On Non-Linear Actions for Massive Gravity

TL;DR

The paper addresses the challenge of constructing ghost-free non-linear massive gravity actions. It introduces a deformed determinant construction that yields a two-parameter family of actions, including a minimal model that isolates non-dynamical determinant pieces and reproduces the Fierz-Pauli structure at quadratic order. It shows that these actions align with the dRGT ghost-free class in four dimensions and explores generalizations to non-flat auxiliary metrics, enabling GR-like backgrounds and cosmological constant screening in suitable setups. A full non-linear ghost freedom proof remains an open issue, but the framework clarifies the structure and equivalences among known constructions and highlights potential phenomenological implications for gravity at large scales.

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.