Metric gravity theories and cosmology:II. Stability of a ground state in f(R) theories

TL;DR

This paper investigates the stability of ground states in f(R) gravity theories, establishing criteria for stability and demonstrating that many such theories possess stable ground states, thus contributing to their viability in cosmology.

Contribution

It applies stability analysis methods from GR to f(R) theories, providing a simple criterion for ground state stability across multiple models.

Findings

13 cases of Lagrangians show effective stability criteria

An infinite number of theories have stable ground states

Further criteria are needed for full viability assessment

Abstract

A fundamental criterion of viability of any gravity theory is existence of a stable ground-state solution being either Minkowski, dS or AdS space. Stability of the ground state is independent of which frame is physical. In general, a given theory has multiple ground states and splits into independent physical sectors. All metric gravity theories with the Lagrangian being a function of Ricci tensor are dynamically equivalent to Einstein gravity with a source and this allows us to study the stability problem using methods developed in GR. We apply these methods to f(R) theories. As is shown in 13 cases of Lagrangians the stability criterion works simply and effectively whenever the curvature of the ground state is determined. An infinite number of gravity theories have a stable ground state and further viability criteria are necessary.