Non linear Fierz-Pauli theory from torsion and bigravity

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.

17 pages

References in corpus (14)

• Resummation of Massive Gravity
• Generalization of the Fierz-Pauli Action
• Covariant Galileon
• DBI and the Galileon reunited
• Multi-field galileons and higher co-dimension branes
• The recovery of General Relativity in massive gravity via the Vainshtein mechanism
• The Higgs Phenomenon in Quantum Gravity
• Selftuned Massive Spin-2
• Spontaneous Lorentz Breaking and Massive Gravity
• Lorentz Breaking Massive Gravity in Curved Space
• The Vainshtein mechanism in the Decoupling Limit of massive gravity
• Graviweak Unification
• Bigravity and Lorentz-violating Massive Gravity
• Elie Cartan's torsion in geometry and in field theory, an essay

Cited by in corpus (22)

• Theoretical Aspects of Massive Gravity
• Confirmation of the Secondary Constraint and Absence of Ghost in Massive Gravity and Bimetric Gravity
• Recent developments in bimetric theory
• The Self-Accelerating Universe with Vectors in Massive Gravity
• The bimetric variational principle for General Relativity
• Consistent massive graviton on arbitrary backgrounds
• Linear spin-2 fields in most general backgrounds
• Modified gravity: a unified approach to metric-affine models
• Extracting Bigravity from String Theory
• Gravitational Waves in Ghost Free Bimetric Gravity
• Infrared modified gravity with propagating torsion: instability of torsionfull de Sitter-like solutions
• Self-accelerating Universe in modified gravity with dynamical torsion
• Dual Massive Gravity
• On the stability of self-accelerating Universe in modified gravity with dynamical torsion
• Absence of a Vainshtein radius in torsion bigravity
• Black holes in torsion bigravity
• Stability of self-accelerating Universe in modified gravity with dynamical torsion: the case of small background torsion
• Gravitational-wave energy and other fluxes in ghost-free bigravity
• Massive graviton on arbitrary background: derivation, syzygies, applications
• Ultralocal energy density in massive gravity
• Spherically symmetric perturbations of a Schwarzschild black hole in torsion bigravity
• Weak field limit in vierbein-Einstein-Palatini formalism and Fierz-Pauli Equation