The gravity lagrangian according to solar system experiments

We comment on, and complete, the analysis of the weak field limit of metric f(R) gravity in T. Chiba, T.L. Smith, and A.L. Erickcek, Phys. Rev. D 75, 124014 (2007).

We discuss solar system constraints on f(G) gravity models, where f is a function of the Gauss-Bonnet term G. We focus on cosmologically viable f(G) models that can be responsible for late-time cosmic acceleration. These models generally give rise to corrections of the form epsilon*(r/rs)^p to the vacuum Schwarzschild solution, where epsilon = H^2 rs^2 << 1, rs is the Schwarzschild radius of Sun, and H is the Hubble parameter today. We generally estimate the strength of modif...

We discuss recent results on the cosmology of extended theories of gravity formulated in the Palatini approach, i.e., assuming that metric and connection are independent fields. In particular, we focus on the attempts to explain the cosmic speedup with f(R) theories and on models that avoid the big bang singularity. The field equations for gravity Lagrangians of the form f(g_{\mu\nu},{R^\alpha}_{\beta\mu\nu}) (including torsion) are explicitly derived and discussed.

Einstein's General Relativity (GR) is possibly one of the greatest intellectual achievements ever conceived by the human mind. In fact, over the last century, GR has proven to be an extremely successful theory, with a well established experimental footing. However, the discovery of the late-time cosmic acceleration, which represents a new imbalance in the governing gravitational field equations, has forced theorists and experimentalists to question whether GR is the correct r...

In order to shed some light on the current discussion about f(R)-gravity theories we derive and discuss the bounds imposed by the energy conditions on a general f(R) functional form. The null and strong energy conditions in this framework are derived from the Raychaudhuri's equation along with the requirement that gravity is attractive, whereas the weak and dominant energy conditions are stated from a comparison with the energy conditions that can be obtained in a direct appr...

We present and discuss the bounds from the energy conditions on a general f(R) functional form in the framework of metric variational approach. As a concrete application of the energy conditions to locally homogeneous and isotropic f(R)-cosmology, the recent estimated values of the deceleration and jerk parameters are used to examine the bounds from the weak energy condition on the free parameter of the family of f(R)=\sqrt{R^2 - R_0^2} gravity theory.

We discuss two aspects of f(R) theories of gravity in metric formalism. We first study the reasons to introduce a scalar-tensor representation for these theories and the behavior of this representation in the limit to General Relativity, f(R)--> R. We find that the scalar-tensor representation is well behaved even in this limit. Then we work out the exact equations for spherically symmetric sources using the original f(R) representation, solve the linearized equations, and co...

In this work, we study cosmological and astrophysical applications of the recently proposed generalized hybrid metric-Palatini gravity theory, which combines features of both the metric and the Palatini approaches to the variational method in $f\left(R\right)$ gravity. This theory arises as a natural generalization of the hybrid metric-Palatini gravity which has been proven to be the first theory to unify the cosmic acceleration with the solar system constraints, without reso...

We study the effects that the gravitational interaction of $f(R)$ theories of gravity in Palatini formalism has on the stationary states of the Hydrogen atom. We show that the role of gravity in this system is very important for lagrangians $f(R)$ with terms that grow at low curvatures, which have been proposed to explain the accelerated expansion rate of the universe. We find that new gravitationally induced terms in the atomic Hamiltonian generate a strong backreaction that...

We investigate a simple generalization of the metric exponential $f(R)$ gravity theory that is cosmologically viable and compatible with solar system tests of gravity. We show that, as compared to other viable $f(R)$ theories, its steep dependence on the Ricci scalar $R$ facilitates agreement with structure constraints, opening the possibility of $f(R)$ models with equation-of-state parameter that could be differentiated from a cosmological constant ($w_{de}=-1$) with future ...