Cosmological phase space of R^n gravity

TL;DR

This paper analyzes the phase space and exact solutions of R^n gravity models, identifying attractors and their compatibility with observational data, and explores the special case of n=2 models approximating a non-singular gravity function.

Contribution

It provides a phase space analysis and exact solutions for R^n gravity models, including the special n=2 case, and compares their late-time behavior with observational data.

Findings

Power law solutions for n ≠ 2 act as attractors.

Certain ranges of n produce models consistent with WMAP data.

Quadratic model admits de Sitter attractor compatible with observations.

Abstract

We present some exact solutions and a phase space analysis of metric $f(R)$-gravity models of the type $R^{n}$. We divide our discussion in $n\neq2$ and $n=2$ models. The later model is a good approximation, at late times to the $f(R) = \frac{2}{\pi}R \tan^{-1}(R/\beta^2)$ gravity model, being this an example of a non--singular case. For $n \neq 2$ models we have found power law solutions for the scale factor that are attractors and that comply with WMAP 5-years data if $n <-2.55 $ or $ 1.67< n < 2$. On the other hand, the quadratic model has the de Sitter solution as an attractor, that also complies with WMAP 5-years data.