Cosmological dynamics in six-order gravity

TL;DR

This paper investigates the effects of adding an $R ox R$ term to $R+R^N$ gravity theories on cosmological solutions and their stability, revealing that for $N=3$ these terms are equally significant.

Contribution

It analyzes the influence of the $R ox R$ term on known solutions in generalized $R+R^N$ gravity and studies their stability using dynamical systems methods.

Findings

For $N=3$, $R ox R$ and $R^N$ terms are equally important for power-law solutions.

Stability of de Sitter solutions is examined for various $N$ values.

The stability analysis includes cases where $N e 3$, using different methods.

Abstract

We consider cosmological dynamics in generalized modified gravity theory with the $R\Box R$ term added to the action of the form $R+R^N$. Influence of $R \Box R$ term to the known solutions of modified gravity is described. We show that in particular case of $N=3$ these two non-Einstein terms are equally important on power-law solutions. These solutions and their stability have been studied using dynamical system approach. Some results for the case of $N \ne 3$ (including stability of de Sitter solution in the theory under investigation) have been found using other methods.