Chiral cosmological model of F(R,R) gravity

We study the modified gravity 𝑓(𝑅,□𝑅), which can be reduced to a chiral cosmological model of a particular type with scalar field observers 𝜒, 𝜑, 𝜙. The method of studying the chiral cosmological model was used for the 𝑓(𝑅, (∇𝑅)2) models, but was first used by Naruko for the more general 𝑓(𝑅) Gracing model. In this paper, equations for chiral fields and the Einstein-Friedmann equations in the Friedmann-Robertson-Walker metric are presented. Note that the solutions for this chosen model are based on a special choice of one of the chiral fields: = - √ 3/2 ln 2. Solutions are considered in the case of reducing the model to a one-field model: two chiral fields of the model depend linearly on the third one. The obtained solutions are of interest, since quantum corrections must also be taken into account in the analysis.