Embeddings of the "New Massive Gravity"

TL;DR

This paper explores various embeddings of the equations of motion for New Massive Gravity, revealing a new scalar-tensor model that is ghost-free and Weyl invariant at linear level, with implications for nonlinear completions and nonlocal modifications.

Contribution

It introduces a novel scalar-tensor model for massive gravitons that is ghost-free and Weyl invariant, expanding the understanding of embeddings of NMG equations.

Findings

A sixth order derivative model with ghosts from Noether gauge embedding.

A new scalar-tensor model that is ghost-free and Weyl invariant at linear level.

Proof that no local, ghost-free embedding exists for linearized NMG equations in terms of one symmetric tensor.

Abstract

Using different types of embeddings of equations of motion we investigate the existence of generalizations of the "New Massive Gravity" (NMG) model with the same particle content (massive gravitons). By using the Weyl symmetry as a guiding principle for the embeddings we show that the Noether gauge embedding approach leads us to a sixth order model in derivatives with either a massive or a massless ghost. If the Weyl symmetry is implemented by means of a Stueckelberg field we obtain a new scalar-tensor model for massive gravitons. It is ghost free and Weyl invariant at linearized level. The model can be nonlinearly completed into a scalar field coupled to the NMG theory. The elimination of the scalar field leads to a nonlocal modification of the NMG. We also prove to all orders in derivatives that there is no local, ghost free embedding of the linearized NMG equations of motion around Minkowski space when written in terms of one symmetric tensor. Regarding that point, NMG differs from the Fierz-Pauli theory, since in later case we can replace the Einstein-Hilbert action by specific $f(R,\Box\, R)$ generalizations and still keep the theory ghost free at linearized level.