An overview of f(R) theories

Source: arXiv


A brief introduction to theories of the gravitational field with a Lagrangian
that is a function of the scalar curvature is given. The emphasis will be
placed in formal developments, while comparison to observation will be
discussed in the chapter by S. Jor\'as in this volume.

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Available from: Santiago E. Perez-Bergliaffa
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    • "It seems well proven that the universe is experiencing an acceleration process [1] [2] [3]. Physicists have elaborated various answers [4] to explain this accelerated state, among them, the following may be mentioned: the existence of a new kind of energy (called 'dark energy' that we could consider to include Einstein's famous cosmological constant) [5], matter creation [6] [7] [8] [9], and a whole set of theories that modify or go beyond the General Theory of Relativity, such as F(R) [10]. The problem in elucidating what is really happening resides in the current data and the precision with which they are obtained. "
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    ABSTRACT: In the first order formalism of gravitational theories, the spacetime connection is considered as an independent variable to vary together with the metric. However, the metric still generates its Levi-Civita connection that turns out to determine the geodesics of matter. Recently, "hybrid" gravity theories have been introduced by constructing actions involving both the independent Palatini connection and the metric Levi-Civita connection. In this study a method is developed to analyse the field content of such theories, in particular to determine whether the propagating degrees of freedom are ghosts or tachyons. New types of second, fourth and sixth order derivative gravity theories are investigated and the so called f(X) theories are singled out as a viable class of "hybrid" extensions of General Relativity.
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    ABSTRACT: The field equations in FRW background for the so called C-theories are presented and investigated. In these theories the usual Ricci scalar is substituted with $f(\mathcal{R})$ where $\mathcal{R}$ is a Ricci scalar related to a conformally scaled metric $\hat{g}_{\mu\nu} = \mathcal{C}(\mathcal{R})g_{\mu\nu}$, where the conformal factor itself depends on $\mathcal{R}$. It is shown that homogeneous perturbations of this Ricci scalar around general relativity FRW background of a large class of these theories are either inconsistent or unstable.
    No preview · Article · May 2013