Cosmological solutions of a chiral self-gravitating model of $f(R,(\nabla R)^2,\square R)$ gravity

TL;DR

This paper explores a modified gravity model involving higher derivatives of the Ricci scalar, reducing it to Einstein gravity with scalar fields, and finds exact cosmological solutions including de Sitter and power-law expansions.

Contribution

It introduces a novel chiral self-gravitating model derived from $f(R,( abla R)^2,ox R)$ gravity and provides explicit cosmological solutions within this framework.

Findings

Exact power law solutions for stiff matter

De Sitter solutions with constant potential

Trigonometric and hyperbolic expansion solutions

Abstract

We study modified $f(R,(\nabla R)^2,\square R)$ gravity and show in detail how it can be reduced to Einstein gravity with a few scalar fields and then represented in the form of chiral self-gravitating model of the special type. In further investigation of the model we focus on cosmology and looking for solutions of the dynamic equations of chiral fields and the Einstein-Friedman equations in the Friedman-Robertson-Walker spacetime. Exact solutions of the considered model for zero and constant potential are found. Between them power law solution corresponded to equation of state for stiff matter, de Sitter solution, trigonometric and hyperbolic expansion solution. Various type of chiral fields evolution support listed above solutions.