Geodesic Deviation Equation in f(R) Gravity

TL;DR

This paper extends the geodesic deviation equation to f(R) gravity within cosmology, providing generalized relations and equations that could impact understanding of gravitational effects in modified gravity theories.

Contribution

It generalizes the GDE and Mattig relation for metric f(R) gravity using the FLRW metric, and derives an equivalent Dyer-Roeder equation in this context.

Findings

Generalized GDE for f(R) gravity

Derived a modified Mattig relation

Presented an equivalent Dyer-Roeder equation

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.