Non linear Fierz-Pauli theory from torsion and bigravity

TL;DR

This paper explores a nonlinear model of massive spin-2 particles with propagating torsion, deriving equations that generalize Fierz-Pauli theory in curved backgrounds and comparing it with bigravity models.

Contribution

It introduces a nonlinear torsion-based massive gravity model that extends Fierz-Pauli equations to curved space and highlights differences from bigravity theories.

Findings

Nonlinear equations reduce to generalized Fierz-Pauli in any background.

The model propagates 8 degrees of freedom, matching bigravity at linear order.

Additional terms in the nonlinear equations suggest non-uniqueness of curved space Fierz-Pauli generalization.

Abstract

The non linear aspects of a recently proposed model of massive spin-2 particles with propagating torsion are studied. We obtain a nonlinear equation which reduces at linear order to a generalized Fierz-Pauli equation in any background space-time with or without a vanishing torsion. We contrast those results with properties of a class of bigravity theories in an arbitrary background Einstein manifold. It is known that the non perturbative spectrum of the bigravity model has 8 propagating physical degrees of freedom. This is identical to the physical propagating degrees of freedom of the massive spin-2 torsion model at the linearized order. The obtained non linear version of the Fierz-Pauli field equations, however, contains terms absent in the bigravity case which indicates that the curved space generalization of the unique flat space space Fierz-Pauli equation is not unique. Moreover, in the torsion massive gravity model the Fierz-Pauli field appears as a derivative of fundamental fields. This, however, does not generate any unwanted pole once coupled to some external sources.