Graviton as a Goldstone boson: Nonlinear Sigma Model for Tensor Field Gravity

Understand

Spontaneous Lorentz invariance violation (SLIV) realized through a nonlinear tensor field constraint H_{}^2=\pm M^2 (M is the proposed scale for Lorentz violation) is considered in tensor field gravity theory, which mimics linearized general relativity in Minkowski space-time.

• We show that such a SLIV pattern, due to which the true vacuum in the theory is chosen, induces massless tensor Goldstone modes some of which can naturally be associated with the physical graviton.
• When expressed in terms of the pure Goldstone modes, this theory looks essentially nonlinear and contains a variety of Lorentz and CPT violating couplings.
• Nonetheless, all SLIV effects turn out to be strictly cancelled in all the lowest order processes considered, provided that the tensor field gravity theory is properly extended to general relativity (GR).