General Tensor Lagrangians from Gravitational Higgs Mechanism

TL;DR

This paper develops a comprehensive tensor Lagrangian framework for gravitational Higgs mechanism, allowing for ghost-free, tachyon-free mass terms and generalizing the linearized Einstein-Hilbert Lagrangian with novel features.

Contribution

It constructs the most general tensor Lagrangian for gravitational Higgs mechanism, demonstrating ghost- and tachyon-free properties and generalizing existing linearized gravity models.

Findings

The Lagrangian admits a consistent expansion around flat space.

It generalizes the kinetic structure beyond Fierz-Pauli form.

The model produces a consistent mass term without higher derivatives.

Abstract

The gravitational Higgs mechanism proposed by 't Hooft in arXiv:0708.3184 involves the spacetime metric g_{mu nu} as well as the induced metric \bar{g}_{mu nu} proportional to \eta_{a b} \partial_{mu} \phi^a \partial_{nu} \phi^b where \phi^{a} (a=0,...,3), as we call it, break all four diffeomorphisms spontaneously via the vacuum expectation values < \phi^a > proportional to x^a. In this framework, we construct and analyze the most general action density in terms of various invariants involving the curvature tensors, connexion coefficients, and the contractions and the determinants of the two metric fields. We show that this action admits a consistent expansion about the flat background such that the resulting Lagrangian possesses several novel features not found in the linearized Einstein-Hilbert Lagrangian with Fierz-Pauli mass term (LELHL-FP): (i) its kinetic part generalizes that of LELHL-FP by weighing the corresponding structures with certain coefficients generated by invariants, (ii) the entire Lagrangian is ghost-- and tachyon--free for mass terms not necessarily in the Fierz-Pauli form, and, (iii) a consistent mass term is generated with no apparent need to higher derivative couplings.