Consistent Spin-Two Coupling and Quadratic Gravitation

TL;DR

This paper explores quadratic higher-derivative gravity, demonstrating a new consistent coupling of a massless spin-two field to gravity, and analyzes the stability and ghost issues of such theories.

Contribution

It introduces a new example of a massless spin-two field consistently coupled to gravity within quadratic gravity frameworks.

Findings

Quadratic gravity is equivalent to a second-order theory with scalar and spin-two fields.

Conditions for the spin-two field to have only spin-two degrees of freedom are derived.

Flat space is the only stable vacuum, but the spin-two field is ghost-like around flat space.

Abstract

A discussion of the field content of quadratic higher-derivative gravitation is presented, together with a new example of a massless spin-two field consistently coupled to gravity. The full quadratic gravity theory is shown to be equivalent to a canonical second-order theory of a massive scalar field, a massive spin-two symmetric tensor field and gravity. The conditions showing that the tensor field describes only spin-two degrees of freedom are derived. A limit of the second-order theory provides a new example of massless spin-two field consistently coupled to gravity. A restricted set of vacua of the second-order theory is also discussed. It is shown that flat-space is the only stable vacuum of this type, and that the spin-two field around flat space is unfortunately always ghost-like.