On Non-Linear Actions for Massive Gravity

TL;DR

This paper develops a systematic approach to constructing potentially ghost-free non-linear massive gravity actions, revealing a general 2-parameter deformation of minimal models and clarifying the role of non-dynamical terms.

Contribution

It introduces a new formalism for massive gravity actions using a deformed determinant, extending previous models and identifying non-contributing terms.

Findings

Constructed a general 2-parameter family of ghost-free massive gravity actions.

Showed that extensions beyond four dimensions vanish, simplifying the theory.

Clarified the role of non-dynamical terms in the formal structure.

Abstract

In this work we present a systematic construction of the potentially ghost-free non-linear massive gravity actions. The most general action can be regarded as a 2-parameter deformation of a minimal massive action. Further extensions vanish in 4 dimensions. The general mass term is constructed in terms of a "deformed" determinant from which this property can clearly be seen. In addition, our formulation identifies non-dynamical terms that appear in previous constructions and which do not contribute to the equations of motion. We elaborate on the formal structure of these theories as well as some of their implications.