Curvature scalar instability in f(R) gravity

TL;DR

This paper investigates the stability of f(R) gravity theories with matter, revealing that the Palatini formalism avoids the curvature scalar instability present in the metric formalism, thus clarifying the conditions for stable modified gravity models.

Contribution

It demonstrates that the curvature scalar instability found in metric f(R) gravity does not occur in the Palatini formalism, providing a deeper understanding of stability conditions in modified gravity theories.

Findings

Instability occurs in metric f(R) gravity with matter.

Palatini formalism does not exhibit this instability.

The difference is due to the formalism's treatment of the gravitational action.

Abstract

An instability in the presence of matter in theories of gravity which include a 1/R correction in the gravitational action has been found by Dolgov and Kawasaki. In the present paper this instability is discussed for f(R) gravity in general. We focus on the Palatini formalism of the theory and it is shown that no such instability occurs in this version of f(R) gravity. The reasons for the appearance of the instability in the metric but not in the Palatini formalism are fully investigated.