Consistent Higher Derivative Gravitational theories with stable de Sitter and Anti-de Sitter Backgrounds

TL;DR

This paper establishes criteria for higher derivative gravity theories to have stable de Sitter and anti-de Sitter backgrounds, including F(R), F(G), and infinite derivative gravity, relevant for quantum gravity and cosmology.

Contribution

It provides the first comprehensive stability criteria for a broad class of covariant, parity-preserving, torsion-free higher derivative gravity theories around (A)dS backgrounds.

Findings

F(R) and F(G) theories can have stable (A)dS solutions.

String-inspired infinite derivative gravity can also be stable around (A)dS backgrounds.

The criteria help identify viable theories for quantum gravity and cosmological applications.

Abstract

In this paper we provide the criteria for any generally covariant, parity preserving, and torsion free theory of gravity to possess a stable de Sitter (dS) or anti-de Sitter (AdS) background. By stability we mean the absence of tachyonic or ghost-like states in the perturbative spectrum that can lead to classical instabilities and violation of quantum unitarity. While we find that the usual suspects, the F(R) and F(G) theories, can indeed possess consistent (A)dS backgrounds, G being the Gauss-Bonnet term, another interesting class of theories, string-inspired infinite derivative gravity, can also be consistent around such curved vacuum solutions. Our study should not only be relevant for quantum gravity and early universe cosmology involving ultraviolet physics, but also for modifications of gravity in the infra-red sector vying to replace dark energy .