f(R) theories

Over the past decade, f(R) theories have been extensively studied as one of the simplest modifications to General Relativity. In this article we review various applications of f(R) theories to cosmology and gravity - such as inflation, dark energy, local gravity constraints, cosmological perturbations, and spherically symmetric solutions in weak and strong gravitational backgrounds. We present a number of ways to distinguish those theories from General Relativity observationally and experimentally. We also discuss the extension to other modified gravity theories such as Brans-Dicke theory and Gauss-Bonnet gravity, and address models that can satisfy both cosmological and local gravity constraints.Comment: 156 pages, 14 figures, Invited review article in Living Reviews in Relativity, Published version, Comments are welcom

Conformal transformation in f(T)f(T) theories

It is well-known that $f(R)$ theories are dynamically equivalent to a particular class of scalar-tensor theories. In analogy to the $f(R)$ extension of the Einstein-Hilbert action of general relativity, $f(T)$ theories are generalizations of the action of teleparallel gravity. The field equations are always second order, remarkably simpler than $f(R)$ theories. It is interesting to investigate whether $f(T)$ theories have the similar conformal features possessed in $f(R)$ theories. It is shown, however, that $f(T)$ theories are not dynamically equivalent to teleparallel action plus a scalar field via conformal transformation, there appears an additional scalar-torsion coupling term. We discuss briefly what constraint of this coupling term may be put on $f(T)$ theories from observations of the solar system.Comment: 4 pages, Revision to be publishe

Future dynamics in f(R) theories

The $f(R)$ gravity theories provide an alternative way to explain the current cosmic acceleration without invoking dark energy matter component. However, the freedom in the choice of the functional forms of $f(R)$ gives rise to the problem of how to constrain and break the degeneracy among these gravity theories on theoretical and/or observational grounds. In this paper to proceed further with the investigation on the potentialities, difficulties and limitations of $f(R)$ gravity, we examine the question as to whether the future dynamics can be used to break the degeneracy between $f(R)$ gravity theories by investigating the future dynamics of spatially homogeneous and isotropic dust flat models in two $f(R)$ gravity theories, namely the well known $f(R) = R + \alpha R^{n}$ gravity and another by A. Aviles et al., whose motivation comes from the cosmographic approach to $f(R)$ gravity. To this end we perform a detailed numerical study of the future dynamic of these flat model in these theories taking into account the recent constraints on the cosmological parameters made by the Planck team. We show that besides being powerful for discriminating between $f(R)$ gravity theories, the future dynamics technique can also be used to determine the fate of the Universe in the framework of these $f(R)$ gravity theories. Moreover, there emerges from our numerical analysis that if we do not invoke a dark energy component with equation-of-state parameter $\omega < -1$ one still has dust flat FLRW solution with a big rip, if gravity deviates from general relativity via $f(R) = R + \alpha R^n$. We also show that FLRW dust solutions with $f''<0$ do not necessarily lead to singularity.Comment: 12 pages, 8 figures. V2: Generality and implications of the results are emphasized, connection with the recent literature improved, typos corrected, references adde

Constraining f(R) theories with cosmography

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 the second uses the dependence of H with z furnished by a given type of extended theory. When applied to f(R) theories together with the redshift drift, the method yields limits on the parameters of two examples (the theory of Hu and Sawicki (2007), and the exponential gravity introduced by Linder (2009)) that are compatible with or more stringent than the existing ones, as well as a limit for a previously unconstrained parameter.Comment: 9 pages, 2 figures; v2: modifications in title and presentation, results unchange

f(R) and f(T) theories of modified gravity

We briefly review f(R) theories, both in the metric and Palatini formulations, their scalar-tensor representations and the chameleon mechanism that could explain the absence of perceptible consequences in the Solar System. We also review f(T) theories, a different approach to modified gravity consisting in a deformation of the teleparallel equivalent of General Relativity. We show some applications to cosmology and cosmic strings. As f(R)'s, f(T) theories are not exempted from additional degrees of freedom; we also discuss this still open issue.Comment: 8 pages, 2 figures. To appear in the Proceedings of the CosmoSul conference (Rio de Janeiro, Brazil, 01-05 August 2011). Added reference