On tidal forces in f(R) theories of gravity

Abstract

Despite the extraordinary attention that modified gravity theories have attracted over the past decade, the geodesic deviation equation in this context has not received proper formulation thus far. This equation provides an elegant way to investigate the timelike, null and spacelike structure of spacetime geometries. In this investigation we provide the full derivation of this equation in situations where General Relativity has been extended in Robertson-Walker background spacetimes. We find that for null geodesics the contribution arising from the geometrical new terms is in general non-zero. Finally we apply the results to a well known class of f(R) theories, compare the results with General Relativity predictions and obtain the equivalent area distance relation.

9 pages, 2 figures

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• Cosmic Acceleration From Matter-Curvature Coupling
• Generalized Mattig's relation in Brans-Dicke-Rastall gravity
• Cosmological reconstructed solutions in extended teleparallel gravity theories with a teleparallel Gauss-Bonnet term
• Geodesic Deviation Equation in $f(R,T)$ Gravity
• Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity
• Perfect fluid solutions of Brans-Dicke and f(R)cosmology
• Cosmic Acceleration and Geodesic Deviation in Chameleon Scalar Field Model
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