dRGT theory of massive gravity from spontaneous symmetry breaking

Understand

In this note we propose a topological action for a Poincare times diffeomorphism invariant gauge theory.

• We show that there is Higgs phase where the gauge symmetry is spontaneous broken to a diagonal Lorentz subgroup and gives the Einstein-Hilbert action plus the dRGT potential terms.
• In this vacuum, there are five (three from Goldstone modes) propagating degrees of freedom which form polarizations of a massive spin 2 particle, an extra healthy heavy scalar (Higgs) mode and no Boulware-Deser ghost mode.
• We further show that the action can be derived in a limit from a topological de Sitter invariant gauge theory in 4 dimensions.