Massive spin-2 particles via embedment of the Fierz-Pauli equations of motion

TL;DR

This paper develops alternative ghost-free models for massive spin-2 particles through an embedding of Fierz-Pauli equations, including higher-order derivative theories and connections to $f(R)$ massive gravities.

Contribution

It introduces new ghost-free models for massive spin-2 particles via an embedding procedure, extending Fierz-Pauli theory with higher derivatives and nonlinear completions.

Findings

Models are free of ghosts at quadratic level

Some models include $f(R)$ massive gravities

Propagator structure remains unchanged by extra terms

Abstract

Here we obtain alternative descriptions of massive spin-2 particles by an embedding procedure of the Fierz-Pauli equations of motion. All models are free of ghosts at quadratic level although most of them are of higher order in derivatives. The models that we obtain can be nonlinearly completed in terms of a dynamic and a fixed metric. They include some $f(R)$ massive gravities recently considered in the literature. In some cases there is an infrared (no derivative) modification of the Fierz-Pauli mass term altogether with higher order terms in derivatives. The analytic structure of the propagator of the corresponding free theories is not affected by the extra terms in the action as compared to the usual second order Fierz-Pauli theory.