The gravity lagrangian according to solar system experiments

We review the state of the art of f(R) theories of gravity (in their various formulations), which have been proposed as an explanation of the cosmic acceleration alternative to dark energy. The successes of f(R) gravity are discussed, together with the challenges imposed by minimal criteria for their viability.

We survey the landscape of $f(R)$ theories of gravity in their various formulations, which have been used to model the cosmic acceleration as alternatives to dark energy and dark matter. Besides, we take into account the problem of gravitational waves in such theories. We discuss some successes of $f(R)$-gravity (where $f(R)$ is a generic function of Ricci scalar $R$), theoretical and experimental challenges that they face in order to satisfy minimal criteria for viability.

Although several models of $f(R)$ theories of gravity within the Palatini approach have been studied already, the interest was concentrated on those that have an effect on the late-time evolution of the universe, by the inclusion for example of terms inversely proportional to the scalar curvature in the gravitational action. However, additional positive powers of the curvature also provide interesting early-time phenomenology, like inflation, and the presence of such terms in...

Alternative theories of gravity have been recently studied in connection with their cosmological applications, both in the Palatini and in the metric formalism. The aim of this paper is to propose a theoretical framework (in the Palatini formalism) to test these theories at the solar system level and possibly at the galactic scales. We exactly solve field equations in vacuum and find the corresponding corrections to the standard general relativistic gravitational field. On th...

We present the first formulation of the recently proposed $f(R,\mathcal{L}_m,T)$ theory of gravity within the Palatini formalism, a well-known alternative variational approach where the metric and connection are treated as independent variables. By applying this formalism, we derive a new set of field equations that exhibit, as expected, distinct properties compared to their metric formalism counterparts. We particularly present the Newtonian limit of this formalism, as well ...

Recently, the phenomenology of f(R) gravity has been scrutinized motivated by the possibility to account for the self-accelerated cosmic expansion without invoking dark energy sources. Besides, this kind of modified gravity is capable of addressing the dynamics of several self-gravitating systems alternatively to the presence of dark matter. It has been established that both metric and Palatini versions of these theories have interesting features but also manifest severe and ...

We motivate and analyze the weak-field limit of a non-analytical Lagrangian for the gravitational field. After investigating the parameter space of the model, we impose constraints on the parameters characterizing this class of theories imposed by Solar-System data, i.e. we establish the validity range where this solution applies and refine the constraints by the comparison with planetary orbits. As a result, we claim that this class of models is viable within different astro...

In the framework of $f(T)$ theories of gravity, we solve the field equations for $f(T)=T+\alpha T^{n}$, in the weak-field approximation and for spherical symmetry spacetime. Since $f(T)=T$ corresponds to Teleparallel Gravity, which is equivalent to General Relativity, the non linearity of the Lagrangian are expected to produce perturbations of the general relativistic solutions, parameterized by $\alpha$. Hence, we use the $f(T)$ solutions to model the gravitational field of ...

In order to constrain $f(R,L_{m})$ gravity from theoretical aspects, its energy conditions are derived in this paper. These energy conditions given by us are quite general and can be degenerated to the well-known energy conditions in General Relativity and $f(R)$ theories of gravity with arbitrary coupling, non-minimal coupling and non-coupling between matter and geometry, respectively, as special cases. To exemplify how to use these energy conditions to restrict $f(R,L_{m})$...

The evidence of the acceleration of universe at present time has lead to investigate modified theories of gravity and alternative theories of gravity, which are able to explain acceleration from a theoretical viewpoint without the need of introducing dark energy. In this paper we study alternative gravitational theories defined by Lagrangians which depend on general functions of the Ricci scalar invariant in minimal interaction with matter, in view of their possible cosmologi...