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

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.