − 2Λ. Thus, unless otherwise stated, and in order to avoid confusion, hereafter f (R) refers to those non-linear models. This alternative, while very attractive for it does not require additional fields, opens, however, a Pandora box that risks spoiling many of the GR predictions that have been verified with high accuracy during the past hundred years (e.g. solar-system tests, binary pulsar phenomenology), including the recent detection of gravitational waves by the LIGO-VIRGO collaboration [10]. Several specific f (R) models have been put forward to explain the cosmic acceleration, but many of them have failed other tests, including more refined cosmological scrutinies (e.g. the analysis of cosmological perturbations and the CMB), solar system (weak gravity tests) and strong gravity tests (e.g. neutron stars). One of the drawbacks of this kind of modifications of gravity is that there is a priori no fundamental principle