Massive Gravity Theories and limits of Ghost-free Bigravity models

TL;DR

This paper develops a broad class of ghost-free bigravity theories extending New Massive Gravity, demonstrating their unitarity, absence of the Boulware-Deser ghost, and their connection to holographic c-theorems and Born-Infeld extensions.

Contribution

It introduces a new class of higher-order curvature theories derived from Lovelock bigravity models that are ghost-free and extend existing massive gravity frameworks.

Findings

Constructed higher-order curvature theories from Lovelock bigravity models.

Proved these theories are free from the Boulware-Deser ghost.

Established a holographic c-theorem within this class of models.

Abstract

We construct a class of theories which extend New Massive Gravity to higher orders in curvature in any dimension. The lagrangians arise as limits of a new class of bimetric theories of Lovelock gravity, which are unitary theories free from the Boulware-Deser ghost. These Lovelock bigravity models represent the most general non-chiral ghost-free theories of an interacting massless and massive spin-two field in any dimension. The scaling limit is taken in such a way that unitarity is explicitly broken, but the Boulware-Deser ghost remains absent. This automatically implies the existence of a holographic $c$-theorem for these theories. We also show that the Born-Infeld extension of New Massive Gravity falls into our class of models demonstrating that this theory is also free of the Boulware-Deser ghost. These results extend existing connections between New Massive Gravity, bigravity theories, Galileon theories and holographic $c$-theorems.