Gravitational theories with stable (anti-)de Sitter backgrounds

TL;DR

This paper constructs the most general torsion-free, parity-invariant covariant gravity theories in four dimensions that are free from ghost and tachyon instabilities around constant curvature backgrounds, including Minkowski, de Sitter, and anti-de Sitter spaces.

Contribution

It derives the conditions for stability of quadratic curvature gravity theories around constant curvature backgrounds, generalizing previous models and clarifying the propagating degrees of freedom.

Findings

Only the transverse traceless spin-2 graviton propagates.

A possible scalar degree of freedom may also propagate.

Stability conditions are established for these theories.

Abstract

In this article we will construct the most general torsion-free parity-invariant covariant theory of gravity that is free from ghost-like and tachyonic nstabilities around constant curvature space-times in four dimensions. Specifically, this includes the Minkowski, de Sitter and anti-de Sitter backgrounds. We will first argue in details how starting from a general covariant action for the metric one arrives at an "equivalent" action that at most contains terms that are quadratic in curvatures but nevertheless is sufficient for the purpose of studying stability of the original action. We will then briefly discuss how such a "quadratic curvature action" can be decomposed in a covariant formalism into separate sectors involving the tensor, vector and scalar modes of the metric tensor; most of the details of the analysis however, will be presented in an accompanying paper. We will find that only the transverse and trace-less spin-2 graviton with its two helicity states and possibly a spin-0 Brans-Dicke type scalar degree of freedom are left to propagate in 4 dimensions. This will also enable us to arrive at the consistency conditions required to make the theory perturbatively stable around constant curvature backgrounds. This will be included as a chapter in the book entitled "At the Frontier of Spacetime - Scalar-Tensor Theory, Bells Inequality, Machs Principle, Exotic Smoothness" (Springer 2016)