Effective Field Theory of Broken Spatial Diffeomorphisms
  We study the low energy effective theory describing gravity with broken
spatial diffeomorphism invariance. In the unitary gauge, the Goldstone bosons
associated with broken diffeomorphisms are eaten and the graviton becomes a
massive spin-2 particle with 5 well-behaved degrees of freedom. In this gauge,
the most general theory is built with the lowest dimension operators invariant
under only temporal diffeomorphisms. Imposing the additional shift and SO(3)
internal symmetries, we analyze the perturbations on a FRW background. At
linear perturbation level, the observables of this theory are characterized by
five parameters, including the usual cosmological parameters and one additional
coupling constant for the symmetry-breaking scalars. In the de Sitter and
Minkowski limit, the three Goldstone bosons are supermassive and can be
integrated out, leaving two massive tensor modes as the only propagating
degrees of freedom. We discuss several examples relevant to theories of massive
gravity.
