Perturbative aspects and conformal solutions of F(R) gravity

TL;DR

This paper explores the stability and solutions of F(R) gravity theories, revealing stability under metric perturbations but potential curvature instabilities with 1/R terms, and constructs explicit dilaton solutions for specific F(R) forms.

Contribution

It provides a stability analysis of F(R) gravity and explicitly constructs kink-like dilaton solutions for certain F(R) models.

Findings

Generic F(R) theories are stable under metric perturbations.

Instabilities may occur against curvature perturbations with 1/R terms.

Explicit kink-like solutions are found for R + γ R^n models.

Abstract

We investigate perturbative aspects of gravity with a general F(R) Lagrangian, as well as nonperturbative dilatonic solutions. For the first part, we are interested in stability and the definition of asymptotic charges. The main result of this study is that, while generic F(R) theories are stable under metric perturbations, they are expected to show instabilities against curvature perturbations when the Lagrangian includes 1/R terms. For the second part, one is interested on exact solutions, and we explicitly construct kink-like solutions of the Liouville type for the dilaton field for F(R) having the form R+\gamma R^n, in two and in four dimensions.