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On Non-Linear Actions for Massive Gravity

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.