Einstein Gravity, Massive Gravity, Multi-Gravity and Nonlinear Realizations

TL;DR

This paper explores the nonlinear realization of symmetries in massive gravity theories using coset construction, revealing new interactions and extending the framework to bi-gravity and multi-metric theories.

Contribution

It introduces a novel approach to formulating ghost-free massive gravity through nonlinear realizations and identifies new parity-violating interactions.

Findings

Discovered a new parity-violating interaction preserving the theory's constraints.

Extended the coset construction approach to bi-gravity and multi-vielbein theories.

Found interactions that vanish on the normal branch but could be significant in other regimes.

Abstract

The existence of a ghost free theory of massive gravity begs for an interpretation as a Higgs phase of General Relativity. We revisit the study of massive gravity as a Higgs phase. Absent a compelling microphysical model of spontaneous symmetry breaking in gravity, we approach this problem from the viewpoint of nonlinear realizations. We employ the coset construction to search for the most restrictive symmetry breaking pattern whose low energy theory will both admit the de Rham-Gabadadze-Tolley (dRGT) potentials and nonlinearly realize every symmetry of General Relativity, thereby providing a new perspective from which to build theories of massive gravity. In addition to the known ghost-free terms, we find a novel parity violating interaction which preserves the constraint structure of the theory, but which vanishes on the normal branch of the theory. Finally, the procedure is extended to the cases of bi-gravity and multi-vielbein theories. Analogous parity violating interactions exist here, too, and may be non-trivial for certain classes of multi-metric theories.