Cosmological dynamics of R^n gravity

TL;DR

This paper analyzes the cosmological dynamics of R^n gravity models, identifying conditions for accelerated expansion and stability of solutions using dynamical systems theory, both with and without matter coupling.

Contribution

It provides a comprehensive dynamical systems analysis of R^n gravity cosmologies, including exact solutions and stability conditions for various parameter ranges.

Findings

Accelerated expansion is a common attractor in R^n cosmologies.

Matter coupling restricts the range of parameter n for viable solutions.

Transient Friedmann-like phases can occur before acceleration dominates.

Abstract

A detailed analysis of dynamics of cosmological models based on $R^{n}$ gravity is presented. We show that the cosmological equations can be written as a first order autonomous system and analyzed using the standard techniques of dynamical system theory. In absence of perfect fluid matter, we find exact solutions whose behavior and stability are analyzed in terms of the values of the parameter $n$. When matter is introduced, the nature of the (non-minimal) coupling between matter and higher order gravity induces restrictions on the allowed values of $n$. Selecting such intervals of values and following the same procedure used in the vacuum case, we present exact solutions and analyze their stability for a generic value of the parameter $n$. From this analysis emerges the result that for a large set of initial conditions an accelerated expansion is an attractor for the evolution of the $R^n$ cosmology. When matter is present a transient almost-Friedman phase can also be present before the transition to an accelerated expansion.