Variations of Infinite Derivative Modified Gravity

Abstract

We consider nonlocal modified Einstein gravity without matter, where nonlocal term has the form P(R)F (□) Q(R). For this model, in this paper we give the derivation of the equations of motion in detail. This is not an easy task and presented derivation should be useful to a researcher who wants to investigate nonlocal gravity. Also, we present the second variation of the related Einstein–Hilbert modified action and basics of gravity perturbations.