Geodesic Deviation Equation in f(R) Gravity

Abstract

In this paper we study the Geodesic Deviation Equation (GDE) in metric f(R) gravity. We start giving a brief introduction of the GDE in General Relativity in the case of the standard cosmology. Next we generalize the GDE for metric f(R) gravity using again the FLRW metric. A generalization of the Mattig relation is also obtained. Finally we give and equivalent expression to the Dyer-Roeder equation in General Relativity in the context of f(R) gravity.

13 pages, 1 figure. Accepted for publication in General Relativity and Gravitation

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• Cosmic Acceleration From Matter-Curvature Coupling
• Generalized Mattig's relation in Brans-Dicke-Rastall gravity
• Geodesic Deviation Equation in $f(R,T)$ Gravity
• Reconstruction of $f(R)$ gravity models for an accelerated universe using Raychaudhuri equation
• On tidal forces in f(R) theories of gravity
• Geodesic Deviation Equation in $\Lambda$CDM $f(T,\mathcal{T})$ gravity
• Geodesic deviation in Saez--Ballester theory
• A generalized $\Lambda$CDM model with parameterized Hubble parameter in particle creation, viscous and $f(R)$ model framework
• Geodesic deviation equation in Brans-Dicke theory in arbitrary dimensions
• Cosmic Acceleration and Geodesic Deviation in Chameleon Scalar Field Model
• Cosmological Models in Modified f(R) Gravity Theories
• Geodesic deviation equation in generalized hybrid Metric-Palatini gravity
• Erratum to: Geodesic Deviation Equation in f(R) Gravity