Massive gravity in Minkowski space via the gravitational Higgs mechanism

In the gravitational Higgs mechanism graviton components acquire mass in the process of spontaneous breaking of diffeomorphisms (via scalar vacuum expectation values). Recently, the gravitational Higgs mechanism was discussed in the context of obtaining massive gravity directly in four dimensions. We discuss a setup, with all diffeomorphisms spontaneously broken by scalars, where the gravitational Higgs mechanism results in massive gravity in Minkowski space with no nonunitary propagating modes. This is achieved by including higher derivative terms in the scalar sector. Decoupling the nonunitary mode (trace of the graviton) then requires tuning a single parameter, namely, the cosmological constant. We also discuss a setup where only spatial diffeomorphisms are broken. In this case we obtain massive gravity in Minkowski space with only transverse modes propagating, so the mode count is the same as for a massless graviton.